Algebra worksheet — GCSE Foundation

1.A taxi charges a fixed fee of £3 plus £2 for every mile travelled. The journey is m miles. Write down an expression for the total cost, in pounds.

2.Factorise fully 56x − 24

3.The formula for the circumference of a circle is C = 2πr, where r is the radius. Make r the subject of the formula.

4.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

5.A sequence has the position-to-term rule n² − 3, where n is the position number. Work out the difference between the 6th term and the 5th term.

6.A number machine multiplies its input by 5. Work out the output when the input is −1.

7.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.

8.Which of these is an inequality?

9.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

10.Solve x² − 5x + 6 = 0 by factorising.

11.Two expressions are 6(x − 1) and 6x − 6. A student says these are equivalent for every value of x. Is the student correct?

12.Leo is three times as old as his brother. His brother is x years old. Write down an expression for Leo's age.

13.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?

14.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.

15.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.