Exam-style Questions: Algebra - Equations and Inequalities

  1. Solve the simultaneous equations:

    5x + 4y = 13

    3x + 8y = 5

    (Marks available: 4)

    Answer

    Answer outline and marking scheme for question: 1

    x = 3, y = -½

    (Marks available: 4)

  2. An orange costs 5 pence more than an apple.

    a) Write down an expression, in terms of y, for the cost of one orange.

    (1 mark)

    b) Write down an expression, in terms of y, for the total cost of 3 apples and one orange.

    (2 marks)

    c) The total cost of 3 apples and one orange is 61 pence.

    Form an equation in terms of y and solve it to find the cost of one apple.

    (3 marks)

    (Marks available: 6)

    Answer

    Answer outline and marking scheme for question: 2

    a) y + 5

    (1 mark)

    b) 3y + y + 5

    (2 marks)

    c) 3y + y + 5 = 61

    (3 marks)

    (Marks available: 6)

  3. a) Solve this inequality

    2x + 3 < 5x + 12

    (3 marks)

    b) (i) Solve this equation

    2x2 + x - 3 = 0

    (3 marks)

    (ii) Sketch the graph of y = 2x2 + x - 3

    (2 marks)

    Show clearly where the graph crosses the x-axis.

    Copyright S-cool

    (Marks available: 8)

    Answer

    Answer outline and marking scheme for question: 3

    a) x > -3 or -3 < x

    (3 marks)

    b)(i) -1½ or 1

    (3 marks)

    (ii) U-shaped curve crossing x-axis twice. Intersections at -1½ or 1.

    (2 marks)

    (Marks available: 8)

  4. A company was contracted to make 840 vans in 90 days.

    After they made 540, the manager worked out the average production per day. He worked out that, if they could increase this average by 1 van per day, they could fulfil the contract in exactly 90 days.

    Let the average for the first 540 be x vans per day.

    a) Write down an equation in x and show that it simplifies to

    Copyright S-cool

    (2 marks)

    b) Use algebra to solve the equation.

    Hence find the average production for the first 540 vans.

    (7 marks)

    (Marks available: 9)

    Answer

    Answer outline and marking scheme for question: 4

    a) Copyright S-cool

    b) x = 9 and -2/3

    (Marks available: 9)