Algebra worksheet — GCSE Foundation

1.Expand and simplify (x − 3)²

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

3.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.

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

5.Which expression means 'y squared, multiplied by 3'?

6.There are 30 students in a Year 10 maths class. There are 2 more boys than girls. Work out the number of boys and the number of girls.

7.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.

8.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.

9.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.

10.A quadratic curve has a root at x = −2 and its turning point has x-coordinate 3. Work out the curve's other root, using the symmetry of the graph.

11.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

12.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.

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

14.Which of these points lies in the first quadrant?

15.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).