Algebra worksheet — GCSE Foundation

1.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

2.Write down the coordinates of the point that is 4 units to the left of the origin and 7 units up.

3.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

4.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

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

6.The first four terms of a sequence are 2, 6, 10, 14. Priya says the nth term is 4n. Work out the correct expression for the nth term.

7.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.

8.The diagram shows the graph of a quadratic function. Which equation could it represent?

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

10.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.

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

12.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.

13.A quadratic curve has a root at x = −2 and its turning point has x-coordinate 3. Work out the curve's other root, using the symmetry of the graph.

14.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.

15.Solve x² − 100 = 0.