Algebra worksheet — GCSE Foundation

1.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?

2.Solve the inequality 5x − 3 > 2x + 9.

3.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

4.A ball is dropped and bounces. The height of each bounce after the first is 8 cm less than the bounce before it. The first bounce reaches 60 cm. Work out the height of the 5th bounce.

5.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.

6.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.

7.A phone company works out a monthly bill, £B, using the formula B = 18 + 0.05t, where £18 is the fixed monthly charge and t is the number of extra text messages sent beyond the free allowance, each charged at 5p. Farida's bill for one month is £24.50. Work out the number of extra text messages, t, she sent.

8.Which of these equations describes a vertical line?

9.Write down the y-intercept of the line with equation y = 3x + 8.

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

11.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.

12.n = 3. Work out the value of (2n)².

13.Amelia is buying books. Each book costs £5 and she has at most £30 to spend. Write down an inequality for x, the number of books she can buy.

14.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

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.