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Chapter 7 Practice Paper: Linear equations and straight-line graphs — question paper

QuizQuipPractice Series
QQ/GCSE-MATHS/CH7

GCSE (9–1) · GCSE Mathematics (Foundation with Higher stretch)

Chapter 7 Practice Paper

Linear equations and straight-line graphs

Duration: 40 minutes
Total: 30 marks
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READ THESE INSTRUCTIONS FIRST

  • Answer all questions.
  • Section A contains ten multiple-choice questions. Choose one answer, A, B, C or D, for each.
  • Section B contains structured questions. Write your answers in the spaces provided.
  • Give gradients and intercepts exactly; use fractions where they arise.
  • The number of marks is given in brackets [ ] at the end of each question or part question.
  • The total mark for this paper is 30.

Original practice material written for the MOE GCSE Mathematics syllabus. It is not an official MOE or school examination paper. Chapter 7: solving linear equations with brackets, fractions and unknowns on both sides, y = mx + c, plotting lines, equations through two points, parallel and perpendicular lines (Higher), and approximate solutions from graphs.

For Examiner’s Use
Section A/ 10
Section B/ 20
Total/ 30

Section A: Multiple-choice questions[10 marks]

Choose one answer for each question. Every correct answer scores one mark.

  1. 1

    Solve 2x + 7 = 19.

    1. Ax = 13
    2. Bx = 6
    3. Cx = 6.5
    4. Dx = 5
    ( )
  2. 2

    Solve 7x − 4 = 4x + 11.

    1. Ax = 2.5
    2. Bx = 15⁄7
    3. Cx = 1
    4. Dx = 5
    ( )
  3. 3

    The gradient of y = 5 − 2x is

    1. A−2
    2. B2
    3. C5
    4. D−5
    ( )
  4. 4

    The y-intercept of y = ½x + 3 is

    1. A(0, ½)
    2. B(3, 0)
    3. C(0, 3)
    4. D(½, 0)
    ( )
  5. 5

    From (0, 2) to (4, 10), the gradient of the segment is

    1. A½
    2. B8
    3. C2
    4. D3
    ( )
  6. 6

    Which line below runs parallel to y = −3x + 2?

    1. Ay = −3x + 9
    2. By = 3x − 2
    3. Cy = −⅓x + 2
    4. Dy = 2x − 3
    ( )
  7. 7

    Solve (3x − 2)⁄4 = 2.

    1. Ax = 2
    2. Bx = 10⁄3
    3. Cx = 3.5
    4. Dx = 6
    ( )
  8. 8

    Through the point (1, 6) runs a line of gradient 4. Which equation is it?

    1. Ay = 4x + 6
    2. By = 4x + 2
    3. Cy = x + 6
    4. Dy = 6x + 4
    ( )
  9. 9

    Flip-and-negate the gradient of y = −2x + 7: the perpendicular gradient is (Higher)

    1. A−2
    2. B2
    3. C−½
    4. D½
    ( )
  10. 10

    The lines y = 3x − 1 and y = 3x + 4

    1. Across once
    2. Bcross twice
    3. Cnever cross
    4. Dcross at the y-axis
    ( )

Section B: Structured questions[20 marks]

Show all your working. Marks are given for method as well as for the final answer.

  1. 11

    Solving equations.

    1. (a)

      Solve 5(x − 2) = 3x + 8.

      [3]
    2. (b)

      Solve (x + 7)⁄2 = 3x.

      [1]
  2. 12

    Lines from points.

    1. (a)

      Find the equation of the line through (1, 2) and (5, 14).

      [3]
    2. (b)

      Does the point (4, 11) lie on this line?

      [1]
  3. 13

    Straight-line graphs.

    1. (a)

      Complete a table for y = 6 − 2x at x = 0, 1, 2, 3 and state the gradient and intercept.

      [3]
    2. (b)

      Write down the coordinates where this line crosses the x-axis.

      [1]
  4. 14

    Meeting at right angles. (Higher)

    1. (a)

      A line runs perpendicular to y = ⅔x + 1 through the point (4, 9). Find its equation.

      [3]
    2. (b)

      Show that the gradients of the two lines multiply to −1.

      [2]
  5. 15

    Linear models. (Higher)

    1. (a)

      Two heaters warm a room: Heater A raises the temperature by T = 5 + 1.5m degrees after m minutes; Heater B by T = 2m degrees. After how many minutes are they at the same temperature?

      [3]

— End of paper —