Algebra worksheet — GCSE Foundation

1.a = 3 and b = 5. Work out the value of a²b.

2.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.

3.Which of these is an identity?

4.Solve 2x² − 32 = 0.

5.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.

6.Make x the subject of the formula y = 3(x + 2).

7.A taxi charges a fixed fee of £3 plus £2 for every mile travelled. The journey is m miles. Write down an expression for the total cost, in pounds.

8.A straight line has equation y = 2x − 7. Write down the coordinates of the point where the line crosses the y-axis.

9.A pizza shop charges a fixed delivery fee of £3, plus £9 for each pizza ordered. Write down the function for the total cost y, in pounds, of ordering x pizzas.

10.The formula for converting a temperature from degrees Celsius, C, to degrees Fahrenheit, F, is F = 1.8C + 32. Work out F when C = 20, and identify what kind of mathematical statement F = 1.8C + 32 is.

11.The nth term of a sequence is 3n + 2. Work out the 4th term of the sequence.

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

13.The point P has coordinates (0, 12). Write down the axis that P lies on and the y-coordinate of P.

14.Write down 0.2x with its coefficient written as a fraction in its simplest form.

15.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.