Algebra worksheet — GCSE Foundation

1.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.

2.Expand 2(x − 13)

3.A curve has equation y = x³ − 4x. Work out the coordinates of the point where the curve crosses the y-axis.

4.Six years ago Harry was three times as old as his brother Leo. Harry is now 24 years old. Work out Leo's age now.

5.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?

6.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.

7.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.

8.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.

9.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

10.In the expression 5x² − 3x + 7, which of these is a single term of the expression?

11.Point A has coordinates (4, −5). Point B has coordinates (4, 3). Work out the distance between A and B.

12.Solve the simultaneous equations 4x + 3y = 25 and 4x − y = 1. Work out the value of y.

13.Which of these equations gives a straight-line graph when plotted?

14.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.

15.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.