Algebra worksheet — GCSE Foundation

1.Solve the inequality 3x − 1 ≤ 11.

2.The point A lies on the x-axis. Which statement about A must be true?

3.Which expression means the same as 3 × a × b?

4.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.

5.Work out the equation of the straight line through the points (−3, 4) and (1, −8).

6.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?

7.Work out the gradient of the straight line with equation 3y = 12 − 6x.

8.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.

9.How many turning points does the graph of y = x² − 7x + 10 have?

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

11.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

12.A wall is tiled in rows, and every row uses the same number of tiles. One row uses 10 tiles, two rows use 20 tiles and three rows use 30 tiles. Work out how many tiles are needed for 7 rows.

13.The graph of t = 240 ÷ s shows how the time, t hours, taken for a car journey of 240 miles depends on its average speed, s mph. Use the relationship to work out the time taken when the average speed is 48 mph.

14.Work out the gradient of the straight line with equation y = (2x/5) − 3.

15.Write down the expression that means the same as m × m × m × n.