Skip to content
QuizQuip
Sign up
Back to Chapter 2
Mark schemePDF

Chapter 2 Practice Paper: Surds — question paper

QuizQuipPractice Series
QQ/S3AM/CH2

Secondary 3 · Additional Mathematics (G3)

Chapter 2 Practice Paper

Surds

Duration: 40 minutes
Total: 30 marks
Name:
Class:
Register No.:
Date:

READ THESE INSTRUCTIONS FIRST

  • Write your name, class and register number in the spaces at the top of this page.
  • Answer all questions.
  • Show all necessary working. Omission of essential working will result in loss of marks.
  • Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.
  • The number of marks is given in brackets [ ] at the end of each question or part question.
  • The total number of marks for each paper is shown on its cover.

Original practice material written for the MOE Additional Mathematics syllabus. It is not an official MOE or school examination paper. Chapter 2 (A3 Surds).

For Examiner’s Use
Section A/ 30
Total/ 30

Section A: Structured questions[30 marks]

Answer all questions in the spaces provided. Show all necessary working — omission of essential working will result in loss of marks. Give exact answers in simplest surd form unless told otherwise.

  1. 1

    This question is about simplifying square roots.

    1. (a)

      Simplify √98, showing your working.

      [2]
    2. (b)

      Simplify √50 + √32 − √18, giving your answer in the form k√2.

      [3]
  2. 2

    Answer the whole of this question without a calculator, giving exact values.

    1. (a)

      Expand and simplify (√5 + 3)(√5 − 4).

      [3]
    2. (b)

      Write 6/(√5 + 2) with a rational denominator, in simplest form.

      [3]
  3. 3

    Solve the equation √(4x + 5) = x.

    1. (a)

      Square both sides and show that x² − 4x − 5 = 0.

      [2]
    2. (b)

      Solve the equation x² − 4x − 5 = 0.

      x =[2]
    3. (c)

      Check both candidates against the original equation and state the final solution.

      [2]
  4. 4

    A rectangle has sides of length (√6 + √2) cm and (√6 − √2) cm.

    1. (a)

      Show that the area of the rectangle is 4 cm².

      [2]
    2. (b)

      Find the perimeter of the rectangle in the form k√6, where k is an integer.

      perimeter =[2]
    3. (c)

      A square has the same area as this rectangle. State the exact side length of the square.

      side length =[2]
  5. 5

    Express (3√2 + 1)/(√2 − 1) in the form p + q√2, where p and q are rational numbers.

    1. (a)

      Write down the conjugate of √2 − 1, and use it to rewrite the fraction with a rational denominator.

      [2]
    2. (b)

      Expand the numerator and simplify the expression to the form p + q√2.

      [3]
    3. (c)

      Verify your answer using √2 ≈ 1.414, correct to 2 decimal places.

      [2]

— End of paper —