Algebra worksheet — GCSE Foundation

1.A quadratic curve has a minimum turning point at (3, −4). Which of these statements about the curve must be true?

2.Factorise fully 12x² + 18x.

3.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.

4.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.

5.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.

6.On a map, where each grid unit represents 1 km, Ravi's house is at (−3, 4) and the library is at (6, 4). Work out the distance between Ravi's house and the library.

7.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.

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

9.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.

10.Solve 6x − 5 = 3x + 13.

11.Expand 7(a + 8)

12.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

13.Expand and simplify 2(a + 6) − 2(a − 7)

14.Solve the simultaneous equations 3x + y = 14 and x + y = 6. Work out the value of x.

15.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.