Pc12 sol c08_8-5
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This document provides examples and explanations for using Pascal's triangle to solve combinations problems. It includes: 1) Using the numbers in row 10 to generate the numbers in row 11 of Pascal's triangle. 2) Using a completed Pascal's triangle to evaluate binomial coefficient expressions like 4C1 and 7C2. 3) Using combinations to determine the numbers in row 13 of Pascal's triangle. 4) Determining specific values in Pascal's triangle, such as the second number in row 20 and the fourth number in row 24.
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no maths
1. This document is an exam paper for GCSE Mathematics (Linear) - 1380 Paper 4 (Calculator) Higher Tier. It contains 26 maths questions to be completed in 1 hour and 45 minutes. Students must show their working and write their answers in the spaces provided.
2. The exam paper provides information for candidates such as the marking scheme and advice to work steadily through all questions. It also contains a blank formulae page that students cannot write on.
3. The first few questions cover topics like currency exchange, geometric transformations, number sequences, scatter graphs, ratios, and solving equations. Students must set out their working clearly to receive full marks.
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The document provides examples of calculating angles between lines and planes in 3 dimensions. It includes calculating angles between a line and plane using tangent, and between two planes. It also provides practice questions involving finding angles between lines and planes given dimensional information about the lines and planes.
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PEA 305.pdf
The document provides information on various number system concepts in Vedic maths including:
1. Methods for multiplying numbers with 11, 9, 99, and 999 using place value concepts.
2. Methods for multiplying two-digit and three-digit numbers using the "criss-cross" method.
3. Shortcuts for finding squares and square roots of numbers.
4. Divisibility rules and their applications.
5. Concepts like remainder theorem, power cycles, and unit digit patterns that are useful for solving problems involving remainders and exponents.
6. Information on factors, multiples, and their properties like total number of factors and sum of factors.
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Pc12 sol c08_8-5
- 1. 10_ch08_pre-calculas12_wncp_solution.qxd 5/23/12 4:23 PM Page 24 Home Quit Lesson 8.5 Math Lab: Assess Your Understanding, page 737 1. These are the numbers in row 10 of Pascal’s triangle. Use these numbers to generate the numbers in row 11. 1 9 36 84 126 126 84 36 9 1 1 1 ؉ 9 01 ؍ 9 ؉ 36 54 ؍ 36 ؉ 84 012 ؍ 621 ؉ 48 021 ؍ 126 ؉ 126 021 ؍ 63 ؉ 48 012 ؍ 48 ؉ 621 252 ؍ 36 ؉ 9 54 ؍ 9 ؉ 1 = 10 1 So, the numbers in row 11 are: 1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1 2. Use the completed Pascal’s triangle on page 735 to evaluate each expression. Use a calculator to verify your answers. a) 4C1 b) 7C2 2nd number in row 5 is 4. 3rd number in row 8 is 21. 4C1 4 ؍ 7C2 12 ؍ c) 6C3 d) 5C0 4th number in row 7 is 20. 1st number in row 6 is 1. 6C3 02 ؍ 5C0 1 ؍ 3. Use combinations to determine the numbers in row 13 of Pascal’s triangle. Use 12Cr and a calculator. 12C0 21 ,1 ؍C1 21 ,21 ؍C2 21 ,66 ؍C3 ,022 ؍ C 21 ,594 ؍C5 21 ,297 ؍C6 21 ,429 ؍C7 ,297 ؍ 12 4 C 21 ,594 ؍C9 21 ,022 ؍C10 21 ,66 ؍C11 21 ,21 ؍C12 1 ؍ 12 8 So, the numbers in row 13 are: 1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1 4. Determine the value of each number in Pascal’s triangle. a) the second number in row 20 n 91 ؍and r 1 ؍ C 91 ؍ 19 1 b) the fourth number in row 24 n 32 ؍and r 3 ؍ C 1771 ؍ 23 3 24 8.5 Math Lab: Pascal’s Triangle—Solutions DO NOT COPY. ©P