Algebra worksheet — GCSE Higher

1.A straight line has equation y = 4 − 3x. Work out the gradient of the line.

2.A circular pond has equation x² + y² = 20, with lengths in metres from the centre of the garden. A straight path runs along the line y = 2x, entering the pond and leaving it again. Work out the coordinates of the two points where the path meets the edge of the pond.

3.Write down the expression that means the same as (x + 7) ÷ 4.

4.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

5.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.

6.By completing the square, find the turning point of the curve y = 2x² − 8x + 3.

7.Which of these equations is equivalent to 5x − 2 = 3x + 8?

8.A sequence begins at 50, and each term after that is found by subtracting 8 from the term before it. Priya says the 8th term of the sequence is negative. Is Priya correct?

9.Work out the value of (x − 4)/2 + 3 when x = 10

10.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.

11.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

12.Which expression is equivalent to 6x − (2x − 5)?

13.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.

14.The formula for converting a temperature from degrees Celsius, C, to degrees Fahrenheit, F, is F = 1.8C + 32. Work out F when C = 20, and identify what kind of mathematical statement F = 1.8C + 32 is.

15.The curve y = 2x² − 12x + 7 has a minimum point. By completing the square, find the value of x at which the minimum occurs.