Algebra worksheet — GCSE Foundation

1.A straight line has equation y = 4x + 3. A second line is parallel to the first line and passes through the point (0, −5). Work out the equation of the second line.

2.A taxi fare, in pounds, for a journey of m miles is given by the formula F = 3 + 2.5m. A journey costs £15.50. Work out the distance travelled, m, by first rearranging the formula to make m the subject, then substituting F = 15.50.

3.Two brothers have ages that add up to 30. The elder brother is 6 years older than the younger brother. Work out the age of the younger brother.

4.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

5.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.

6.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.

7.Which of these rules generates the sequence 6, 11, 16, 21, …?

8.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.

9.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.

10.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.

11.Which of these is a term, rather than a whole expression, an equation, or a formula?

12.A mobile phone plan charges a fixed monthly fee plus an amount for each gigabyte of data used. The total cost £C for using g gigabytes in a month is given by C = 15 + 2g. What does the number 2 represent in this formula?

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

14.Which expression means 'y squared, multiplied by 3'?

15.There are 30 students in a Year 10 maths class. There are 2 more boys than girls. Work out the number of boys and the number of girls.