Algebra worksheet — GCSE Higher

1.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

2.Work out the coordinates of the reflection of (6, −3) in the y-axis.

3.A cafe sells coffees at £c each and pastries at £p each. Three coffees and two pastries cost £9.60. Two coffees and two pastries cost £7.60. Work out the price of one coffee.

4.A circle has centre (0, 0) and passes through the point (5, 12). Work out the equation of the circle.

5.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.

6.Write down the first four terms of the sequence with nth term 6n − 5.

7.Expand and simplify (x + 1)(x + 2)(x + 3).

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

9.Describe a sequence of two transformations that maps the graph of y = x² onto the graph of y = −(x − 5)².

10.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

11.A Fibonacci-type sequence is defined by aₙ = aₙ₋₁ + aₙ₋₂ for n ≥ 3. Given that a₁ = 5 and a₃ = 17, work out a₂.

12.By completing the square, find the turning point of the curve y = x² + 8x − 3.

13.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.

14.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.

15.Which of these is a formula, rather than an expression, an equation, or an identity?