Algebra worksheet — GCSE Higher

1.A company's weekly profit, P thousand pounds, when it makes x thousand items is modelled by P = x² − 8x + 12, for x ≥ 0. Work out the values of x for which the company makes a loss.

2.n = 3. Work out the value of (2n)².

3.The graph of y = f(x) has a maximum turning point at (5, 8). Which of these correctly gives the corresponding turning point on the graph of y = −f(x + 1), and its type?

4.The graph of y = x³ − 5x is reflected in the y-axis. Work out the equation of the image.

5.Points A(8, 15) and B(−8, 15) both lie on the circle x² + y² = 289, which has centre (0, 0). Work out the length of the chord AB.

6.A rule turns each input into an output. An input of 0 gives an output of −1, an input of 1 gives an output of 1, and an input of 2 gives an output of 3. Work out the rule, writing the input as x and the output as y.

7.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.

8.How many turning points does the graph of y = x² − 7x + 10 have?

9.Which of these statements is an identity?

10.Solve 4(x − 3) = 2x + 6.

11.A sequence has nth term 3n + 4. Two terms are missing from the list of its first five terms: 7, 10, _, 16, _. Work out the missing 3rd and 5th terms added together.

12.The graph of y = f(x) passes through the point (2, 5). Write down the coordinates of the corresponding point on the graph of y = f(x − 4) + 1.

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

14.Which expression is equivalent to 0.5(4x + 6) − x?

15.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?