P2 Solid Geometry
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The document contains 5 math problems involving calculating volumes of 3D shapes: 1. Finding the height of a cone joined to a cylinder given the volumes is 231 cm^3. 2. Calculating the volume of a solid cone with a cylinder removed. 3. Finding the volume of a cylinder with a hemispherical section removed. 4. Determining the volume of a solid formed by joining a cone and hemisphere. 5. Calculating the volume of a container made of a cuboid and a cylindrical quadrant.
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This document contains sample answers and solutions to exercises in a math textbook. It includes:
1) Answers to standard form exercises and diagnostic tests in Chapter 1.
2) Answers to quadratic expressions exercises and diagnostic tests in Chapter 2.
3) Answers to sets exercises and diagnostic tests in Chapter 3.
4) Sample exercises and answers on mathematical reasoning in Chapter 4.
5) Sample exercises and answers on straight lines in Chapter 5.
The document provides concise worked out solutions to math problems across multiple chapters in a standardized format for student practice and review.
F4 07 Probability I
1. A document contains sample probability questions and answers about events such as rolling dice, picking cards or balls from boxes, coin tosses, and surveys.
2. The questions ask students to determine the sample space of events, calculate probabilities of outcomes, predict expected numbers of outcomes, and solve for unknown values.
3. The answers provided include writing out sample space elements, listing outcomes, calculating probabilities as fractions or decimals, and finding values that satisfy given probability equations.
F4 06 Statistics Iii
The document provides examples and exercises on statistics concepts like mean, median, mode, range, class intervals, frequency distributions, and pictographs. It contains 10 questions with multiple parts testing understanding of these concepts through calculations and interpreting data presented in tables and diagrams.
F4 05 The Straight Line
This document contains 10 multi-part math word problems involving straight lines. The problems ask students to determine gradients, equations, intercepts, and coordinates from diagrams showing straight lines and geometric shapes like triangles, parallelograms, and perpendicular lines. Students must use properties of parallel and perpendicular lines as well as the slope-intercept form of a line to analyze the diagrams and solve the multi-step problems.
F4 04 Mathematical Reasoning
1. The document presents an exercise on mathematical reasoning with 5 questions.
2. The questions test a variety of mathematical logic skills, including determining if statements are true or false, writing implications, completing arguments with valid premises, and using quantifiers to form true statements.
3. The final section provides a diagnostic test to further assess skills in mathematical statements, implications, argument structures, and applying properties of shapes and numbers.
F4 03 Sets
The document contains examples and exercises on sets and Venn diagrams. It includes questions that ask the reader to:
1) Shade regions in Venn diagrams that represent given sets;
2) Find the number of elements in sets defined within Venn diagrams;
3) List elements that are the intersection or union of given sets; and
4) Draw additional sets in incomplete Venn diagrams based on defined conditions.
F4 02 Quadratic Expressions And
The document contains examples and exercises on quadratic expressions and equations. It includes expanding expressions, factorizing expressions, solving quadratic equations, and word problems involving quadratic equations. The exercises cover a range of skills related to quadratic expressions and equations.
F4 01 Standard Form
The document provides examples and exercises on standard form and rounding numbers to significant figures. It includes rounding numbers, expressing numbers in standard form, evaluating expressions in standard form, and calculating the mass of a carbon dioxide molecule. The diagnostic test at the end contains 10 multiple choice questions testing concepts related to standard form and significant figures.
Probability Modul
The document discusses probability and provides examples and solutions. It defines probability as the number of favorable outcomes divided by the total number of possible outcomes. It gives examples of calculating probabilities of events such as choosing balls of different colors from a bag. It also discusses combined events and finding probabilities of "or" and "and" events.
P2 Matrices Test
1. The matrix M is equal to [-4 2; -5 3]. The values of x and y that satisfy the simultaneous equations are x=5 and y=-4.
2. The values of m and p are m=1/2 and p=4. The values of x and y that satisfy the simultaneous equations are x=7 and y=11/2.
3. The values of k and h are k=1/11 and h=5. The values of x and y that satisfy the simultaneous equations are x=-1 and y=3.
P2 Plans & Elevation Test
1. A solid right prism with a rectangular base is shown. Plans and elevations are drawn to scale of the prism and when combined with a solid cuboid.
2. A solid with a cuboid and half cylinder joined is shown. Plans and elevations are drawn to scale of the solid and when combined with a solid right prism.
3. A solid consisting of a right prism and half cylinder is shown. Plans and elevations are drawn to scale.
4. A solid right prism is shown. Plans and elevations are drawn to scale of the prism and when combined with a solid cuboid.
5. A solid right prism with trapez
P2 Graphs Function
The document contains 10 math problems involving graphing functions and inequalities on Cartesian planes. The problems involve sketching graphs of functions, finding coordinates that satisfy equations, drawing lines to solve equations, and shading regions defined by inequalities. Tables are used to list x and y values satisfying equations.
