Algebra worksheet — GCSE Foundation

1.A student says that (x + 4)² is equivalent to x² + 16. For which value of x do the two expressions give the SAME result, making it look (misleadingly) like the student could be right?

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

4.Which of these equations is equivalent to 5x − 2 = 3x + 8?

5.The perimeter, P, of a rectangle with length l and width w is calculated using P = 2l + 2w. What kind of mathematical statement is P = 2l + 2w?

6.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

7.The solution to an inequality is n ≤ 5. Write down the largest integer value of n that satisfies this inequality.

8.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.

9.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.

10.Work out the coordinates of the reflection of (6, −3) in the y-axis.

11.A rectangle has length (2x + 5) cm and width (x − 2) cm. Work out an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form.

12.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?

13.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.

14.A model rocket's height is given by h = −5t² + 20t, where h is in metres and t is in seconds. A student says the graph of h against t is n-shaped. Which statement gives the correct verdict on the SHAPE and the reason that settles it from the equation?

15.Which of these is an expression?