Algebra worksheet — GCSE Higher

1.Factorise fully 56x − 24

2.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

3.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?

4.Write down the expression that means 5 more than half of n.

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.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.

7.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.

8.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

9.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

10.Which of these equations represents the graph of y = 2ˣ translated by 3 units in the positive y-direction?

11.A rectangular photo has length (x + 3) cm and width x cm. Its area is 40 cm². Work out the value of x.

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

13.The graph of y = f(x) crosses the x-axis at x = −3 and x = 7, and crosses the y-axis at (0, 21). A second graph crosses the x-axis at x = −7 and x = 3, and crosses the y-axis at the same point, (0, 21). The second graph is y = g(x). Which of these could be the equation of g(x)?

14.A caterer uses the formula C = 6p + 20 to work out the total cost, £C, of a buffet for p people, where £20 covers fixed costs. A customer is charged £92. Work out how many people, p, the buffet was for.

15.A table shows y = x² − 6x + 5 at these points (x, y): (0, 5), (1, 0), (2, −3), (3, −4), (4, −3), (5, 0), (6, 5). Using the symmetry shown, write down the x-coordinate of the turning point.