This document contains information on various math topics organized under different subheadings:
1. The topics covered include algebra, shapes, data, numbers, adding/subtracting decimals and fractions, direct proportion, BIDMAS rules, factors and HCF, factor trees, directed numbers, equivalent fractions, ratio, finding percentages, HCF and LCM, indirect proportion, fractions/decimals/percentages, limits, multiples, multiplying/dividing fractions and decimals, ordering fractions and decimals, percentage increase/decrease, and rounding to significant figures.
2. There are examples and multi-step problems provided under each topic for practice.
3. The document serves as a review of various math concepts and skills for
This document contains topics related to algebra, shape, data, numbers, decimals, fractions, proportions, BIDMAS rules, factors and HCF, directed numbers, ratios, percentages, fractions and decimals, limits, multiples, and fractions. It includes examples and multi-step problems involving these mathematical concepts.
The document contains a series of math word problems and questions. It tests ordering numbers from least to greatest, finding averages, converting between percentages and decimals, solving multi-step word problems, identifying geometric shapes and properties, and determining logical sequences and patterns. The questions cover a wide range of elementary and middle school math concepts.
This document contains 60 math questions and their answers from the MATH COUNTS 2009 School Competition Countdown Round. It provides sample questions to demonstrate the format and prohibits reproducing or publishing the full questions and answers.
The document contains 22 math word problems. The problems cover a variety of topics including fractions, ratios, percentages, geometry, probability, and algebra. They range in complexity from simple calculations to multi-step problems. The answers provided are numerical values, algebraic expressions, or ratios expressed as common fractions.
The document contains 51 math and probability questions from the GMAT exam. The questions cover a range of topics including arithmetic, algebra, geometry, percentages, and counting/probability. For each question, multiple choice options for the answer are provided.
This document contains a countdown round from the 2009 MATH COUNTS chapter competition, consisting of 62 multiple choice math questions with answers. The questions cover a wide range of math topics including arithmetic, algebra, geometry, probability, and word problems. The summary provides an overview of the type and scope of questions included in the document without reproducing any specific questions or answers.
1. The document contains 52 math and word problems ranging from simple arithmetic to more complex algebra, geometry, and word problems.
2. Many problems involve calculating values based on information provided such as the steps to solve an equation, properties of shapes, or conversions between units.
3. The correct answers to each problem are listed as multiple choice options, requiring identification of the right solution from the options given.
This document contains topics related to algebra, shape, data, numbers, decimals, fractions, proportions, BIDMAS rules, factors and HCF, directed numbers, ratios, percentages, fractions and decimals, limits, multiples, and fractions. It includes examples and multi-step problems involving these mathematical concepts.
The document contains a series of math word problems and questions. It tests ordering numbers from least to greatest, finding averages, converting between percentages and decimals, solving multi-step word problems, identifying geometric shapes and properties, and determining logical sequences and patterns. The questions cover a wide range of elementary and middle school math concepts.
This document contains 60 math questions and their answers from the MATH COUNTS 2009 School Competition Countdown Round. It provides sample questions to demonstrate the format and prohibits reproducing or publishing the full questions and answers.
The document contains 22 math word problems. The problems cover a variety of topics including fractions, ratios, percentages, geometry, probability, and algebra. They range in complexity from simple calculations to multi-step problems. The answers provided are numerical values, algebraic expressions, or ratios expressed as common fractions.
The document contains 51 math and probability questions from the GMAT exam. The questions cover a range of topics including arithmetic, algebra, geometry, percentages, and counting/probability. For each question, multiple choice options for the answer are provided.
This document contains a countdown round from the 2009 MATH COUNTS chapter competition, consisting of 62 multiple choice math questions with answers. The questions cover a wide range of math topics including arithmetic, algebra, geometry, probability, and word problems. The summary provides an overview of the type and scope of questions included in the document without reproducing any specific questions or answers.
1. The document contains 52 math and word problems ranging from simple arithmetic to more complex algebra, geometry, and word problems.
2. Many problems involve calculating values based on information provided such as the steps to solve an equation, properties of shapes, or conversions between units.
3. The correct answers to each problem are listed as multiple choice options, requiring identification of the right solution from the options given.
This document contains 54 multiple choice questions testing various math and problem solving skills. The questions cover topics like arithmetic, algebra, geometry, ratios, functions and more. They range in difficulty from basic calculations to more complex word problems requiring multiple steps to solve. The full set of questions and possible answer choices are provided for review.
This document appears to be an answer key for a math practice exam for a 3rd period class at Colegio San Patricio for the 2009-2010 school year. It provides answers to binary conversion problems, number line problems, true/false problems evaluating mathematical statements, word problems involving algebra, and expressions involving simplification and writing in algebraic form. The document concisely summarizes the essential information and key for a math practice exam.
1) The value of the expression 44 + 4 × 4 − 4 is 268.
2) Two of the four statements about sequences and patterns are true - that it follows the Fibonacci sequence and is an arithmetic sequence with a common difference of 4.
3) The area of the gray region overlapping two rectangles is 32 cm^2.
The document is a sample test containing 71 math word problems. It provides the questions, answers, and formatting for a state-level math competition countdown round. The questions cover a range of math topics and vary in difficulty.
The document contains 75 math word problems and their answers. It appears to be from a math competition with questions ranging in difficulty from basic arithmetic to more complex algebra and probability questions. Many questions involve multi-step word problems involving variables, equations, ratios, percentages and geometric shapes.
The document discusses equations and their properties. It begins by defining an equation as a statement that shows the relationship between two or more quantities. Equations can contain known or unknown quantities. Letters like x, y, z are usually used to denote unknown quantities or variables. The four basic arithmetic operations can be applied to variables as well. Simultaneous equations can be solved using elimination or substitution methods. The nature of solutions to simultaneous equations can be unique, infinite, or none. The document provides examples and explanations of simple equations, solving single-variable equations, and solving simultaneous equations.
The document is a set of math word problems and their answers from the 2008 MATH COUNTS National Competition Countdown Round. It includes 20 problems covering topics like percentages, ratios, proportions, arithmetic and algebraic sequences, probability, geometry, and more. The problems have a range of difficulties and ask test-takers to determine quantities, values, ratios, and sums based on the information provided.
Gmat quant topic 8 probability solutionsRushabh Vora
1. The document contains multiple probability word problems involving coin flips, exam questions, picking items from different groups, weather outcomes, and more.
2. Key aspects involve counting the total possible outcomes and favorable outcomes to calculate probabilities, and using combinations, permutations, and other counting methods.
3. The correct solutions utilize precise calculations and reasoning to determine the probabilities requested in each problem.
The document contains 35 math and word problems. The assistant provides concise 3-sentence summaries for each problem:
1) A man discusses promoting entrepreneurship and free education for all. He needs support from others to achieve these goals.
2) The problem asks to rearrange the letters in "PROBLEM" to make 7-letter words without repetition, with the answer being 5040 possible arrangements.
3) The problem asks the probability that the third coin tossed will be heads if 10 coins are tossed simultaneously, with the answer being 1/2 or 512 possible outcomes out of 1024 total.
4) The problem asks to count the ways to post 5 letters into 3 post boxes with any number allowed
The document discusses questions related to decimals, fractions, and quantitative aptitude tests. It provides examples of questions on topics like square roots, scientific notation, and permutations and combinations. It also provides links to download presentations on related topics like profit and loss, ratios, and business mathematics.
This document provides solutions to ratio and proportion problems along with explanations. Some key points:
- The ratio of 4:9, 3:4, and 2:3 and 9:7 compounded is 2:21
- If ratio is 7:10 and difference is 105, the numbers are 245 and 350
- Given ratios of P:Q and P:R, the ratio of Q:R is 27:22
- Given ratio of X:Y and values of X^2Y + XY^2 and X^3 + Y^3, the ratio is 84:91
- Given ratios and one speed, the speed of the other train can be calculated
- To make the ratios 19:
This document contains a series of math quizzes covering various topics like multiplication, factoring, exponents, algebra, angles, and more. It includes over 50 questions testing skills like finding products, factoring numbers, solving equations, calculating angles of circles, and evaluating expressions. The quizzes start with simpler questions and increase in difficulty, containing up to 6 possible answer choices. After each short quiz, the number of correct answers is reported out of the total number of questions. At the end of the document, the participant is congratulated for getting all questions correct across every quiz.
