Algebra worksheet — GCSE Foundation

1.A table of values is being drawn for the graph of y = x³. Work out the value of y when x = −2.

2.A ball's height, h metres, t seconds after being thrown follows h = (t − 1)(9 − t). Given that the ball is at ground level at t = 1 and t = 9, work out at what time t the ball reaches its maximum height, using symmetry.

3.To solve 5x − 4 = 2x + 8, Chloe's working is shown. Line 1: 5x − 4 = 2x + 8. Line 2: 3x − 4 = 8. Line 3: 3x = 4. Line 4: x = 4/3. Chloe has made a mistake in her working. Which line contains the mistake?

4.Simplify (5x² + 3x − 2) − (2x² − x + 5)

5.A hot air balloon is at a height of 20 m and rises at a steady rate. After 4 minutes it is at a height of 52 m. Work out the rate at which the balloon rises, in metres per minute.

6.Expand 7(a + 8)

7.On a map, where each grid unit represents 1 km, Ravi's house is at (−3, 4) and the library is at (6, 4). Work out the distance between Ravi's house and the library.

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.Solve (3x + 2)/5 = (x + 4)/3

10.x = 5. Work out the value of 3x² − 4.

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

12.Solve the inequality 6.3x + 1.8 ≤ 40. Hence write down the greatest number with exactly one decimal place that satisfies the inequality.

13.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

14.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).

15.A sequence begins at 50, and each term after that is found by subtracting 8 from the term before it. Priya says the 8th term of the sequence is negative. Is Priya correct?