Algebra worksheet — GCSE Foundation

1.Solve the inequality 6x ≥ 18.

2.Solve 5x² − 15x = 0.

3.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.

4.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

5.Which expression means 'add 3 to n, then multiply the result by 4'?

6.The diagram shows the graph of a straight line, drawn on a grid numbered from −5 to 5 on both axes. Which equation could represent the line?

7.The point P has coordinates (0, 12). Write down the axis that P lies on and the y-coordinate of P.

8.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.

9.Expand and simplify 2(a + 6) − 2(a − 7)

10.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.

11.Solve the simultaneous equations x + y = 15 and x − y = 3. Work out the value of x.

12.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.

13.A rule turns each input into an output. An input of 0 gives an output of −1, an input of 1 gives an output of 1, and an input of 2 gives an output of 3. Work out the rule, writing the input as x and the output as y.

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

15.y = x + 4. Work out the value of y when x = 3.