There are three key steps to solving this problem:
1. Sammy started with x flavors and threw out y flavors, so he now has x - y flavors remaining.
2. To create combinations, we use the formula nCr = n!/(r!(n-r)!). Where n is the number of total flavors and r is the number we are combining.
3. Since we want 10-flavor combinations, and we know the number of flavors remaining is x - y, we can plug this value into the formula in place of n.
The key information needed is the original number of flavors (x) and the number thrown out (y) to determine the number remaining for combinations.
This document contains a summary of questions and answers from multiple rounds of a math exam for Class 9 and 10 students. In the first round, it provides 5 multiple choice questions on topics of numbers, algebra, and trigonometry, along with the answers. The second round contains 7 additional multiple choice questions covering geometry, trigonometry, and algebra. The third round includes 4 short answer questions on volumes, areas, and ratios. Finally, the fourth round lists 8 algebra questions ranging from basic operations to solving equations to polynomial factorization.
This document contains 60 math questions from a school competition countdown round. The questions cover a variety of math topics including percentages, probability, geometry, number properties, and algebra. They range in difficulty from basic calculations to multi-step word problems.
1) The document describes a mental ability test consisting of 12 multiple choice questions arranged in a 4x3 grid.
2) Teams will take turns choosing a question from the grid and will have a time limit to answer based on difficulty. Correct answers earn 10 points.
3) A sample question is provided to illustrate the multiple choice format. The questions cover a range of math, logic, and reasoning skills.
This document is a released test from the 2010 Virginia Standards of Learning for 4th grade mathematics. It contains 38 multiple choice questions assessing skills in number and number sense, computation and estimation, measurement and geometry, and probability and statistics. The test was developed by the Virginia Department of Education and is intended to measure students' mastery of the state mathematics standards.
This document provides a summary of mathematics content and activities for Grade VII students in Indonesia. It covers two chapters:
Chapter 1 focuses on whole numbers, including expressing temperatures in whole numbers, performing calculations with whole numbers, drawing number lines, and solving word problems involving addition, subtraction, multiplication and division of whole numbers.
Chapter 2 covers fractional numbers, including writing fractions in numeral and word form, reducing fractions to simplest form, comparing and ordering fractions, expressing fractions as mixed numbers or whole numbers, and performing calculations with fractions.
The document contains 75 math word problems with answers. It is a countdown round from a 2008 MATH COUNTS chapter competition. The problems cover a range of math topics including arithmetic, algebra, geometry, probability, and word problems. The answers are provided in numeric form following each problem statement.
The document discusses the real number system and different types of real numbers. It defines rational numbers as numbers that can be written as a fraction a/b, and irrational numbers as numbers that cannot be written as a fraction, such as the square root of 2. It provides examples of evaluating square roots and comparing real numbers using inequality symbols. It also covers ordering numbers from least to greatest and expressing decimals as rational numbers or repeating decimals.
The document is Indiana University's strategic plan for online education. Some of the main recommendations include establishing quality standards for online education equivalent to in-person programs, focusing online undergraduate offerings on alternative sections of popular courses rather than full degrees, and offering graduate programs and certificates online to meet the needs of Indiana residents and professionals in fields with large enough markets. It also recommends investing in instructional design support, technology support, and improvements to the online learning platform. The plan addresses issues like pricing, inter-campus coordination, and establishing a leadership office to oversee online education strategy and management.
Lightning Talk #9: How UX and Data Storytelling Can Shape Policy by Mika Aldabaux singapore
How can we take UX and Data Storytelling out of the tech context and use them to change the way government behaves?
Showcasing the truth is the highest goal of data storytelling. Because the design of a chart can affect the interpretation of data in a major way, one must wield visual tools with care and deliberation. Using quantitative facts to evoke an emotional response is best achieved with the combination of UX and data storytelling.
This document contains 54 multiple choice questions testing various math and problem solving skills. The questions cover topics like arithmetic, algebra, geometry, ratios, functions and more. They range in difficulty from basic calculations to more complex word problems requiring multiple steps to solve. The full set of questions and possible answer choices are provided for review.
This document appears to be an answer key for a math practice exam for a 3rd period class at Colegio San Patricio for the 2009-2010 school year. It provides answers to binary conversion problems, number line problems, true/false problems evaluating mathematical statements, word problems involving algebra, and expressions involving simplification and writing in algebraic form. The document concisely summarizes the essential information and key for a math practice exam.
1) The value of the expression 44 + 4 × 4 − 4 is 268.
2) Two of the four statements about sequences and patterns are true - that it follows the Fibonacci sequence and is an arithmetic sequence with a common difference of 4.
3) The area of the gray region overlapping two rectangles is 32 cm^2.
The document is a sample test containing 71 math word problems. It provides the questions, answers, and formatting for a state-level math competition countdown round. The questions cover a range of math topics and vary in difficulty.
The document contains 75 math word problems and their answers. It appears to be from a math competition with questions ranging in difficulty from basic arithmetic to more complex algebra and probability questions. Many questions involve multi-step word problems involving variables, equations, ratios, percentages and geometric shapes.
The document discusses equations and their properties. It begins by defining an equation as a statement that shows the relationship between two or more quantities. Equations can contain known or unknown quantities. Letters like x, y, z are usually used to denote unknown quantities or variables. The four basic arithmetic operations can be applied to variables as well. Simultaneous equations can be solved using elimination or substitution methods. The nature of solutions to simultaneous equations can be unique, infinite, or none. The document provides examples and explanations of simple equations, solving single-variable equations, and solving simultaneous equations.
The document is a set of math word problems and their answers from the 2008 MATH COUNTS National Competition Countdown Round. It includes 20 problems covering topics like percentages, ratios, proportions, arithmetic and algebraic sequences, probability, geometry, and more. The problems have a range of difficulties and ask test-takers to determine quantities, values, ratios, and sums based on the information provided.
Gmat quant topic 8 probability solutionsRushabh Vora
1. The document contains multiple probability word problems involving coin flips, exam questions, picking items from different groups, weather outcomes, and more.
2. Key aspects involve counting the total possible outcomes and favorable outcomes to calculate probabilities, and using combinations, permutations, and other counting methods.
3. The correct solutions utilize precise calculations and reasoning to determine the probabilities requested in each problem.
The document contains 35 math and word problems. The assistant provides concise 3-sentence summaries for each problem:
1) A man discusses promoting entrepreneurship and free education for all. He needs support from others to achieve these goals.
2) The problem asks to rearrange the letters in "PROBLEM" to make 7-letter words without repetition, with the answer being 5040 possible arrangements.
3) The problem asks the probability that the third coin tossed will be heads if 10 coins are tossed simultaneously, with the answer being 1/2 or 512 possible outcomes out of 1024 total.
4) The problem asks to count the ways to post 5 letters into 3 post boxes with any number allowed
The document discusses questions related to decimals, fractions, and quantitative aptitude tests. It provides examples of questions on topics like square roots, scientific notation, and permutations and combinations. It also provides links to download presentations on related topics like profit and loss, ratios, and business mathematics.
This document provides solutions to ratio and proportion problems along with explanations. Some key points:
- The ratio of 4:9, 3:4, and 2:3 and 9:7 compounded is 2:21
- If ratio is 7:10 and difference is 105, the numbers are 245 and 350
- Given ratios of P:Q and P:R, the ratio of Q:R is 27:22
- Given ratio of X:Y and values of X^2Y + XY^2 and X^3 + Y^3, the ratio is 84:91
- Given ratios and one speed, the speed of the other train can be calculated
- To make the ratios 19:
This document contains a series of math quizzes covering various topics like multiplication, factoring, exponents, algebra, angles, and more. It includes over 50 questions testing skills like finding products, factoring numbers, solving equations, calculating angles of circles, and evaluating expressions. The quizzes start with simpler questions and increase in difficulty, containing up to 6 possible answer choices. After each short quiz, the number of correct answers is reported out of the total number of questions. At the end of the document, the participant is congratulated for getting all questions correct across every quiz.
