Algebra worksheet — GCSE Foundation

1.Here are the first five terms of an arithmetic sequence: 4, 7, 10, 13, 16. Work out the 9th term.

2.A quadratic graph has roots at x = −3 and x = 5, and it crosses the y-axis at (0, −15). Work out the equation of the curve in the form y = (x − a)(x − b).

3.A rule turns each input into an output. An input of 0 gives an output of −1, an input of 1 gives an output of 1, and an input of 2 gives an output of 3. Work out the rule, writing the input as x and the output as y.

4.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.

5.Work out the value of a² − 2b when a = −3 and b = 4.

6.Which of these is a formula, rather than an expression, an equation, or an identity?

7.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.

8.A rectangle has width x cm. Its length is 3 cm more than its width. The perimeter of the rectangle is 38 cm. Form an equation and solve it to find x.

9.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

10.A box contains 6 chocolates. Write down an expression for the total number of chocolates in c boxes.

11.A sequence has the position-to-term rule: the term is the position number multiplied by itself. Its first five terms are 1, 4, 9, 16, 25. Work out the 8th term.

12.A theatre's front row has 18 seats. Each row behind has 4 more seats than the row in front. Which row has exactly 62 seats?

13.A sequence begins at 50, and each term after that is found by subtracting 8 from the term before it. Priya says the 8th term of the sequence is negative. Is Priya correct?

14.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.

15.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.