Algebra worksheet — GCSE Higher

1.A van's value depreciates by 18% each year. After 2 years it is worth £5,379.20. Work out its value when it was new, correct to the nearest pound.

2.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.

3.A curve has equation y = x³ − 4x. Work out the coordinates of the point where the curve crosses the y-axis.

4.The braking distance of a car, in metres, is estimated using the formula d = 0.4v² + 6, where v is the speed in mph. A car travelling at 35 mph brakes. Work out the estimated braking distance.

5.A cyclist's speed rises from rest to a maximum — quickly at first, then more and more slowly — so her speed-time graph is a curve that is concave down (its gradient decreases as time goes on). A trapezium estimate is made for the distance travelled during this phase, using two points on the curve. Is the trapezium estimate an overestimate or an underestimate of the true distance, and why?

6.Work out the value of 3a − 2b when a = 5 and b = 4

7.A geometric sequence has first term 3 and common ratio √3. Work out the position of the first term of the sequence that exceeds 30.

8.Work out the value of 4p² − 3 when p = 2.5

9.A rectangle has width x cm. Its length is 3 cm more than its width. The perimeter of the rectangle is 38 cm. Form an equation and solve it to find x.

10.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.

11.Simplify 2/(x + 1) + 3/(x − 2), giving your answer as a single fraction.

12.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

13.A circle has centre (0, 0) and equation x² + y² = 100. Work out which one of these points lies on the circle.

14.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

15.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.