Algebra worksheet — GCSE Higher

1.Which expression means 'triple c, then add double d'?

2.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.

3.The nth term of a sequence is n² + 4n. Work out the term number, n, for which the term equals 45.

4.A circle has equation x² + y² = 25. Does the point (3, 4) lie on this circle?

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

6.Work out the value of (x − 4)/2 + 3 when x = 10

7.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.

8.A model rocket's height is given by h = −5t² + 20t, where h is in metres and t is in seconds. A student says the graph of h against t is n-shaped. Which statement gives the correct verdict on the SHAPE and the reason that settles it from the equation?

9.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.

10.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

11.A student solves the simultaneous equations 2x + y = 11 and x − y = 1 by elimination, adding the two equations together. Which of these is the correct result of that step?

12.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

13.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.

14.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.

15.A candle is 30 cm tall and burns down at a steady rate of 1 cm per hour. Write down the function for the height of the candle y, in centimetres, after x hours.