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Grade 9 Maths Booklet Solutions PDF

16/10/2022

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Exam Dates:

Worked Solutions

Contents

  • Surds
  • Algebraic Proofs
  • Algebra
  • Transformations of Graphs
  • Equations of Circles
  • Quadratic and Other Sequences
  • Completing the Square
  • Inverse and Composite Functions
  • Expanding More Than Two Binomials
  • Nonlinear Simultaneous Equations
  • Solving Quadratic Inequalities
  • Shape, Space, and Measure
  • Circle Theorems
  • Vectors
  • Sine and Cosine Rules
  • Area Under Graphs
  • Data Handling
  • Histograms
  • Capture-Recapture
  • Probability
  • Set Theory
  • Ratio and Proportion
  • Proportion
  • Percentages - Reverse

Page numbers

  • 3
  • 7
  • 26
  • 34
  • 38
  • 46
  • 50
  • 55
  • 63
  • 66
  • 69
  • 73

Surds

Things to Remember

  1. The symbol √ means square root.
  2. To simplify surds, find all its factors.
  3. To rationalise the denominator, find an equivalent fraction where the denominator is rational.

Questions:

  1. Work out (5+√3)(5-√3)
  • Give your answer in its simplest form.
    = 22
    (a) Rationalise the denominator of 1/√3
    (b) Expand (2+√3)(1+√3)
  • Give your answer in the form a + b√3 where a and b are integers.
    = 18+2√5
    (Total 3 marks)
  1. Rationalise the denominator of √3/√3
    (a) Rationalise the denominator of -√3/53
    (b) Expand and simplify (√3+ √15)²
  • Give your answer in the form a + b√3 where a and b are integers.
    = 18+2√45
    (Total 7 marks)
  1. Expand and simplify (√3-√2)(√3-√2)
    (a) Write down the value of 49¹/2
    (b) Write √45 in the form k√5, where k is an integer.
    = 3√5
    (Total 2 marks)
  2. Expand and simplify (√3-√√2)(√3-√√2)
    (Total 2 marks)

Algebraic Proofs

Things to Remember

  • Start by expanding the brackets, then factorize.
  • Remember the following:
  1. 2n even number
  2. 2n +1 odd number
  3. a(bn + c) multiple of a
  4. Consecutive numbers are numbers that appear one after the other.

Questions:

  1. Expand and simplify x(x + 1)(x - 1) = x(x² - 1)
    (Total 2 marks)
  2. Prove that n³-n is a multiple of 6 for all possible values of n.
    (Total 2 marks)
  3. Prove that (2n + 3)² (2n - 3)² is a multiple of 8 for all positive integer values of n.
    (Total for question = 3 marks)
  4. Prove algebraically that (2n + 1)² (2n + 1) is an even number for all positive integer values of n.
    (Total for question is 5 marks)
  5. Prove algebraically that the difference between the squares of any two consecutive integers is equal to the sum of these two integers.
    (Total for Question is 4 marks)
  6. Factorise x² + 7x
    Factorise y² - 10y + 16
    (Total for Question is 6 marks)
  7. The expression 2t² + 5t + 2 can never have a value that is a prime number. Explain why.
    (Total for Question is 3 marks)
  8. Factorise 3t + 12
    Expand and simplify 7(2x + 1) + 6(x + 3)
    (Total for Question is 6 marks)
  9. Prove that (n-1)² + n² + (n + 1)² = 3n² + 2

Summary - Maths

  • Edexcel mathematics grade 9 booklet solutions PDF
  • Aiming for grade 9 answers
  • GCSE grade 9 maths questions PDF
  • Chapter 1 mathematics solutions GCSE
  • Maths class 9 PDF

In this article, we will talk about the Edexcel mathematics grade 9 booklet solutions PDF, providing aiming for grade 9 answers to various GCSE grade 9 maths questions. The chapter 1 mathematics solutions GCSE include algebra, surds, circles, and more. The article provides a PDF download for maths class 9 as well.

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GCSEs Notes, Currently doing A level

Frequently asked questions on the topic of Maths

Q: Work out (5+√3)(5-√3) and give your answer in its simplest form.

A: The answer is 22. Rationalise the denominator of 1/√3. The expansion of (2+√3)(1+√3) is 18+2√5.

Q: Rationalise the denominator of √3/√3 and -√3/53. Also, expand and simplify (√3+ √15)².

A: The rationalisation of √3/√3 and -√3/53 is 1 and -√3/53 respectively. The expansion and simplification of (√3+ √15)² is 18+2√45.

Q: Expand and simplify (√3-√2)(√3-√2) and find the value of 49¹/2. Also, write √45 in the form k√5.

A: The expansion and simplification of (√3-√2)(√3-√2) is 3√5. The value of 49¹/2 is 7 and √45 can be written as 3√5.

Q: Expand and simplify x(x + 1)(x - 1) and prove that n³-n is a multiple of 6 for all possible values of n.

A: The expansion and simplification of x(x + 1)(x - 1) is x(x² - 1). The proof that n³-n is a multiple of 6 is true for all possible values of n.

Q: Prove algebraically that (2n + 1)² (2n + 1) is an even number for all positive integer values of n and factorise x² + 7x.

A: The algebraic proof that (2n + 1)² (2n + 1) is an even number for all positive integer values of n is true. The factorisation of x² + 7x is x(x + 7).

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