Algebra worksheet — GCSE Foundation

1.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

2.The diagram shows a straight line passing through the origin, drawn on a numbered grid. Which of these points lies on the line?

3.Isla says that the lines y = 2x + 1 and y = −2x + 3 are parallel. Write down the statement that gives the correct answer for the correct reason.

4.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

5.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.

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

7.Point P has coordinates (5, 2). Point P is rotated 180° about the origin to point Q. Write down the coordinates of Q.

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

9.Here are the first five terms of an arithmetic sequence: 4, 7, 10, 13, 16. Work out the 9th term.

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

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

12.y = 3x − 2. Work out the value of y when x = 4.

13.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.

14.Which of these statements is an equation with exactly one solution?

15.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.