Algebra worksheet — GCSE Foundation

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

2.The solution set of an inequality is x ≥ 7. Write down the value that does NOT satisfy this inequality.

3.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

4.Write down the expression that means the same as m × m × m × n.

5.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.

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

7.On a map, where each grid unit represents 1 km, Ravi's house is at (−3, 4) and the library is at (6, 4). Work out the distance between Ravi's house and the library.

8.The solution to an inequality is n ≤ 5. Write down the largest integer value of n that satisfies this inequality.

9.The diagram shows a straight line passing through the origin, drawn on a numbered grid. Which of these points lies on the line?

10.Solve 3x + 14 = 8x − 6

11.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.

12.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

13.A hall is set out in rows of chairs for an assembly. Row 1 has 50 chairs, row 2 has 45 chairs, row 3 has 40 chairs, and row 4 has 35 chairs, with each row after the first having 5 fewer chairs than the one before. Work out an expression, in terms of n, for the number of chairs in row n.

14.Simplify p + p + p.

15.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.