Algebra worksheet — GCSE Foundation

1.Make x the subject of the formula y = 5x + 3.

2.Write down the expression that means the same as (x + 7) ÷ 4.

3.Jack is x years old. His brother Kwame is 3 years older than Jack. Write down an expression for Kwame's age.

4.An equation has exactly one value of x that makes it true, but an identity is true for every value of x. Which of these best explains why 3x + 5 = 20 is an equation rather than an identity?

5.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.

6.In a sequence, each term is half the term before it. The sequence begins 100, 50, 25. Write down the next term.

7.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.

8.The first five cube numbers are 1, 8, 27, 64, 125. Write down the next cube number in the sequence.

9.How many turning points does the graph of y = x² − 7x + 10 have?

10.A student solves the simultaneous equations 2x + y = 11 and x − y = 1 by elimination, adding the two equations together. Which of these is the correct result of that step?

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

12.Solve 6x + 4 = 28

13.A rectangular photo has length (x + 3) cm and width x cm. Its area is 40 cm². Work out the value of x.

14.A candle is 30 cm tall when lit and burns at a constant rate. After burning for 5 minutes, its height is 20 cm. The height h cm after t minutes is given by h = 30 − mt. Work out the value of m.

15.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.