There are three key steps to solving this problem:
1. Sammy started with x flavors and threw out y flavors, so he now has x - y flavors remaining.
2. To create combinations, we use the formula nCr = n!/(r!(n-r)!). Where n is the number of total flavors and r is the number we are combining.
3. Since we want 10-flavor combinations, and we know the number of flavors remaining is x - y, we can plug this value into the formula in place of n.
The key information needed is the original number of flavors (x) and the number thrown out (y) to determine the number remaining for combinations.
This document contains a summary of questions and answers from multiple rounds of a math exam for Class 9 and 10 students. In the first round, it provides 5 multiple choice questions on topics of numbers, algebra, and trigonometry, along with the answers. The second round contains 7 additional multiple choice questions covering geometry, trigonometry, and algebra. The third round includes 4 short answer questions on volumes, areas, and ratios. Finally, the fourth round lists 8 algebra questions ranging from basic operations to solving equations to polynomial factorization.
This document contains 60 math questions from a school competition countdown round. The questions cover a variety of math topics including percentages, probability, geometry, number properties, and algebra. They range in difficulty from basic calculations to multi-step word problems.
1) The document describes a mental ability test consisting of 12 multiple choice questions arranged in a 4x3 grid.
2) Teams will take turns choosing a question from the grid and will have a time limit to answer based on difficulty. Correct answers earn 10 points.
3) A sample question is provided to illustrate the multiple choice format. The questions cover a range of math, logic, and reasoning skills.
This document is a released test from the 2010 Virginia Standards of Learning for 4th grade mathematics. It contains 38 multiple choice questions assessing skills in number and number sense, computation and estimation, measurement and geometry, and probability and statistics. The test was developed by the Virginia Department of Education and is intended to measure students' mastery of the state mathematics standards.
This document provides a summary of mathematics content and activities for Grade VII students in Indonesia. It covers two chapters:
Chapter 1 focuses on whole numbers, including expressing temperatures in whole numbers, performing calculations with whole numbers, drawing number lines, and solving word problems involving addition, subtraction, multiplication and division of whole numbers.
Chapter 2 covers fractional numbers, including writing fractions in numeral and word form, reducing fractions to simplest form, comparing and ordering fractions, expressing fractions as mixed numbers or whole numbers, and performing calculations with fractions.
The document contains 75 math word problems with answers. It is a countdown round from a 2008 MATH COUNTS chapter competition. The problems cover a range of math topics including arithmetic, algebra, geometry, probability, and word problems. The answers are provided in numeric form following each problem statement.
The document discusses the real number system and different types of real numbers. It defines rational numbers as numbers that can be written as a fraction a/b, and irrational numbers as numbers that cannot be written as a fraction, such as the square root of 2. It provides examples of evaluating square roots and comparing real numbers using inequality symbols. It also covers ordering numbers from least to greatest and expressing decimals as rational numbers or repeating decimals.
The document is Indiana University's strategic plan for online education. Some of the main recommendations include establishing quality standards for online education equivalent to in-person programs, focusing online undergraduate offerings on alternative sections of popular courses rather than full degrees, and offering graduate programs and certificates online to meet the needs of Indiana residents and professionals in fields with large enough markets. It also recommends investing in instructional design support, technology support, and improvements to the online learning platform. The plan addresses issues like pricing, inter-campus coordination, and establishing a leadership office to oversee online education strategy and management.
Lightning Talk #9: How UX and Data Storytelling Can Shape Policy by Mika Aldabaux singapore
How can we take UX and Data Storytelling out of the tech context and use them to change the way government behaves?
Showcasing the truth is the highest goal of data storytelling. Because the design of a chart can affect the interpretation of data in a major way, one must wield visual tools with care and deliberation. Using quantitative facts to evoke an emotional response is best achieved with the combination of UX and data storytelling.
This document summarizes a study of CEO succession events among the largest 100 U.S. corporations between 2005-2015. The study analyzed executives who were passed over for the CEO role ("succession losers") and their subsequent careers. It found that 74% of passed over executives left their companies, with 30% eventually becoming CEOs elsewhere. However, companies led by succession losers saw average stock price declines of 13% over 3 years, compared to gains for companies whose CEO selections remained unchanged. The findings suggest that boards generally identify the most qualified CEO candidates, though differences between internal and external hires complicate comparisons.
We’re all trying to find that idea or spark that will turn a good project into a great project. Creativity plays a huge role in the outcome of our work. Harnessing the power of collaboration and open source, we can make great strides towards excellence. Not just for designers, this talk can be applicable to many different roles – even development. In this talk, Seasoned Creative Director Sara Cannon is going to share some secrets about creative methodology, collaboration, and the strong role that open source can play in our work.
The impact of innovation on travel and tourism industries (World Travel Marke...Brian Solis
From the impact of Pokemon Go on Silicon Valley to artificial intelligence, futurist Brian Solis talks to Mathew Parsons of World Travel Market about the future of travel, tourism and hospitality.
Reuters: Pictures of the Year 2016 (Part 2)maditabalnco
This document contains 20 photos from news events around the world between January and November 2016. The photos show international events like the US presidential election, the conflict in Ukraine, the migrant crisis in Europe, the Rio Olympics, and more. They also depict human interest stories and natural phenomena from various countries.
The Six Highest Performing B2B Blog Post FormatsBarry Feldman
If your B2B blogging goals include earning social media shares and backlinks to boost your search rankings, this infographic lists the size best approaches.
1) The document discusses the opportunity for technology to improve organizational efficiency and transition economies into a "smart and clean world."
2) It argues that aggregate efficiency has stalled at around 22% for 30 years due to limitations of the Second Industrial Revolution, but that digitizing transport, energy, and communication through technologies like blockchain can help manage resources and increase efficiency.
3) Technologies like precision agriculture, cloud computing, robotics, and autonomous vehicles may allow for "dematerialization" and do more with fewer physical resources through effects like reduced waste and need for transportation/logistics infrastructure.
Alhikmah preparation for checkpoint math paper 2Wina Winarni
This document contains 20 math problems for a checkpoint exam covering various topics:
1) Matching shapes to their names
2) Rounding a number to the nearest thousand
3) Identifying equivalent expressions
4) Finding the lowest recorded temperature from a data table
5) Calculating probability using numbers of different colored socks
6) Calculating percentages and ratios to solve problems about test scores
7) Identifying reflections and rotations of shapes
8) Calculating gradients, drawing graphs from tables of values, and solving simultaneous equations graphically
9) Adding brackets to make an expression true
10) Identifying the calculation with the largest answer
11) Interpreting data from bar graphs and determining which class performed
Alhikmah preparation for checkpoint math paper 2Wina Winarni
This document contains 20 math problems for a checkpoint exam covering various topics:
1) Matching shapes to their names
2) Rounding a number to the nearest thousand
3) Identifying equivalent expressions
4) Finding the lowest recorded temperature from a data table
5) Calculating probability using numbers of different colored socks
6) Calculating percentages to determine number of correct test answers
7) Identifying reflections and rotations of shapes
8) Calculating gradient, drawing a line graph, and solving simultaneous equations from graphs
9) Adding brackets to make an expression true
10) Identifying the calculation with the largest answer
11) Determining which class performed better on a test based on range of scores
Preparation for checkpoint math paper 2Wina Winarni
This document contains 20 math problems and questions for a checkpoint exam. The questions cover a range of topics including shapes, rounding numbers, expressions, temperature, probability, ratios, graphs, simultaneous equations, fractions, statistics, maps, factorizing expressions, word problems involving time, speed, and distance, geometry, volumes, and the Pythagorean theorem. The questions are presented in the student's native language with translations provided.
This document contains 30 multiple choice questions related to mathematics and statistics concepts. It tests topics like geometry, probability, permutations, averages, and distributions. For each question, the relevant concepts and steps to solve are provided. The questions range in difficulty from identifying basic shapes to calculating probabilities and averages from distributions.
Here are the steps to solve indirect proportion problems:
1) If A is indirectly proportional to B and when A = 5, B = 6:
a) k = 5/6
b) A = k/B
c) A = 5/6 when B = 3 => A = 5/18
d) A = 5/6 when B = 15 => A = 1/15
e) B = 6 when A = 1 => B = 6
f) B = -6 when A = -3 => B = -6
2) If A is indirectly proportional to B and when A = 7, B = 12:
a) k = 7/12
b) A
This document contains a review sheet for a math final exam. It includes multiple choice and short answer questions covering topics like geometry, algebra, ratios, and word problems. It also provides the answers to the multiple choice section. The short answer questions require showing work and include problems finding areas, writing equations, comparing ratios, and solving word problems involving money.
