Algebra worksheet — GCSE Higher

1.The table shows some values of f(x): when x = 0, f(x) = 5; when x = 1, f(x) = 8; when x = 2, f(x) = 4; when x = 3, f(x) = 1. Work out the value of f(x − 1) when x = 2.

2.A market trader builds a display of oranges in a rectangular block. The block is n oranges wide and 4 oranges longer than it is wide. The number of oranges needed is 5 when n = 1, 12 when n = 2, 21 when n = 3, 32 when n = 4, and 45 when n = 5. Work out an expression, in terms of n, for the number of oranges needed for a display of width n.

3.A caterer uses the formula C = 6p + 20 to work out the total cost, £C, of a buffet for p people, where £20 covers fixed costs. A customer is charged £92. Work out how many people, p, the buffet was for.

4.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.

5.Work out the period of the graph of y = cos x, in degrees.

6.Write y = x² + 12x + 40 in the form (x + a)² + b, and hence write down the minimum value of y.

7.The 2nd term of a geometric sequence is 6 and the 4th term is 24. Given that all the terms of the sequence are positive, work out the common ratio.

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

9.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

10.Simplify 5a/6 − a/3

11.When a number is added to its square the result is 30. Work out the possible values of the number.

12.Factorise fully 12x² + 18x.

13.x = 5. Work out the value of 3x² − 4.

14.Solve x² − 8x + 3 = 0 by completing the square. Give your answers in surd form.

15.A recipe gives the cooking time, in minutes, for a chicken as T = 40m + 20, where m is the mass in kg. A chicken has a mass of 1.8 kg. Work out the cooking time in hours and minutes.