Algebra worksheet — GCSE Foundation

1.A statement contains an equals sign and one unknown letter, and it is only true for particular value(s) of that letter. What is this type of statement called?

2.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.

3.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.

4.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?

5.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

6.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.

7.Solve x² − 100 = 0.

8.Solve the simultaneous equations x + y = 1 and 2x + y = 5.

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

10.Work out the distance of the point (−6, 4) from the x-axis.

11.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.

12.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.

13.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.

14.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.

15.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.