Maths revision game_solutions
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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.
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1) The document discusses factoring quadratic trinomials of the form ax^2 + bx + c and solving quadratic equations.
2) Key aspects of quadratics are reviewed, including that they produce parabolic graphs and always have two solutions.
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1) Take half the coefficient of the x-term and square it. Add this to both sides of the equation.
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3) Take the square root of both sides to isolate the variable term.
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The document provides instructions for students to:
1) Plot the points (3,4), (1,2), (-1,0) on a graph and connect them to draw a line.
2) Draw a table of values for the quadratic equation y = x^2 + 3x - 5 and plot those points on a graph.
3) Estimate the minimum point and solutions of the equation by analyzing the graph.
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1. The sequence is a geometric sequence with first term a1 = 3 and ratio r = 3. The specific formula is an = 3(3)n-1. The sum of the first 20 terms is 1743392200 and the infinite sum is 3072.
2. The sequence is a geometric sequence with first term a1 = 1/90 and ratio r = 3. The specific formula is an = (3/90)(3)n-1. The sum of the first 20 terms is 174339220/9 and the infinite sum is 1/30.
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1. The document discusses absolute value functions of the form y = a|x - h| + k, where a ≠ 0.
2. It explains how to find the vertex (h, k) and line of symmetry x = h of an absolute value function graph.
3. It also describes how the graph opens up or down depending on whether a is positive or negative, and how the width compares to y = |x| depending on the value of |a|.
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APEX INSTITUTE was conceptualized in May 2008, keeping in view the dreams of young students by the vision & toil of Er. Shahid Iqbal. We had a very humble beginning as an institute for IIT-JEE / Medical, with a vision to provide an ideal launch pad for serious JEE students . We actually started to make a difference in the way students think and approach problems.
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The document explains how to solve quadratic equations by completing the square. It defines a perfect square trinomial as having the form x^2 + bx + c, where c is the square of half of b. It provides steps for completing the square, which involves adding a constant term to both sides of the equation such that the left side becomes a perfect square trinomial that can be factorized. This process results in the solution(s) to the quadratic equation. Two examples demonstrating this process are included.
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The document discusses solving quadratic equations by completing the square. It provides examples of perfect square trinomials and explains the steps to solve quadratic equations using completing the square. These steps include: 1) moving terms to one side of the equation, 2) finding the term to complete the square and adding it to both sides, 3) factoring the perfect square trinomial, 4) taking the square root of both sides, and 5) solving for the two possible solutions. It also provides a second example where the quadratic coefficient is not 1, requiring dividing all terms by this coefficient first before completing the square.
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This document contains instructions for 5 math activities involving numbers:
1. Creating a "magic box" using addition of numbers in rows and columns.
2. Guessing a number by reversing digits, subtracting, and reversing the answer.
3. Determining a missing digit by adding digits, subtracting from the original number, and using divisibility by 9.
4. A probability activity using objects and counting possibilities.
5. Repeating a 3-digit number and dividing the result by 11, 1001.
Quadratic functions my maths presentation
1. The document discusses key concepts related to quadratic equations including factorizing, solving, graphing, finding roots and axis of symmetry, locating maximum/minimum values, and using graphs to solve related equations and inequalities.
2. The key steps provided to factorize a quadratic equation are to find the product and factors of the coefficients that add up to the middle term, and then pair the factors.
3. To solve a quadratic equation, take all terms to one side, factorize, set each factor equal to 0 and solve for x to find the two roots.
Class 10 Cbse Maths Sample Paper Term 1 Model 2
Cbse class 10 maths sample paper term 1 model 2 - http://cbse.edurite.com/cbse-maths/maths-cbse-class-10.html
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This document contains 8 questions regarding various topics in applied mathematics for a first semester M.Tech degree examination. The questions cover topics such as significant figures, accuracy, precision, and round off errors; solving equations using methods like Regula-Falsi, Newton's formula, Bairstow method, and Graeffe's root squaring; numerical integration using Romberg's method; solving systems of linear equations using Gauss-Jordan and triangularization methods; eigen values and vectors using inverse power and Rutishauser methods; linear transformations and their properties; least squares solutions; and constructing orthogonal sets using Gram-Schmidt process. Students are required to answer any 5 full questions out of the 8 questions provided.
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This document contains notes from a math class that covered various topics:
- Warm-up exercises solving equations for variables.
- Khan Academy stats showing over 38 hours spent on problems over the weekend.
- Continued work on solving equations for variables and formulas for perimeter, area, distance, and temperature conversions.
- Explanations and examples of solving equations with absolute values.
Sequences
A sequence is a set of terms that follow a pattern or rule. If the sequence continues indefinitely, it is called an infinite sequence, otherwise it is finite. The rule allows you to write an expression for the nth term (un). Common examples include arithmetic sequences where the difference is constant, and geometric sequences where each term is obtained by multiplying the previous term by a fixed value. A recurrence relation defines each term in terms of the preceding ones. To solve problems involving sequences, you determine the expression for successive terms and find sums by adding terms up using the Greek letter sigma. Exam questions may involve finding individual terms, sums, or showing sums are divisible.