Mathematics Keynotes 2
Here are the key steps to solve quadratic equations:
1. Factorize the quadratic expression if possible. This allows using the zero product property.
2. Use the quadratic formula if factorizing is not possible:
x = (-b ± √(b^2 - 4ac)) / 2a
3. Solve for the roots. The roots are the values of x that make the quadratic equation equal to 0.
4. Check your solutions in the original equation to verify they are correct roots.
5. Determine the nature of the roots:
- If the discriminant (b^2 - 4ac) is greater than 0, there are two real distinct roots.
- If the discriminant
P1 Bearing Modul
1) Bearings are defined as the angle measured clockwise from north to the straight line between two points.
2) Examples of bearings are shown between points P and Q, with the bearing of Q from P measured as the angle from north to the line PQ.
3) An exercise asks the reader to draw diagrams showing the direction of Q relative to P for different given bearings, and to state the bearings of P from Q and Q from P based on the diagrams.
Module 15 Plan And Elevation
The document contains instructions and diagrams for 6 mathematics problems involving plans and elevations of 3D shapes. Students are asked to draw the plans and elevations of prisms, combined prisms, and prisms with half-cylinders attached. The problems involve multiple steps of interpreting diagrams, identifying corresponding sides between views, and drawing the views to scale.
Module 14 Probability
This document contains a math probability worksheet with 10 problems. It provides the questions, tables of data, and diagrams related to calculating probabilities of random events. The questions cover topics like picking marbles from a box, choosing members from sport teams, selecting students based on residential areas, and other scenarios involving groups with different characteristics. The document also includes the answers to all 10 problems in the worksheet.
Module 13 Gradient And Area Under A Graph
1) The document provides examples and questions related to calculating gradient, area under graphs, speed, velocity, and distance from speed-time and distance-time graphs.
2) It includes 10 multi-part questions testing concepts like calculating rate of change of speed, uniform speed, total distance, meeting time, and average speed.
3) Detailed step-by-step answers are provided for each question at the end to demonstrate how to apply the concepts to calculate the requested values.
Module 12 Matrices
1. The document contains 10 mathematics word problems involving matrix operations and inverses.
2. The problems require finding inverse matrices, solving systems of equations using matrices, and calculating values that satisfy matrix equations.
3. Detailed step-by-step solutions are provided for each problem.
Module 11 Tansformation
This document provides a series of math word problems involving transformations. It includes:
1) Five sections with multiple parts assessing skills with translations, reflections, rotations, and enlargements/reductions. Problems include finding coordinates of transformed points and describing transformations.
2) Diagrams of figures on Cartesian planes along with their transformed images under different combinations of transformations.
3) Calculating areas of transformed figures when given the area of the original figure.
The document assesses a wide range of skills with geometric transformations, providing practice applying concepts of translations, reflections, rotations, and scale changes to specific word problems and diagrams.
Module 10 Graphs Of Functions
This document contains 6 math problems involving graphing functions. Each problem has parts that involve:
1) Completing a table of values for a function.
2) Graphing the function on graph paper using given scales.
3) Finding specific values from the graph.
4) Drawing and finding values from a linear function related to the original.
The problems provide practice graphing and extracting information from graphs of quadratic, cubic, rational, and other polynomial functions. The document demonstrates how to set up and solve multi-step math word problems involving graphing functions.
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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...
ここ3000字までしか入らないけどタイトルの方がたくさん文字入ると思います。
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P2 Solid Geometry
- 1. ppr maths nbk Solid geometry 1.Diagram 1 shows a solid formed by joining a cone and a cylinder. 4 cm Diagram 1 The diameter of the cylinder and the diameter of the base of the cone are both 7 cm. The volume of the solid is 231 cm².By using π = 22 , calculate the height, in cm, of the cone. 7 Answer: 2.Diagram 2 shows a solid cone with radius 9 cm and height 14 cm. A cylinder with radius 3 cm and height 7 cm is taken out of the solid. Diagram 2 Calculate the volume,in cm³,of the remaining solid. (Use π = 22 ) 7
- 2. ppr maths nbk 3.Diagram 3 shows a cylinder. The shaded area with the shape of a hemisphere of radius 3 cm was removed. 7 cm Diagram 3 Find the volume , in cm³ , of the remaining solid. ( Use π = 22) 7 4.Diagram 4 shows a solid formed by joining a cone and a hemisphere. The diameter of the hemisphere is 10 cm and the slant height is 13 cm. Diagram 4 Calculate the volume , in cm³, of the solid
- 3. ppr maths nbk 5.Diagram 5,shows a container for storing bread consists of a cuboid and a quadrant of a cylinder. U V 30 cm W 15 cm Q R 20 cm 7cm Calculate the volume, in cm³ , of the container . ( Use π = 22 ) 7
- 4. ppr maths nbk ANSWER (DAIGNOSTIC TEST) 1. height = 6 2. volume = 990 3. volume = 141.43 4. volume = 576.19 5. volume = 10155