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Chapter 5 Practice Paper: Equations and Inequalities — question paper

QuizQuipPractice Series
QQ/S3EM/CH5

Secondary 3 · Elementary Mathematics (G2 / G3)

Chapter 5 Practice Paper

Equations and Inequalities

Duration: 40 minutes
Total: 30 marks
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Class:
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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.
  • Geometrical instruments and an approved calculator may be used.
  • 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 Elementary Mathematics syllabus. It is not an official MOE or school examination paper. Chapter 5 (N7 Equations and Inequalities: linear and fractional equations, simultaneous equations, quadratics by factor/formula/completing the square, linear inequalities).

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 non-exact numerical answers correct to 3 significant figures where appropriate.

  1. 1

    This question is about linear equations.

    1. (a)

      Solve 4x + 3 = x − 6.

      [1]
    2. (b)

      Solve 5(y − 2) = 3y + 8.

      [2]
  2. 2

    Solve (3x − 2)/5 = (x + 4)/2.

    1. (a)

      Clear the fractions by cross-multiplying.

      [1]
    2. (b)

      Hence solve the equation.

      [2]
  3. 3

    Two straight lines have equations y = 2x − 5 and 4x + 3y = 25.

    1. (a)

      Find the x-coordinate of the point where the lines meet.

      [3]
    2. (b)

      Write down the coordinates of the meeting point.

      [1]
  4. 4

    This question is about a quadratic equation.

    1. (a)

      Factorise 2x² + 5x − 12.

      [2]
    2. (b)

      Hence solve 2x² + 5x − 12 = 0.

      [2]
  5. 5

    The expression x² − 4x − 7 is given.

    1. (a)

      Show that x² − 4x − 7 = 0 can be written as (x − 2)² = 11.

      [2]
    2. (b)

      Hence write down the two roots of the equation x² − 4x − 7 = 0, each correct to 3 significant figures.

      [2]
  6. 6

    This question is about the expression 2x² − 12x + 5.

    1. (a)

      Express 2x² − 12x + 5 in the form a(x − p)² + q.

      [3]
    2. (b)

      State the minimum value of 2x² − 12x + 5 and the value of x at which it occurs.

      [2]
  7. 7

    The product of a positive number and the number that is 6 greater than it is 135. The smaller number is n.

    1. (a)

      Form an equation in n and show that it simplifies to n² + 6n − 135 = 0.

      [1]
    2. (b)

      Solve the equation and state the two numbers.

      [3]
  8. 8

    An inequality is given.

    1. (a)

      Solve 4 − 3x ≥ −5.

      [2]
    2. (b)

      List all the positive integers that satisfy the inequality in (a).

      [1]

— End of paper —