Algebra worksheet — GCSE Foundation

1.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.

2.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

3.Write down the gradient of the line with equation y = 7x − 2.

4.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?

5.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

6.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.

7.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

8.Simplify 5x + 3y − 2x + y.

9.Solve 6x − 5 = 3x + 13.

10.Work out the value of 2(x + 2) when x = −5

11.Solve x² − 2x − 24 = 0.

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

13.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.

14.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

15.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.