This document appears to be a mathematics post-test from September 2008 consisting of 57 multiple choice questions covering various math topics such as arithmetic, algebra, geometry, ratios, and word problems. The test was administered by the St. Louis Review Center in Manila, Philippines and includes questions testing concepts like operations with fractions and decimals, properties of numbers, measurement conversions, and geometric shapes.
This module introduces ratio, proportion, and the Basic Proportionality Theorem. Students will learn about ratios, proportions, and how to use the fundamental law of proportions to solve problems involving similar triangles. The module is designed to help students apply the definition of proportion to find unknown lengths, illustrate and verify the Basic Proportionality Theorem and its converse, and develop skills for solving geometry problems involving triangles. Exercises cover writing and simplifying ratios, setting up and solving proportions, determining if ratios form proportions, and applying the Basic Proportionality Theorem.
This module introduces ratio, proportion, and the Basic Proportionality Theorem. Students will learn about ratios, proportions, and how to use the fundamental law of proportions to solve problems involving triangles. The module is designed to teach students to apply the definition of proportion of segments to find unknown lengths and illustrate and verify the Basic Proportionality Theorem and its Converse. Examples are provided to demonstrate how to express ratios in simplest form, find missing values in proportions, determine if ratios form proportions, and solve problems involving angles and segments in triangles using ratios and proportions.
This document contains a 65-question multiple choice mathematics exam covering topics such as mean, median, mode, and range; data interpretation from graphs and tables; order of operations; ratios and proportions; percentages; geometry (lines, angles, polygons); and more. The questions require students to choose the correct answer, perform calculations, classify shapes, interpret data, and explain mathematical statements.
This document describes the rules and structure of a mental math competition consisting of 5 rounds. It provides sample questions and answers for each round, with the rounds getting more difficult. The competition involves teams answering math problems within time limits, with points awarded for correct answers and deducted for incorrect ones. Teams can optionally pass questions to other teams in some rounds. The final round involves answering multiple questions at once within a time limit.
Factors n multiple hcf and lcm remaindderTamojit Das
This document contains multiple questions about number systems and number theory concepts including factors, factor sums, highest common factors (HCF), least common multiples (LCM), remainders, and factorials. Specifically, it asks the reader to find factors, factor sums, HCFs, LCMs, remainders when dividing numbers, unit digits of numbers and expressions, and values related to factorials and their properties. The questions cover a wide range of number theory topics and require calculating various properties of numbers.
This document provides examples of math word problems and their step-by-step solutions. It begins with problems involving operations with fractions, decimals, and percentages. Later problems involve calculating percentages of quantities, percentage increases and decreases, and other rate and percentage applications. The document demonstrates how to set up and solve a variety of math problems systematically using proper order of operations and step-by-step work.
1) The document contains multiple math word problems involving ratios, percentages, expressions, equations, sequences, geometry, and probability.
2) Questions involve finding the area of shapes, expanding and simplifying expressions, making variables the subject of formulas, estimating values, and finding lengths, probabilities, and other values.
3) The problems cover a range of math concepts and skills including operations, algebraic manipulation, geometry, statistics, and probability.
1. The document provides instructions and rules for a mathematics challenge competition involving 25 multiple choice questions.
2. The questions cover a range of mathematical topics including number theory, geometry, probability, and algebra.
3. Competitors have 90 minutes to answer as many questions as possible, with scoring based on correct answers and penalties for incorrect answers.
This document contains an aptitude test with 3 sections - quantitative, logical and verbal ability. It consists of 50 multiple choice questions to be completed within 90 minutes. The quantitative section includes number series, arithmetic operations and data interpretation questions. The logical section contains puzzles and the verbal section focuses on vocabulary including synonyms.
This document contains 62 aptitude questions and their answers. The questions cover a range of topics including percentages, ratios, time/work problems, probability, and data interpretation. The questions vary in difficulty from basic arithmetic to multi-step word problems. The goal of the questions is to assess logical thinking and problem solving abilities.
Mathematics high school level quiz - Part IITfC-Edu-Team
The document outlines the format and questions for a mathematics quiz with multiple rounds. It begins with a two-part quiz where groups are given problem cards to solve. The subsequent rounds include warm-up questions testing concepts like geometry, averages, and number puzzles, as well as "real math" and logic rounds. Later rounds involve problem-solving, model-making to demonstrate algebraic identities, and a final written work discussion period.
This document provides 100 numerical aptitude questions asked in campus placements by companies like Infosys, TCS, CTS, Wipro and Accenture, along with their solutions. It aims to help students target their learning and know more than their competitors. Some key topics covered include number systems, time and work problems, percentages, and geometry. The author provides contact information for students who have additional doubts.
This document provides information about an assessment pack for Year 6 mathematics from TeeJay Publishers. It includes:
- 19 assessments that match the content of each chapter in the Year 6 textbook.
- Six block assessments that are cumulative and cover the main outcomes in number, fractions/decimals, measurement, geometry, algebra, and statistics/probability.
- A final end-of-year diagnostic assessment with write-on and non-write-on versions.
- A complete set of answers for the assessments.
The assessments are meant to be used with TeeJay's Year 6 textbook, course planner, and homework support pack.
This document provides examples of simple algebraic formula substitution problems at a level 5 difficulty. It includes examples of substituting values for variables in addition, subtraction, multiplication, and division formulae. It also includes a word problem example where clues using the algebraic formula substitutions must be solved to uncover the word "pen" being spelled.
This document shows how to substitute positive and negative integers into formulas. It provides two examples, showing that g + o = 4 by substituting the values for g (-1) and o (6) from the provided number lines. It demonstrates how to perform calculations with positive and negative numbers according to their positions on the number line.
These starter cards are designed to be used for mental math exercises with students from key stages 2 to 4. The cards cover topics in algebra and can be used to generate questions for students at different ability levels. Key questions are provided on the back of each card to guide students in their responses. The cards are meant to be adapted to match the abilities of the class and can be used individually or in groups to encourage problem solving and discussion.
This document provides instructions for solving simultaneous equations using non-graphical methods. It demonstrates the step-by-step process of numbering the equations, eliminating variables, solving for the values of each variable, and checking the solutions in multiple examples.
This document contains 10 algebra simplification questions with multiple choice answers. The questions cover combining like terms, distributing, factoring, and simplifying expressions with variables. Correct answers are provided after each question.
The document contains 7 sections of numerical sequences authored by Lesley Hall from Soar Valley College. Each section contains a series of numbers in increasing order, with the totals for each series ranging from 31 to 98.
The document contains a math quiz asking the reader to identify whether expressions are equivalent by responding "YEHAW" if they are equivalent or "YAHOO" if they are not equivalent. There are 10 expression pairs for the reader to evaluate and identify as equivalent or not equivalent.
The document contains examples of arithmetic sequences and their term-to-term and position-to-term rules. It provides sequences and asks the reader to determine the rule for the nth term. It also includes word problems about taxi fares and matchstick patterns that can be represented by sequences. The document covers generating terms of sequences, justifying expressions for the nth term, and extending work to quadratic sequences.
This document appears to be a quiz on algebra concepts with 15 multiple choice questions of increasing difficulty. It tests skills like simplifying expressions, expanding brackets, and solving equations. The quiz is set up like a game show with questions worth increasing amounts of money up to the final question worth £1,000,000.
This document contains multiple examples and problems related to trigonometry, Pythagorean theorem, algebra, number work, formulas, and probability. It includes examples of finding hypotenuses using Pythagorean theorem, calculating trigonometric ratios, factorizing algebraic expressions, solving simultaneous equations, expanding brackets, converting between fractions and decimals, calculating percentages, identifying sequences, writing formulas, finding probabilities, calculating volumes of shapes, and describing regions with inequalities.
This document provides an overview of assessing pupils' progress in mathematics based on two major areas: 1) using and applying mathematics, shape, space and measure, and handling data and 2) number and algebra. It includes examples for each area at different levels ranging from level 2 to level 8 based on the UK national curriculum levels. The examples describe tasks students complete and the thinking demonstrated at each level.
