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.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.

3.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

4.y = x + 4. Work out the value of y when x = 3.

5.Make m the subject of the formula w = m − 8.

6.A cafe sells coffees at £c each and pastries at £p each. Three coffees and two pastries cost £9.60. Two coffees and two pastries cost £7.60. Work out the price of one coffee.

7.The point C is 6 units to the right of the origin and 0 units up. Write down the coordinates of C.

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

9.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

10.A cyclist's journey is shown on a distance–time graph. The graph is a straight line from (0 minutes, 0 km) to (40 minutes, 12 km). Work out her speed in kilometres per hour.

11.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.

12.Write down the gradient of the line with equation y = 7x − 2.

13.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.

14.The formula for the profit, £P, made on an item is P = S − C, where S is the selling price and C is the cost price. Make S the subject of the formula.

15.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.