Algebra worksheet — GCSE Foundation

1.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.

2.Amelia is buying books. Each book costs £5 and she has at most £30 to spend. Write down an inequality for x, the number of books she can buy.

3.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?

4.Solve 4(x − 3) = 2x + 6.

5.A table of values is being drawn for the graph of y = x³. Work out the value of y when x = −2.

6.Write down the y-intercept of the line with equation y = 3x + 8.

7.Write down the expression that means the same as p + p + p + q.

8.A conversion graph shows that 5 miles is equivalent to 8 kilometres. Use this to work out how many kilometres are equivalent to 20 miles.

9.To rearrange the formula y = 3x − 8 to make x the subject, Priya writes: 'Add 8 to both sides to get y + 8 = 3x, then divide both sides by 3 to get x = y + 8 ÷ 3.' Work out the correct expression for x.

10.Tom is asked to classify the statement 5(2x − 3) = 10x − 15. Which statement about it is correct?

11.Work out the coordinates of the reflection of (6, −3) in the y-axis.

12.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.

13.Write down the expression that means the same as m² × m × 3.

14.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

15.A distance-time graph shows a car travelling at a constant speed, covering 90 km in 2 hours. Work out the car's speed in km/h.