Algebra worksheet — GCSE Higher

1.A circle has centre (0, 0) and equation x² + y² = 8. Work out the radius of the circle, giving your answer as a surd in its simplest form.

2.The curve y = −x² + 6x − 5 has a maximum point. Use completing the square to find its coordinates.

3.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.

4.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?

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

6.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

7.A circle has centre (0, 0) and equation x² + y² = 100. A straight line is drawn from the origin through the point P(8, 9). Work out whether P lies inside, on, or outside the circle.

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

9.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.

10.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.

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

12.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.

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

14.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

15.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.