Printable · GCSE Higher · ages 14-16
Algebra worksheet — GCSE Higher
Fifteen questions across the algebra statements at Higher tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.
Algebra worksheet — GCSE Higher
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- 1.A taxi company charges a £2.50 booking fee plus £1.80 per mile. A journey costs £15.10 in total. Work out the number of miles travelled.
- 2.A region R satisfies y ≤ x + 1, x + y ≤ 5 and y ≥ 0. Which of these correctly describes R in words?
- 3.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.
- 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.y = 3x − 8
- 5.The first five terms of a quadratic sequence are 4, 7, 12, 19, 28. Work out an expression, in terms of n, for the nth term.
- 6.Work out the smallest positive value of x, in degrees, for which y = tan x is undefined.y = tan(x)
- 7.Which expression means 'triple c, then add double d'?
- 8.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.
- 9.Factorise 6x² − 7x − 3.
- 10.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.
- 11.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).
- 12.A speed-time graph shows a constant speed of 15 m/s for 20 seconds. Work out the distance travelled, using the area under the graph.
- 13.Write down the expression that means the same as m² × m × 3.
- 14.Work out the value of 3a − 2b when a = 5 and b = 4
- 15.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.
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