Algebra worksheet — GCSE Foundation

1.A distance-time graph shows a car travelling at a constant speed, covering 90 km in 2 hours. Work out the car's speed in km/h.

2.Solve the simultaneous equations 3x + y = 14 and x + y = 6. Work out the value of x.

3.Which of these statements is an equation with exactly one solution?

4.The simultaneous equations x = 2 and x + y = 9 are given. Work out the value of y.

5.A rectangular garden has width w metres and length (w + 3) metres. A gardener writes its perimeter as 2w + 3. Which statement corrects the gardener's mistake?

6.Expand and simplify (x − 3)²

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

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

9.Make b the subject of the formula a = 5b.

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

11.To rearrange the formula y = 3x − 8 to make x the subject, Priya writes: 'Add 8 to both sides to get y + 8 = 3x, then divide both sides by 3 to get x = y + 8 ÷ 3.' Work out the correct expression for x.

12.The first five square numbers are 1, 4, 9, 16, 25. Write down the next square number in the sequence.

13.Write down the gradient of the line with equation y = 6 + 4x.

14.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.

15.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.