The document describes a manual containing 25 math-related magic tricks for teachers. It includes tricks involving cards, dice, and mental math. The introduction explains how magic can make math more fun and engaging for students by providing mysteries for them to solve.
This document appears to be a quiz game involving fractions, decimals, and percentages. A series of questions are asked to test knowledge of concepts like comparing fractional amounts, writing fractions as decimals, determining percentages from decimals and vice versa, and performing fraction and percentage calculations. Two teams, the Red Team and Green Team, earn points by answering the questions correctly.
The document appears to be a math game where players simplify algebraic expressions for points. It contains 25 problems where the user is prompted to simplify an expression like "2(x+4)" and points are awarded to either the Red or Green team.
This document appears to be a math game where teams earn points by answering questions about order of operations and math terms correctly. The questions cover terms like addition, indices, multiplication, division, brackets, square, cube, percentage and operations in the BIDMAS order of operations. Teams earn points for each correct answer.
The document provides examples for expanding brackets in algebra. It begins with learning objectives to expand brackets and lists key terms. Examples are then shown of expanding various expressions containing brackets, such as 2(3a+2), 3(2b+1), and 7a(2b-3c). Students are asked to expand additional examples and the answers are provided. The document concludes with a worksheet for students to practice expanding brackets.
The document provides examples of maths questions and explanations at Key Stage 3 Level 6. It covers topics such as number and algebra, shape space and measures, and data handling. Examples include solving equations, properties of shapes, calculating percentages, drawing charts from data, and calculating volume and area. Formulas for calculating circumference, area of circles and volume of cuboids are also presented.
The document outlines the objectives and homework for a math lesson. The lesson objectives are to learn how letters can represent unknown values and how to expand and simplify brackets. The homework includes sharing sweets equally among students, expanding brackets with letters, and solving word problems that involve distributing numbers over brackets with letters for unknown values. The homework provides 4 practice problems for students to work out.
The document contains 10 quick questions testing understanding of formulas for calculating speed, time, cost, pay, and exponents. Each question includes the relevant formula and values to calculate the answer, with multiple choice responses. The questions cover formulas for speed of falling objects, cooking time, taxi fare, average speed, pay based on number of items made, and exponents.
The document summarizes the Fundamental Theorem of Arithmetic, which states that every integer greater than 1 can be written as a product of prime numbers. It provides examples of decomposing different integers into their prime factors. It then explains how to find the prime factors of a number by drawing out its factor tree. Finally, it outlines Euclid's proof of the theorem by contradiction, showing that assuming any integer cannot be written as a product of primes leads to a logical contradiction.
Goodbye Windows 11: Make Way for Nitrux Linux 3.5.0!SOFTTECHHUB
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Welcome to UiPath Test Automation using UiPath Test Suite series part 6. In this session, we will cover Test Automation with generative AI and Open AI.
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What will you get from this session?
1. Insights into integrating generative AI.
2. Understanding how this integration enhances test automation within the UiPath platform
3. Practical demonstrations
4. Exploration of real-world use cases illustrating the benefits of AI-driven test automation for UiPath
Topics covered:
What is generative AI
Test Automation with generative AI and Open AI.
UiPath integration with generative AI
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
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- Key themes to consider in developing and maintaining your privacy program
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Webinar Recording: https://www.panagenda.com/webinars/hcl-notes-and-domino-license-cost-reduction-in-the-world-of-dlau/
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We’ll show you how to fix common misconfigurations that cause higher-than-expected user counts, and how to identify accounts which you can deactivate to save money. There are also frequent patterns that can cause unnecessary cost, like using a person document instead of a mail-in for shared mailboxes. We’ll provide examples and solutions for those as well. And naturally we’ll explain the new licensing model.
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- Understanding the DLAU tool and how to best utilize it
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* Live demos with code snippets
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#MongoDB #VectorSearch #AI #SemanticSearch #TechInnovation #DataScience #LLM #MachineLearning #SearchTechnology
9. Direct Proportion
1. If A is directly proportional to B, write an equation in the form A=kB linking the two variables
if when A= 8 B= 4.
2. All of the variables below are directly proportional, write an equation linking them:
1. V= 12 when M =4
2. T= 5 when S=1
3. Y= 34 when x=2
4. H=48 when M=4
5. P= 5 when N=10
3. B is directly proportional to C, when B is 18 C is 27.
1. Write an equation linking B and C
2. Find B when C= 66
3. Find C when B = 30
4. Z is directly proportional to Y, when Z =55, Y=5
1. Write an equation linking Z and Y
2. Find Y when Z = 77
3. Find Z when Y=0.1
5. N is directly proportional to L, when N=1.8 L =0.6
1. Write an equation linking N and L
2. Find L when N= 3.2
3. Find N when L=0.5
10. Bidmas
A)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
(3 + 3 ) x 4
4x2–5
(5 + 7) ÷ 6
5x3+5
(9 – 4 ) + 5
1+1–1
2 x (15 – 2)
(5 x 4 ) + 2
(8 + 2 ) ÷ 10
(21 x 1 ) – 2
B)
1.(1 + 14) – (5 x 3 )
2.(10 + 6 ) ÷ (4 x 2)
3.(1 + 2 ) x (6 – 3)
4.(2 x 6 ) – (14 ÷ 2)
5.(7 x 2) ÷ ( 20 – 6)
6.(3 x 10) – (2 x 2)
7.(9 x 5) – ( 2 x 10)
C)
1.
2.
3.
4.
5.
6.
(3 x 3 – 4 ) x (2 + 2)
2 x (13 – 4) – (23 ÷ 23)
3 x (1 + 4) – (5 x 2)
4 x (3 + 2) – ( 24 – 5)
7 x ( 4 ÷ 2 ) ÷ ( 3 x 5 -1 )
((9 + 7 x 3 ) ÷ 10) – 1
11. Factors and HCF
1) Find all the factors of the following numbers:
1) 20
2) 24
3) 27
4) 32
5) 40
6) 50
7) 56
8) 120
9) 200
2) 2 only has 2 factors (1 and 2), how many numbers can you find between 1 and 30 which have exactly 2
factors? (these are called prime numbers)
3) Find the highest common factors of the following pairs of numbers:
1) 18 and 54
2) 25 and 45
3) 12 and 18
4) 27 and 108
5) 30 and 75
4) Find the HCF of these pairs of numbers:
1) 90 and 450
2) 96 and 480
3) 39 and 195
12. Factor Trees
1. Draw factor trees for the following numbers:
a) 20
b) 24
c) 48
d) 90
e) 81
f) 50
g) 75
h) 120
i) 200
j) 1800
2. Using your factor trees from question 1, write the numbers as products of
their prime factors .
14. Directed Numbers 2
1) I am £250 into my overdraft () but then I get paid £535, how much
will I have in my bank account?
2) The temperature at the North Pole is -17°C; luckily the temperature in
my living room is 40°C warmer than that, what is the temperature in my
living room?
3) I have £32 and each month for 4 months I have to pay £15 to my
mobile phone, if I don’t put any money into my account, how far will I
be into my overdraft?
4) I jump out of a plane 125m above the ocean, I travelled 191m before I
stop, how far am I from the surface of the water?
5) I am playing air hockey with my friend, because I am amazing I agree
start on -9 points, we play first to 14, how many points do I need to
score?
16. Ratio
1.
2.
3.
4.
5.
6.
7.
8.
There are 10 girls and 15 boys in a class, what is the ratio of girls to boys in its simplest
form?
There are 14 cats and 16 dogs in an animal shelter, what is the ratio of cats to dogs in its
simplest form?
There 22 caramels and 55 fudges in a bag of sweets, what is the ratio of caramels to fudges
in its simplest form?