April 1, 2014
1) The document discusses factoring quadratic trinomials of the form ax^2 + bx + c and solving quadratic equations.
2) Key aspects of quadratics are reviewed, including that they produce parabolic graphs and always have two solutions.
3) Methods for solving quadratics by factoring and setting equal to 0 are presented along with examples.
4) Applications of quadratic equations to problems involving sums of integers and their squares and finding dimensions of triangles based on given areas are demonstrated.
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The document provides steps for completing the square to solve quadratic equations:
1) Take half the coefficient of the x-term and square it. Add this to both sides of the equation.
2) Simplify the trinomial on the left side into a perfect square.
3) Take the square root of both sides to isolate the variable term.
Examples are provided to demonstrate solving quadratic equations by completing the square.
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1) 224-1 can be factorized as (212+1)(212-1)
2) 212-1 can be further factorized as (26+1)(26-1)
3) Therefore, 224-1 = (212+1)(26+1)(26-1)
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Directions: Please show all of your work for each problem. If applicable, you may find Microsoft Word’s equation editor helpful in creating mathematical expressions in Word. The option of hand writing your work and scanning it is acceptable.
1. List all the factors of 88.
2. List all the prime numbers between 25 and 60.
3. Find the GCF for 16 and 17.
4. Find the LCM for 13 and 39.
5. Write the fraction in simplest form.
6. Multiply. Be sure to simplify the product.
7. Divide. Write the result in simplest form.
8. Add.
9. Perform the indicated operation. Write the result in simplest form. –
10. Perform the indicated operation. Write the result in simplest form. ÷
11. Find the decimal equivalent of rounded to the hundredths place.
12. Write 0.12 as a fraction and simplify.
13. Perform the indicated operation. 8.50 – 1.72
14. Divide.
15. Write 255% as a decimal.
16. Write 0.037 as a percent.
17. Evaluate. 56 ÷ 7 – 28 ÷ 7
18. Evaluate. 9 42
19. Multiply: (-1/4)(8/13)
20. Translate to an algebraic expression: Twice x, plus 5, is the same as -14.
21. Identify the property that is illustrated by the following statement. 5 + 15 = 15 + 5
22. Identify the property that is illustrated by the following statement.
(6 · 13) 10 = 6 · (13 · 10)
23. Identify the property that is illustrated by the following statement.
10 (3 + 11) = 10 3 + 10 11
24. Use the distributive property to remove the parentheses in the following expression. Then simplify your result where possible. 3.1(3 + 7)
25. Add. 14 + (–6)
26. Subtract. –17 – 6
27. Evaluate. 3 – (–3) – 13 – (–5)
28. Multiply.
29. Divide.
30. Evaluate. (–6)2 – 52
31. Evaluate. (–9)(0) + 13
32. A man lost 36 pounds (lb) while dieting. If he lost 3 pounds each week, how long has he been dieting?
33. Write the following phrase using symbols: 2 times the sum of v and p
34. Write the following phrase using symbols. Use the variable x to represent the number: The quotient of a number and 4
35. Dora puts 50 cents in her piggy bank every night before she goes to bed. If M represents the money (in dollars) in her piggy bank this morning, how much money (in dollars) is in her piggy bank when she goes to bed tonight?
36. Write the following geometric expression using the given symbols.
times the Area of the base (A) times the height(h)
37. Evaluate if x = 12, y = , and z = .
38. A formula that relates Fahrenheit and Celsius temperature is . If the current temperature is 59°F, what is the Celsius temperature?
39. If the circumference of a circle whose radius is r is given by C = 2πr, in which π ≈ 3.14, find the circumference when r = 15 meters (m).
40. Combine like terms: 9v + 6w + 4v
41. A rectangle has sides of 3x – 4 and 7x + 10. Provide a simplified expression for its perimeter.
42. Subtract 4ab3 from the sum of 10ab3 and 2ab3.
43. Use the distributive property to remove the p.
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The document discusses several key concepts regarding polynomials:
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- Multiple choice and short answer questions are provided to test understanding of these concepts.
Algebra unit 8.7
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Cbse sample-papers-class-10-maths-sa-ii-solved-1
The document provides information about a math exam including:
- It is divided into 4 sections with various question types and marks.
- Section A has 8 multiple choice 1-mark questions.
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2period review andanswers
The document contains a math review with examples of different techniques for counting combinations and permutations, as well as examples involving polynomials, solid geometry, and volume. It provides the steps to solve problems involving multiplication to find combinations, factoring polynomials, finding volumes of 3D shapes, and determining angle measures using parallel lines and a transversal.
2period review andanswers
The document contains a math review with examples of different techniques for counting combinations and permutations, as well as examples involving polynomials, solid geometry, and volume. It provides the steps to solve problems involving multiplication to find combinations, factoring polynomials, finding volumes of geometric shapes, and determining angle measures using parallel lines and a transversal.
