Algebra worksheet — GCSE Higher

1.How many turning points does the graph of y = x² − 7x + 10 have?

2.Amelia's mother is three times as old as Amelia. Four years ago her mother was five times as old as Amelia was then. Work out Amelia's age now.

3.The first five terms of a quadratic sequence are 4, 7, 12, 19, 28. Work out an expression, in terms of n, for the nth term.

4.A phone company works out a monthly bill, £B, using the formula B = 18 + 0.05t, where £18 is the fixed monthly charge and t is the number of extra text messages sent beyond the free allowance, each charged at 5p. Farida's bill for one month is £24.50. Work out the number of extra text messages, t, she sent.

5.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.

6.Work out the value of n² − n when n = −3

7.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

8.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.

9.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.

10.A rectangle has length (2x + 5) cm and width (x − 2) cm. Work out an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form.

11.The graph of y = f(x) has x-intercepts at x = −1 and x = 4. Which statement correctly describes the x-intercepts of y = f(2 − x)?

12.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.

13.A box holds n pencils. A shop has 6 full boxes and 4 loose pencils. All of these pencils are shared equally between 2 classes. Write down the expression for the number of pencils each class receives.

14.The mean of four numbers is 12.5. Three of the numbers are 8, 15 and 19. Form an equation using n for the fourth number, and solve it to find n.

15.A student attempts to prove that the sum of any three consecutive integers is a multiple of 3. Line 1: Let the three consecutive integers be n, n + 1 and n + 2. Line 2: Their sum is n + (n + 1) + (n + 2) = 3n + 2. Line 3: 3n + 2 leaves a remainder of 2 when divided by 3, so it is not a multiple of 3. Line 4: So the sum of three consecutive integers is not always a multiple of 3. Which line contains the FIRST error?