Algebra worksheet — GCSE Foundation

1.Write down the gradient of the line with equation y = −x + 3.

2.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.

3.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

4.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?

5.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.

6.Solve the inequality 3x − 1 ≤ 11.

7.Noah says that y = 3 is the solution of the equation y + 10 = 12. Noah is wrong. Work out the correct value of y.

8.A speed-time graph for a car shows the speed increasing steadily from 5 m/s to 17 m/s over 6 seconds. Work out the acceleration of the car, in m/s².

9.A straight line has equation y = 4x + 3. A second line is parallel to the first line and passes through the point (0, −5). Work out the equation of the second line.

10.Given that (x − 4)(x + 9) = 0, write down the two solutions of x.

11.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

12.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.

13.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

14.A taxi fare in pounds is given by F = 2.50 + 1.20m, where m is the number of miles travelled. Sam takes a taxi for a journey of 6 miles. Work out the fare.

15.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.