Algebra worksheet — GCSE Foundation

1.Yuki is y years old. Her brother is 4 years younger than Yuki. Write down an expression, in terms of y, for the brother's age in 5 years' time.

2.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

3.A sequence has the position-to-term rule: the term is the position number multiplied by itself. Its first five terms are 1, 4, 9, 16, 25. Work out the 8th term.

4.Simplify 5x + 3y − 2x + y.

5.Simplify 5a/6 − a/3

6.Work out the value of a² − 2b when a = −3 and b = 4.

7.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

8.Write down the expression that means the same as m² × m × 3.

9.Which of these is a formula, rather than an expression, an equation, or an identity?

10.Work out the gradient of the straight line with equation y = (2x/5) − 3.

11.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.

12.To rearrange y = 2x − 5 to make x the subject, Sam writes: 'Add 5 to both sides to get y + 5 = 2x, then divide both sides by 2 to get x = (y + 5)/2.' Which statement about Sam's method is correct?

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

14.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.

15.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.