2period review and answers
The document contains a math review with examples of different techniques for counting combinations and permutations, as well as examples involving polynomials, solid geometry, and other math concepts. It provides the steps and work for 14 different math problems, showing how to use techniques like multiplication, combinations, and permutations to calculate things like the number of combinations for choosing food items or essays. It also includes examples of multiplying polynomials, finding volumes of solids, and solving geometry problems involving parallel lines and transversals.
Study materialfor class 10 Mathematics
This document contains a collection of study material and practice questions related to number systems, polynomials, and systems of linear equations for Class 10. There are over 50 questions covering topics like divisibility rules, factorization, rational and irrational numbers, operations on polynomials including finding zeros, and solving and graphing systems of linear equations. The questions range from straightforward applications of concepts to more complex multi-step problems and proofs.
Power point presentationof class 9 maths HERONS FORMULA
This document provides an overview of Heron's formula for calculating the area of a triangle given the lengths of its three sides. It begins with examples of finding the area of right triangles, equilateral triangles, and isosceles triangles by calculating the height. It then introduces Heron's formula, which allows calculating the area directly from the side lengths. The document provides examples of applying the formula to find the areas of various triangles. It concludes by explaining how Heron's formula can be used when the height is difficult to determine.
Upcat math 2014 solution
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.
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Directions Please show all of your work for each problem. If app.docx
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Power point presentationof class 9 maths HERONS FORMULA
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みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
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みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
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Maths revision game_solutions
- 1. Trig & Pythag - 1 What is Pythagoras’ theorem? a² + b² = h² (where h is the hypotenuse)
- 2. Trig & Pythag - 2 How long is the hypotenuse? h = 18cm 10cm 15cm
- 3. Trig & Pythag - 3 What are the trigonometric formulae? sin A=opp hyp cos A=adj hyp tan A=opp adj
- 4. Trig & Pythag - 4 Find angle A A A = 53° 6cm B 8cm C
- 5. Trig & Pythag - 5 A ladder leans against a vertical wall so that is makes an angle of 35° with the wall. The top of the ladder is 2m up the wall. How far out is the foot of the ladder? 2.9 m
- 6. Algebra - 1 Factorise the following expression: 12z² – 6z = 6z(2z – 1)
- 7. Algebra - 2 Expand the following expression: (x + 3)(x + 6) = x² + 9x + 18
- 8. Algebra - 3 Factorise the following expression: x² + 5x + 6 = (x + 3)(x + 2)
- 9. Algebra - 4 Solve the following pair of simultaneous equations: x+y=5 3x + y = 11 x=3 y=2
- 10. Algebra - 5 Expand the following expression: (5x – 2)(5x + 2) = 25x² – 4
- 11. Number work - 1 Write the following fraction as a mixed number: 25 = 8⅓ 3
- 12. Number work - 2 Without a calculator work out: 1.23 – 0.67 = 0.56
- 13. Number work - 3 Fill in the blank: 3.7 x 4.2 = 15.54
- 14. Number work - 4 Express 12mm as a percentage of 6cm. 20%
- 15. Number work - 5 Write the following number as an ordinary Number: 3.45 x 10³ - 9 x 10-¹ 3450 – 0.9 = 3499.1
- 16. Formulas - 1 What are the next 3 terms of this sequence? 2, 5, 10, 17, 26, 37, 40…
- 17. Formulas - 2 If R = pq – w R=2 Find R when p = 2, q = 3 and w = – 4
- 18. Formulas - 3 A taxi firm charges 50p per mile plus a fixed charge of £2.00. Write down a formula for the cost (C) of hiring this taxi to travel ‘n’ miles. C = 2 + 0.5n
- 19. Formulas - 4 If y = zx – 4w w=3 Find w when y = 3, z = 3 and x = 5
- 20. Formulas - 5 Use an appropriate formula to find the radius of the following circle. Give your answer 3 sf r = 3.18cm Circumference = 20cm
- 21. Pot Luck - 1 Give the inequality which describes the shaded region. x≤2
- 22. Pot Luck - 2 Sally writes the letters of the word ‘MATHEMATICS' on separate cards and places them in a bag. She then draws a card at random. What is the probability that Sally chooses the letter 'A'? P(A) = 2 11
- 23. Pot Luck - 3 You are about to leave for holiday, but you forgot socks! You race back to your room, but all the lights are off, so you can't see the colour of the socks. Never mind, because you remember that in your drawer there are ten pairs of white socks, ten pairs of black socks, and eleven pairs of blue socks, but they are all mixed up. How many of your socks do you need to take before you can be sure to have at last one matching pair? 4 socks
- 24. Pot Luck - 4 What is the volume of this prism? Volume = 40cm³
- 25. Pot Luck - 5 Give the set of inequalities which describe the unshaded region. x≤3 y≥x y≥1