Algebra worksheet — GCSE Higher

1.Yusuf has £40 saved and adds £6 each week. His sister Aisha has £10 saved and adds £11 each week. After how many weeks will they have saved the same amount?

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

3.Make x the subject of the formula y = 4x − 3.

4.The graph of y = f(x) passes through the point (0, 4). Work out the y-coordinate of the point where the graph of y = −f(x) + 5 crosses the y-axis.

5.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.

6.The graph of y = f(x) has a minimum point at (4, −1). Write down the coordinates of the corresponding turning point on the graph of y = −f(x).

7.In a shop a shirt costs £x and a pair of trousers costs £(2x + 30). Together the two items cost at least £150. Work out the lowest possible price of the shirt.

8.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.

9.Which of these is an identity?

10.Solve 4x − (2x − 6) = 18

11.The tangent to a curve at the point (6, 1) has gradient −3. Work out the y-coordinate of the point where this tangent crosses the y-axis.

12.A company's weekly profit, in £, is modelled by y = f(x), where x is the number of weeks since launch. The graph of y = f(x) has a maximum at (10, 45000). A rival company uses the same marketing strategy but starts trading 6 weeks later and has fixed costs £8000 higher every week, so its profit is modelled by y = f(x − 6) − 8000. In which week does the rival's maximum weekly profit occur, and what is it?

13.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.

14.Work out the value of n² − n when n = −3

15.The graph of y = f(x) has a minimum turning point at (4, −5). The graph of y = f(x) + a has a minimum turning point whose minimum VALUE is 2. Work out the value of a, and state the coordinates of the minimum turning point of y = f(x) + a.