Algebra worksheet — GCSE Foundation

1.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

2.Solve 6x − 5 = 3x + 13.

3.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

4.Solve 2(x + 3) = 10

5.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

6.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?

7.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.

8.Which expression is equivalent to 4(x − 2) + 10?

9.The formula for converting a temperature in Fahrenheit, F, to Celsius, C, is C = 5(F − 32) ÷ 9. Work out C, to 1 decimal place, when F = 98.6.

10.Which of these is an identity?

11.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

12.Amelia is buying books. Each book costs £5 and she has at most £30 to spend. Write down an inequality for x, the number of books she can buy.

13.Oliver has m stickers and gives 5 of them away. The number he has left is L = m − 5. Work out L when m = 8.

14.The graph of a straight line has equation y = 4x − 5. Beth says the y-intercept is 4. Work out the correct y-intercept.

15.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.