Algebra worksheet — GCSE Foundation

1.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.

2.Which expression means 'triple c, then add double d'?

3.Factorise fully 12x² + 18x.

4.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.

5.A gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.

6.A point lies on the y-axis. What can be said about the x-coordinate of that point?

7.Simplify (5x² + 3x − 2) − (2x² − x + 5)

8.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.

9.A line segment has one endpoint at (−6, 2) and its midpoint at (−1, 5). Work out the coordinates of the other endpoint.

10.Make x the subject of the formula y = 2x − 9.

11.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

12.In the expression 5x² − 3x + 7, which of these is a single term of the expression?

13.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

14.Yuki is y years old. Her brother is 4 years younger than Yuki. Write down an expression, in terms of y, for the brother's age in 5 years' time.

15.To rearrange y = 2x − 5 to make x the subject, Sam writes: 'Add 5 to both sides to get y + 5 = 2x, then divide both sides by 2 to get x = (y + 5)/2.' Which statement about Sam's method is correct?