Simplify these ratio to their simplest forms:
a) 48:60
b) 45:75
c) 63:108
d) 25:40:80
e) 24:56:96
f) 120:180:600
g) 320:400:440
Archie and Charlie share their Thomas the tank engine toys in the ratio 1:4, how many do
they each get if they have:
a. 10 toys
b.30 toys c.45 toys
Tom and Jerry share sweets in the ratio 2:3, how many do they each get if they share:
a. 20 sweets
b.30 sweets c.55 sweets
Sue and Linda share some money in the ratio 3:7, how many do they each get if they share:
a. £30
b.£60
c.£90
Mike, Dave and Henry share some little bits of blue tack in the ratio 1:2:3, how many do
they each get if they share:
a. 60 pieces
b.72 pieces c.300 pieces
17. Finding Percentages
1) Some percentages I can find easily by doing a single sum, what single sums can I
do to find:
a. 10%
b. 50% c.25%
2) If I know 10% how can I find:
a. 5%
b. 1%
c. 20 %
d. 90%
3) If I know 50% how can I find:
a. 5%
b. 25%
4) Find:
a. 30% of 250
b. 40% of 500 c. 15% of 220
d. 75% of 84
5) Find:
a. 35% of 440
b. 65% of 450 c. 16% of 220
d. 82% of 96
6) Find:
a. 94% of 640
b. 8% of 520 c. 27% of 220
d. 53% of 96
7) Compare you methods for the questions above with a partner, where they the
same ?
19. HCF and LCM
Find the Highest Common Factor
of these numbers:
•18 and 30
•15 and 20
•16 and 24
•12 and 36
•20 and 30
•28 and 70
•39 and 65
•38 and 57
Find the Lowest Common
Multiple of these numbers
•6 and 7
•4 and 6
•5 and 8
•10 and 4
•16 and 5
•14 and 21
•2.2 and 5
•0.4 and 7
20. Indirect Proportion
1. If A is indirectly proportional to B and when A= 5 B= 6 :
1.Find k
2.Write an equation linking A and B
3.Find A when:
1. B=3
2.B=15
4.Find B when:
1. A=1
2.A=-3
2. If A is indirectly proportional to B and when A= 7 B= 12 :
1.Find k
2.Write an equation linking A and B
3.Find A when:
1. B=4
2.B=6
4.Find B when:
1. A=10
2.A=2
3. If A is indirectly proportional to B and when A= -4 B= 10 :
1.Find k
2.Write an equation linking A and B
3.Find A when:
1. B=-8
2.B=10
4.Find B when:
1. A=-1
2.A=-0.5
4. If A is indirectly proportional to B and when A= 24 B= 0.5 :
1.Find k
2.Write an equation linking A and B
3.Find A when:
a.B=6
b.B= -3
4.Find B when:
a.A= -2
b.A= 100
22. Limits
1) These numbers have been rounded
to the nearest 10, write down the
largest and smallest values they
could be:
1) 50
2) 80
3) 110
2) These numbers have been rounded
to the nearest whole number, write
down the upper and lower limits:
1) 3
2) 17
3) 23
4) 100
5) -3
3) These lengths have been rounded to
the nearest 10th of a cm, write the
upper and lower limits:
1) 12.5cm
2) 21.7cm
3) 35.8cm
4) 52.1cm
5) 80.4cm
4) A field is 100m wide and 120m long, both lengths have been
rounded to the nearest metre.
a) Find the perimeter and area of the field if these
measurements are accurate
b) Find the largest and smallest possible perimeter
c) Find the largest and smallest possible area.
5) A rectangle has it’s area rounded to the nearest whole number,
it becomes 40cm2. One side of the rectangle is exactly 10cm; find
the maximum and minimum lengths the other length could have.
6) Two lengths of wood are stuck together and their combined
length is rounded to the nearest mm and it is 14.9cm, one length
is rounded to the nearest mm and is 7.1cm. Find the minimum
and maximum length of the other length.
23. Multiples
A.
1.
2.
3.
4.
5.
List the first 5 multiples of:
5
7
12
14
19
C.
1.
2.
3.
4.
5.
List 3 numbers which are in:
3 and 4 times tables
3 and 5 times tables
10 and 4 times tables
9 and 2 times tables
12 and 10 times tables
B.
1.
2.
3.
4.
5.
6.
What is the:
9th multiple of 8
7th multiple of 6
12th multiple of 12
11th multiple of 10
13th multiple of 5
5th multiple of 13
D.
1.
2.
3.
4.
5.
What is the lowest common multiple of:
5 and 6
7 and 8
4 and 8
9 and 6
5 and 6
E. What is the lowest common multiple of:
1. 13 and 5
2. 15 and 12
3. 16 and 10
4. 14 and 21
5. 21 and 70
25. Multiplying and dividing decimals
Multiplying
1 a)
b)
c)
d)
e)
0.8
0.5
0.1
0.6
0.3
x
x
x
x
x
7
7
6
4
3
=
=
=
=
=
2 a)
b)
c)
d)
e)
0.2
0.4
0.8
0.9
0.6
x
x
x
x
x
0.5
0.7
0.1
0.9
0.1
=
=
=
=
=
3 a)
b)
c)
d)
e)
1.9
1.6
1.6
1.7
1.3
x
x
x
x
x
0.3
0.5
0.5
0.2
0.7
=
=
=
=
=
4 a)
b)
c)
d)
e)
5.4
5.2
8.3
4.6
8.2
x
x
x
x
x
0.11
0.97
0.73
0.11
0.75
=
=
=
=
=
Dividing
1
2
a)
b)
c)
d)
e)
3.2
4.8
7.2
2.4
1.8
÷
÷
÷
÷
÷
4
8
9
6
3
a)5.6 ÷ 0.7
b)6.3 ÷ 0.7
c)2.7 ÷ 0.3
d)4.9 ÷ 0.7
e)2.8 ÷ 0.7
f)1.65 ÷ 0.15
g) ÷ 0.12
h)27.3 ÷ 1.3
i)0.03 ÷ 0.005
j)0.99 ÷ 0.0009
27. Ordering Decimals
1. For each pair of numbers say
which is bigger by adding > or <.
a) 0.2
0.7
b)0.3
0.1
c)0.7
0.9
d)0.3
0.4
e)0.6
0.3
f)0.24
0.2
g)0.3
0.39
h)0.4
0.35
i)0.9
0.85
j)0.22
0.3
2. Try these:
a) 0.04
0.05
b)0.02
0.09
c)0.12
0.02
d)0.04
0.23
e)0.4
0.04
3. These are trickier:
a) 2.34
0.09
b)4.49
4.0003
c)5.01
5.1
d)6.32
6.325
e)7.436
7.43
f)8.35
8.345
4. Put these decimals in ascending order (smallest to
biggest):
a. 0.2
0.3
0.15
b. 0.7
0.64
0.072
c. 0.85
0.9
0.425
d. 0.734
0.7345
0.7335
e. 6.234
6.009 6.4
28. Percentage Increase
1. Explain how you would use a calculator to increase
an amount by a given percent.
2. Increase the following amounts by 42%
a)£225
b) £306
c)£125
d)£448
e)£512
3. A TV costs £120, how much will it cost if its price is
increased by:
a) 12%
b)31%
c)55%
d)62.5%
e)99.9%
4. Simon puts £70 in a bank, each year the money in
his bank increase by 5.5%, how much does he have
in:
a) 1 year
b)2 years
c)5 years?
a) Explain how you would use a calculator to
decrease an amount by a given percent.
b) Decrease the following amounts by 28%
a) £225
b) £306
c) £125
d) £448
e) £512
c) A TV costs £120, how much will it cost if its
price is decreased by:
a) 19%
b) 32%
c) 79%
d) 73.5%
e) 42%
d) A car bought for £6, 500 depreciates in value
by 12.5% each year, how much will it be
worth after:
a) 1 year
b) 2 years
c) 5 years?
30. Rounding to Decimal Places
•Round the following numbers to a) 1 decimal place b) 2 decimals places c) 3 decimal places
a) 1.463884266
b) 1.572660902
c) 3.783345228
d) 6.3931313
e) 0.640368898
f) 0.326119942
g) 4.249504359
h) 4.44692939
i) 1.447852851
j) 0.069143754
1. Work out the following on a calculator and
give the answer to 2 decimal places;
a) 3.104 x 5.938
b) 2.99 x 8.82
c) 7.1537÷ 3.111
d) 14.772
31. Reverse Percentages
1. What would you multiply an amount by to
increase it by:
a) 15%
b)25%
c)4%
d)0.5%
e)13.5%
2. Find the original prices of these prices that
have been increased by the given percentage:
a) Cost= £49.5 after 10% increase
b)Cost= £74.75 after 15% increase
c)Cost= £61 after 22% increase
d)Cost= £104 after 30% increase
e)Cost= £120 after 50% increase
3. I have £252 in my bank account; this is due to
me earning 5% interest on what I originally had
put in. How much money did I have originally
in my bank account?
