Algebra worksheet — GCSE Foundation

1.n = 3. Work out the value of (2n)².

2.Simplify p + p + p.

3.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.

4.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

5.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

6.A currency conversion graph shows that £4 is equivalent to 5 US dollars. Use this to work out how many US dollars are equivalent to £24.

7.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

8.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.

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

10.A car park charges a £4 fixed fee plus £3 for each hour. Kofi has exactly £25 to spend on parking. Using the inequality 4 + 3h ≤ 25, work out the greatest number of whole hours, h, he can park for.

11.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.

12.The point C is 6 units to the right of the origin and 0 units up. Write down the coordinates of C.

13.Write down the gradient of the line with equation y = 6 + 4x.

14.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.

15.Factorise fully 5x + 5y − 5