Algebra worksheet — GCSE Foundation

1.A recipe gives the cooking time, in minutes, for a chicken as T = 40m + 20, where m is the mass in kg. A chicken has a mass of 1.8 kg. Work out the cooking time in hours and minutes.

2.Write down the gradient of the line with equation y = 6 + 4x.

3.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.

4.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.

5.Which expression means the same as a × a × a?

6.Six years ago Harry was three times as old as his brother Leo. Harry is now 24 years old. Work out Leo's age now.

7.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.

8.The graph of t = 240 ÷ s shows how the time, t hours, taken for a car journey of 240 miles depends on its average speed, s mph. Use the relationship to work out the time taken when the average speed is 48 mph.

9.A square tile has an area of 144 cm². Work out the side length of the tile.

10.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?

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

12.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.

13.The mean of four numbers is 12.5. Three of the numbers are 8, 15 and 19. Form an equation using n for the fourth number, and solve it to find n.

14.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.

15.The formula for the perimeter of a square is P = 4s, where s is the side length. Make s the subject of the formula.