4. What would you multiply an amount
by to decrease it by:
a) 15%
b)25%
c)4%
d)0.5%
e)13.5%
5. Find the original prices of these items
that have been decreased by the given
percentage:
a) Cost= £72 after 10% decrease
b) Cost= £93.5 after 15% decrease
c) Cost= £42.5 after 35% decrease
d) Cost= £4 after 40% decrease
e) Cost= £67.50 after 55% decrease
6. A Cars value has dropped by 11.5% it
is now worth £3053.25, what was it
worth when it was new?
40. Finding the gradient
1) Find the gradient between the points:
a) (3,5) and (4,7)
b) (5,9) and (7,17)
c) (4,6) and (5,7)
d) (1,4) and (4,19)
e) (0,11) and (4,23)
2) Find the gradient between these points:
a) (2,5) and (3,-3)
b) (2,8) and (3,2)
c) (4,8) and (4,8)
d) (8,15) and (6,33)
e) (7,12) and (4,42)
f) (4,8) and (3,14)
a) Find the gradient between these points:
a) (3,5) and (4,5.5)
b) (5,9) and (7,8)
c) (4,6) and (5,6.75)
d) (1,4) and (4,4.75
e) (0,11) and (4,11.4)
41. Formulae
A) Isaac Newton’s second law of motion states F=ma (force= mass x acceleration)
1.Find F if:
a.M=10 and a=5
b.M=12 and a=12
c.M=0.5 and a=11
2.Find a if:
a.F=100 and M=20
3.Find m if:
a.F=36 and a=12
B) Density equal volume divided by mass
1.Write a formula for density
a.Find D if
i.M=10 and v= 40
ii.M=12 and v=72
iii.M=5 and v=90
b.Find M if:
i.D=4 and v=52
c.Find v if:
i.D=8 and m=11
C) Electrical power (p) is equal to voltage (V) squared divided by resistance (r)
1.Write a formula for power
2.Find p if:
a.V= 4 and r=8
b.V=9 and r=3
3.Find r if:
a.P=16 and v=8
4.Find v if:
a.P=20 and r=5
43. Laws of indices
1. Simplify:
a) A2 x A
b) A4 x A2
c) A8 x A2
d) 3A9 x A3
e) 4A2 x 5A1
2. Simplify:
a) A10 ÷ A
b) A21 ÷ A7
c) A20 ÷ A4
d) 9A12÷ 3A6
e) 12A6 ÷ 4A4
3. Simplify:
a) (A2)4
b) (A3)3
c) (A2)6
d) (2A9)2
e) (3A4)3
1. Simplify:
a) A0
b) B0
c) 990
d) 520
e) 0.0610
2. Simplify:
a) A-4
b) A-6
c) A-2
d) 2A-4
e) 9A-3
3. Simplify fully:
a) 25A4 ÷ 5A7
b) 3A9 x 2A-3
c) (A2)6 x (2A2)2
d) (2A3)8 ÷ (2A4)6
e) (A2)-6
46. The quadratic equation
1. For each of these equations, what is a, b and c? (the first one has been
done for you)
a) 2x2+4x -3 =0
a=2
b=4
c=-3
b) 6x2+x - 10=0
c) x2-4x -5=0
d) 2x2-10x + 7=0
e) 0.5x2+8x + 2=0
2. Use your answers from question one to find the possible values for x.
3. Rearrange these equations to the form ax2 + bx + c =0, then solve with the
quadratic equation:
a) 2x2+ 9x -2 =10
b) 4x + 5x2 - 10=2
c) x2 + 5x -3=x
d) 2x2-10x - 2= x2
e) 3x2 + 6 + 2x =8 + 7x
47. Factorising Quadratics
1. Factorise and solve:
a) X2 + 8X + 12= 0
b) X2 + 7X + 10= 0
c) X2 + 13X + 12= 0
d) X2 + 18X + 70=0
e) X2 + X – 20=0
f) X2 - 4X- 12=0
g) X2 - 12X + 20=0
2. Rearrange, factorise and solve
a) X2 + 21X + 32=12
b) X2 + 8X -5 = 20
c) X2 + 6X + 23 = 5 – 3X
3. Solve
a) 3X2 + 21X + 51=15
b) 2X2 +18 + 10=-6
c) 4X2 -8X -4= 36 + 4x
48. Sequences
1.
2.
3.
4.
5.
Copy down the following sequences and add the next three terms:
a) 36
9
12
15
b) 27
12
17
22
c) 410
16
22
28
d) 13
24
35
46
57
e) 50
48
46
44
42
For each of the questions in question what is rule to find the next term in the
sequence. (This is called the term to term rule)
Copy the following sequences, write the term to term rule and find the next 3 terms.
a) 0.3
0.7
1.1
1.5
1.9
b) 1.4
1.7
2
2.3
2.6
c) 40
39.5
39
38.5
38
d) 5.9
5.3
4.7
4.1
3.5
e) 11.4
12.5
13.6
14.7
15.8
Copy the following sequences, write the term to term rule and find the next 3 terms.
a) 50
-5
-10
-15
b) 3
-1
-5
-9
-13
c) -20
-16
-12
-8
-4
d) -30
-27.5
-25
-22.5
-20
Copy the following sequences, write the term to term rule and find the next 3 terms.
a) 1
2
4
8
16
b) 1
3
6
10
15
c) 1
3
7
13
21
49. The Nth term
•1) Find the nth term of the following sequences:
a) 4
7
10
13
16
b) 2
7
12
17
22
c) 4
10
16
22
28
d) 13
24
35
46
57
e) 1
9
17
25
33
•2) Take the following nth terms and find the first 5 terms
a) 3n + 1
b) 4n +2
c) 5n + 5
d) 4n – 1
e) 6n + 3
f) 10n -3
•3) If the nth term is 7n + 4 what is
a. The 4th term
b. The 12th term
•4) If the nth term is 8n - 2 what is
a. The 4th term
b. The 12th term
•5) If the nth term is 11n + 3 what is
a. The 4th term
b. The 12th term
•6) If the nth term is n + 9 what is
a. The 4th term
b. The 12th term
c. The 100th term
c. The 100th term
c. The 100th term
c. The 100th term
53. Solving Equations
1.
2.
3.
Find x if:
a) 7x= 42
b) 12x=36
c) 5x = 40
d) 10x = 110
e) How did you answer these questions?
Find x if:
a) X + 10 = 17
b) X + 15 = 27
c) X + 25 = 30
d) X- 9 = 15
e) X – 13 = 40
f) How did you answer these questions?
Find x if
a) 3x + 6 =21
b) 7x + 11 = 67
c) 5x + 4 = 24
d) 9x – 2 =25
e) 11x – 14= 30
f) 10x - 7= 53
g) 12x + 11= 155
h) 15x - 14= 61
i) 13x + 25 = 90
j) How did you answer these questions?
54. Substituting
1. If A is 5 what is:
a) 5A
b) 11A
c) 6A – 10
d) 9A + 15
e) 100-5A
2. If B is 7 what is
a) 2(B+8)
b) 3(B-5)
c) B(B+5)
d) 9(10-B)
e) (3+B)X(B-5)
3. If A= 6 and B=7 what is:
a) A+B
b) B-A
c) 6A+2B
d) AB
e) A(B+1)
f) A2B
55. Trial and Improvement
1.
2.
3.
