Algebra worksheet — GCSE Higher

1.A circle has centre (0, 0) and passes through the point (12, 35). Work out the equation of the circle.

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

3.Simplify (5x² + 3x − 2) − (2x² − x + 5)

4.On a map, where each grid unit represents 1 km, Ravi's house is at (−3, 4) and the library is at (6, 4). Work out the distance between Ravi's house and the library.

5.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

6.Solve the inequality 2(3x − 1) ≥ 4x + 8.

7.Write down the first four terms of the sequence with nth term 6n − 5.

8.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.

9.There are 30 students in a Year 10 maths class. There are 2 more boys than girls. Work out the number of boys and the number of girls.

10.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

11.The graph of y = f(x) has a minimum turning point at (2, −3). The graph of y = −f(x) + a has a maximum turning point at (2, 9). Work out the value of a.

12.A sequence has nth term 3n + 4. Two terms are missing from the list of its first five terms: 7, 10, _, 16, _. Work out the missing 3rd and 5th terms added together.

13.A sequence is defined by aₙ = aₙ₋₁ + aₙ₋₂ for n ≥ 3. Given that a₃ = 11 and a₅ = 29, work out a₁.

14.The first four terms of a sequence are 2, 6, 10, 14. Priya says the nth term is 4n. Work out the correct expression for the nth term.

15.Work out the equation of the straight line through the points (−3, 4) and (1, −8).