Algebra worksheet — GCSE Higher

1.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.

2.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

3.Solve x² + 3x − 10 = 0.

4.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

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.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

7.Solve the inequality 5x − 3 > 2x + 9.

8.A line has equation y = −4x + 1. Work out the equation of the line perpendicular to it that passes through the point (0, 3).

9.Factorise 3x² + 10x − 8.

10.f(x) = x + 2 and g(x) = x². Work out the value of x for which fg(x) = gf(x).

11.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

12.By completing the square, find the turning point of the curve y = 3x² + 12x + 7.

13.A candidate solves the simultaneous equations y = x − 2 and y = x² − 4x + 2 by substitution. They write: "x − 2 = x² − 4x + 2, so x² − 3x + 4 = 0." Which of these is a correct comment on the candidate's working?

14.Which expression is equivalent to 6x − (2x − 5)?

15.The simple interest, £I, earned on a savings account is given by the formula I = PRT/100, where P is the amount invested in pounds, R is the interest rate per year and T is the time in years. Rearrange the formula to make P the subject.