Algebra worksheet — GCSE Higher

1.A park is drawn on a grid in which 1 unit represents 1 km. The car park is at the point (0, 0) and the lake is at the point (3, 5). Work out the direct distance, in km, from the car park to the lake, giving your answer to 1 decimal place.

2.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?

3.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.

4.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

5.Line P has equation y = −2x + 5 and line Q has equation 2y = x + 6. Are lines P and Q perpendicular to each other?

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

7.Make x the subject of the formula y = 4(x − 6).

8.A plumber charges a call-out fee plus an hourly rate. The total cost, y in pounds, of a job lasting x hours is given by y = 45x + 60. Work out the total cost of a job that lasts 3 hours.

9.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?

10.Solve the simultaneous equations y = x + 1 and x² + y² = 25, giving both pairs of solutions.

11.The tangent to a curve at the point where x = 4 passes through the points (2, 5) and (6, 21). Use these two points to estimate the gradient of the curve at x = 4.

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

13.The point (6, 8) lies on the circle x² + y² = 100. Work out the gradient of the tangent to the circle at (6, 8).

14.Work out the value of 3x² − 4x when x = −2.

15.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.