Algebra worksheet — GCSE Foundation

1.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

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

3.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.

4.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

5.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?

6.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.

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

8.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?

9.Solve 6x + 4 = 28

10.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.

11.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.

12.Grace has t books. Noah has 1 book fewer than Grace. Write down an expression for the number of books Noah has.

13.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

14.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

15.Write down the gradient of the line with equation y = −x + 3.