Algebra worksheet — GCSE Higher

1.The first five terms of a sequence are 7, 9, 13, 19, 27. By finding the second difference, work out the coefficient of n² in the nth term.

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

3.A phone company works out a monthly bill, £B, using the formula B = 18 + 0.05t, where £18 is the fixed monthly charge and t is the number of extra text messages sent beyond the free allowance, each charged at 5p. Farida's bill for one month is £24.50. Work out the number of extra text messages, t, she sent.

4.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

5.The graph of y = f(x) has a minimum turning point at (2, −3). The graph of y = −f(x) + a has a maximum turning point at (2, 9). Work out the value of a.

6.A car accelerates uniformly from rest at 2.5 m/s² until it reaches a speed of 20 m/s, then travels at this constant speed for a further 30 seconds. Work out the total distance travelled.

7.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.

8.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

9.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.

10.The point (3, 4) lies on the circle x² + y² = 25, which has centre (0, 0). Work out the gradient of the tangent to the circle at (3, 4).

11.Work out the value of the discriminant b² − 4ac for the equation 2x² + 3x − 2 = 0.

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

13.f(x) = x³ − 3x² − 4. Work out the pair of consecutive integers between which the solution of f(x) = 0 lies.

14.Mia buys 3 identical notebooks and a pen costing £1.50. She pays a total of £9.90. Form an equation using n for the cost of one notebook, and solve it to find n.

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