Algebra worksheet — GCSE Foundation

1.Solve the simultaneous equations 2x + y = 7 and x − y = 2.

2.The formula for converting a temperature in Fahrenheit, F, to Celsius, C, is C = 5(F − 32) ÷ 9. Work out C, to 1 decimal place, when F = 98.6.

3.A formula is F = 4s. A pupil says that when s = 5 the value of F is 9, because they added 4 and 5 instead of multiplying. Work out the correct value of F when s = 5.

4.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.

5.A ball is dropped and bounces. The height of each bounce after the first is 8 cm less than the bounce before it. The first bounce reaches 60 cm. Work out the height of the 5th bounce.

6.For the equation 2x + 3 = 11, and the inequality 2x + 3 > 11, which statement correctly compares their solutions?

7.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.

8.Which of these is an equation, rather than an expression, a formula or an identity?

9.A number machine multiplies its input by 3. The output is 15. Work out the input.

10.A ball is thrown in the air. Its height, h metres, above the ground after t seconds is given in this table: when t = 0, h = 0; when t = 1, h = 15; when t = 2, h = 20; when t = 3, h = 15; when t = 4, h = 0. Use the table to find the two times, in seconds, at which the ball is at ground level.

11.Write down the number of terms in the expression 4x² − 7x + 3.

12.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.

13.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.

14.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

15.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.