Chapter 1 Practice Paper: Linear Graphs and Simultaneous Linear Equations — question paper

Section A: Multiple-choice questions[10 marks]

Answer all questions. For each question, write the letter (A, B, C or D) of the correct answer in the brackets provided.

1. 1

   State the gradient of y = 5 − 2x.

   1. A5
   2. B2
   3. C−2
   4. D5/2
   ( )
2. 2

   Which point lies on the line y = 3x + 1?

   1. A(1, 4)
   2. B(2, 6)
   3. C(1, 2)
   4. D(3, 1)
   ( )
3. 3

   A line passes through (0, −3) with gradient 2. Its equation is

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

   Where does the line 2x + 3y = 12 cross the x-axis?

   1. A(0, 4)
   2. B(6, 0)
   3. C(0, 12)
   4. D(4, 0)
   ( )
5. 5

   The lines y = 2x + 1 and y = 2x − 5 are

   1. Aperpendicular
   2. Bthe same line
   3. Cparallel
   4. Dmeeting at (0, 1)
   ( )
6. 6

   The lines y = x + 2 and y = 3x intersect at

   1. A(1, 3)
   2. B(3, 1)
   3. C(0, 2)
   4. D(2, 4)
   ( )
7. 7

   For the pair x + y = 10 and x − y = 2, x equals

   1. A4
   2. B2
   3. C10
   4. D6
   ( )
8. 8

   If 2x + y = 8 and x = 3, then y equals

   1. A5
   2. B2
   3. C8
   4. D11
   ( )
9. 9

   On a graph, the solution of a pair of simultaneous linear equations is shown by

   1. Athe y-intercept of the first line
   2. Bthe origin
   3. Cthe point where the two lines cross
   4. Dthe steepest point on either line
   ( )
10. 10

    Three notebooks and two files cost $13. One notebook and two files cost $7. What is the cost of one notebook?

    1. A$3
    2. B$2
    3. C$7
    4. D$13
    ( )

Section B: Structured questions[20 marks]

Answer all questions in the spaces provided. Show your working clearly.

1. 1

   A linear function is given by y = 2x + 3.

   Table of values

   x	−2	−1	0	1	2
   y			3

   1. (a)

      Find the four missing values of y in the table, for x = −2, −1, 1 and 2.

      [2]
   2. (b)

      Write down the gradient of the line, and the coordinates of its y-intercept.

      [2]
   3. (c)

      A student claims that (4, 11) lies on this line. Verify the claim.

      [1]
2. 2

   Solve the pair of simultaneous equations x + 2y = 11 and x − y = 2.

   1. (a)

      Explain why subtracting the second equation from the first eliminates x.

      [1]
   2. (b)

      Find the value of y.

      [2]
   3. (c)

      Find x. Then confirm the pair works in x + 2y = 11.

      [2]
3. 3

   Solve the pair of simultaneous equations y = 3x − 1 and x + 2y = 12 by substitution.

   1. (a)

      Replace y in x + 2y = 12 by (3x − 1), writing brackets.

      [2]
   2. (b)

      Solve for x.

      x =[1]
   3. (c)

      Find y, then write the solution of the pair as coordinates (x, y).

      [2]
4. 4

   At a fun fair, 3 scooter rides and 2 bumper-car rides cost $19. One scooter ride and 2 bumper-car rides cost $9.

   1. (a)

      Using s for the price of a scooter ride and b for a bumper-car ride, form two equations from the receipts.

      [2]
   2. (b)

      Solve the pair to find the price of each ride.

      [2]
   3. (c)

      Find the total cost of 4 scooter rides and 1 bumper-car ride.

      total =[1]