Algebra worksheet — GCSE Higher

1.Solve the simultaneous equations 2x + y = 7 and x + 2y = 8.

2.The tangent to a curve at the point (6, 1) has gradient −3. Work out the y-coordinate of the point where this tangent crosses the y-axis.

3.Which expression is equivalent to 7x − 3(2x − 6)?

4.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

5.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.

6.f(x) = 3x − 2. Find f⁻¹(x).

7.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.

8.The graph of y = f(x) has roots at x = −1 and x = 4, and crosses the y-axis at (0, −8). Which statement about the graph of y = f(x − 3) is correct?

9.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

10.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

11.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.

12.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.

13.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.

14.A straight line has equation y = 4x + 3. A second line is parallel to the first line and passes through the point (0, −5). Work out the equation of the second line.

15.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.