Use trial and improvement to find the positive solution to these quadratic equations to 1 dp,
you may like to use a table, the table for the first question has been drawn for you.
a) X2 + 3x -30=0
x
X2
+3x
-30
Big or small?
b) X2 + 3x -30=0
c) X2 + 2x -20=0
d) X2 + 4x -10=0
e) X2 -2x -5=0
Use trial and improvement to find the positive solution to these quadratic equations to 2dp
a) 3X2 - 5x -10=0
b) 2X2 + 2x -25=0
Use trial and improvement to find the positive solution to these quadratic equations to 3dp
a) X2 + x -6=0
b) 3X2 - 2x -11=0
56. Writing Expressions
1. My age is C, write expressions for the ages of the members of my family if:
a) My brother is 3 years older than me
b) My sister is 2 years younger than me
c) My mum is double my age
d) My dad is 5 years older than my mum
e) My Gran is 4 times my age
f) My Grand Dad is twice my Dads age
2. If I have S sweets, write an expression for the number of sweets my friends have if I:
a) I give Tom all my sweets and he has 5 of his own
b) I give Alan half of my sweets
c) I eat four sweets then give Simon the rest
d) I give Lucy a quarter of my sweets, then an extra 1
3. My favourite song last M minutes, how long do I spend listening to music if:
a) I listen to the song once and hour all day (and including when I’m asleep)
b) I listen to half the song 8 times
c) I listen to the intro (a quarter of the song) 5 times
d) I listen to my song, then the next one which is exactly twice as long
e) I listen to my song, then the next one which is exactly twice as long, and do this 5
times throughout the day
4. If a rectangle has lengths x and y, write an expression for:
a) The area of the rectangle
b) The area covered by 6 rectangles
c) The perimeter of the rectangle
57. Y=mx +c
1. Copy and complete:
a) A line with a positive gradient will go from ________ left to ________right
b) A line with a negative gradient will go from ________ left to ________right
2. Look at the equations below, write down the gradient and the coordinates of the line they represent.
a) Y=3x+4
b) Y= 2x-5
c) Y=6x+9
d) Y=x- 7
e) Y=10x
f) Y=5+8x
g) Y=7-11x
3. Draw an axis from -10 to 10, plot the following lines
a) Y = 2x + 3
b) Y = 3x – 2
c) Y = -2x + 5
d) Y = -3x + 9
4. Find the gradient of the line between these pairs of coordinates by dividing the change in y by the change in x.
a) (3,3)
(5,5)
b) (5,5)
(6,7)
c) (1,2)
(3,8)
d) (10,9)
(6,1)
e) (15,20) (10,5)
5. Using the gradient worked out in the last question and one of the coordinates, find the value of c for the line between the
pairs of points in question 4.
6. Write out the equation of the line between the pairs of points in question 4 in the form y=mx+c
77. Worded Pythagoras
1. A hunter fires an arrow to kill a bird, the bird falls 20m and the hunter has to walk 40m to pick it up,
how far did the arrow travel to the bird?
2. A boat travels 45 miles east then 60 miles north, how far is it from where it started?
3. A swimming pool is 25m by 12m, if someone swam from one corner to the other, how far would they
have swum?
4. A kite is flying on a string which is 10m, the kite is flying 6m of the ground, if the kite plummets
straight down how far will the kite flyer have to walk to pick it up?
5. A totem pole is tied to the ground with ropes stuck in the ground with pegs, if the rope is 14m long
and the pole is 9m long, how far will the pegs be from the base of the totem pole?
6. A fly is 1m of the ground and 70cm away from a chameleon, the chameleon s tongue flies out a
catches the fly, how long is the chameleon’s tongue?
7. A lighthouse shine a light on a ship, the light beam is 80m long, the ship is 110m away from the base
of the lighthouse, how tall is the lighthouse?
8. A man falls from the top mountain, he travels 2.5km and the mountain is 1.7km, how far has he
travelled horizontally?
9. A helicopter floats 120m above a helipad, a dog is 85m from the helipad, if the dog could fly, how far
would it have to fly to get to helicopter?
83. Mean
1. Find the mean from these numbers:
a) 5,3,4
b) 10, 11, 1, 7
c) 15, 8, 7, 10
d) 14, 2, 4, 1, 4
e) 7, 8, 5, 10, 4, 2
f) 24, 26, 32, 17, 1
g) 0.2, 0.1, 0. 5, 0.3
h) 20, 9, 3, 8, 8, 8
i) 17, 18, 15, 10, 8, 2, 10
j) 0,0,0,0,0,18
2. How would you find the:
a) Mean age of players in a football team
b) Mean height of a family
c) Mean number of sweets eaten by boys in a day
d) Mean number of hours spent watching TV for a pupil each night
e) Mean number of times someone says “LOL” a day
3. Write down 3 possible lists of numbers if there are:
a) 4 numbers with a mean of 6
b) 5 numbers with a mean of 8
c) 7 numbers with a mean of 9
84. Mean, Mode, Median and Range
1. Which of these could you not find a median for?
a) Height
b) Favourite colour
c) Score in a test
d) Favourite football team
2. Find the mean, mode, median and range for these sets of numbers:
a) 5,7,2,8,8
b) 2,12,6,3,2
c) 15,4,11,6,4
d) 20,30,35,15,15
e) 4,7,0,14,0,19,5
f) 2,9,18,12,7,2,6
g) 21,13,15,2,15,3,1
3. Write 3 different lists of 5 numbers which have a mean of 7.
4. Write 3 lists of numbers which have a median of 11
5. Would mode be a good thing to find if we were looking at pupils exact journey time to school? Explain
your answer.
6. Can any of mean, median, mode and range be negative? Explain your answer
90. Probability as Fractions
1. I have some counters in a bag. There are 3 blue,
5 red and 2 green. What is the probability I pick
out:
a) A blue
b) A red
c) A green
d) A purple
e) A blue or red
f) A red or green
2. I am picking my socks at random today, I have 4
pairs with stripes on, 10 with spots, 5 with
clowns and 1 with maths pictures. What is the
probability I will pick out:
a) Spotty socks
b) Clown socks
c) Maths Socks
d) Clown or spotty socks
e) Maths or stripe socks
3. I have a pack of card (without jokers)
what is the probability I pick:
a) A Red card
b) A heart
c) A Club
d) A heart or a club
e) A 2
f) A King
g) A picture card
h) A number card smaller than 6
i) A number card greater than 6
j) An even number
k) An odd number
l) A red number 3
m) A black Queen or red Jack
n) A King of Hearts or a 5
92. Listing Outcomes
1. If I flip a coin and roll a dice, list all the possible outcomes I could get.
2. I spin two fair spinners number 1 to 3.
a) Copy and complete the table to show all the possible outcomes.
Spinner 1
Spinner 2
Total
3. When I have breakfast I have a drink and something to eat. The drinks I
choose from are tea, coffee and juice and I eat a bagel, toast or cereal.
Write down all the different combinations I could have for breakfast.
4. If I toss 1 coin there are 2 possible outcomes, find the number of outcomes
for:
a. 2 coins
b. 3 coins
c. 4 coins
d. X coins
5. Lucy, Amy and George are going to have their photo taken so they sit in a
line:
a) How many different ways could they order themselves?
b) Andy joins them, how many different ways could they order themselves
now?
94. Tree Diagrams
A) I have a bag with 20 balls in, there are 13 pink, 7 orange pull a ball out, put it back then pull another.
1.Draw a tree diagram showing all possible outcomes
2.Use your tree diagram to find the probability of getting:
a.2 pink
b.2 orange,
c.A pink and an orange.
B) The probability I have toast for breakfast is 0.6, the probability I will miss my bus is completely unrelated to my breakfast choice and is 0.2
1.What is the probability I will NOT:
a.Have toast for breakfast
b.Miss my bus
2.Draw a tree diagram showing all possible outcomes
3.Use your tree diagram to find the probability of:
a.Having toast and missing my bus
b.Not having toast and missing my bus
c.Not having toast and not missing my bus
C) I am tossing a coin and rolling a dice:
1.Draw a tree diagram to show all possible outcomes.
2.Use your tree diagram to find the probability of:
a.A head a 3
b.A tails and a number bigger than 4
c.A tails with a 3 or a heads with a 1
D) I have some songs on my mp3 player, 4 are rock, 7 are Pop and 11 are Hip Hop. I put my mp3 player on shuffle and listen to 2 songs (it is
possible to listen to the same song twice in a row)
1.Draw a tree diagram to show all the possible outcomes,
a.Find the probability that I will listen to:
i.Hip Hop then Pop
ii.Rock twice
iii.A Rock song and a pop song in any order
iv.2 songs which are the same style (rock and rock or pop and pop ect.)