Algebra worksheet — GCSE Higher

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

2.Kai writes the expression 8 − 3x + 5x² and says it has three terms. Ryan says it only has two terms because a number on its own is not a term. Work out the correct number of terms in the expression.

3.A circle has centre (0, 0) and equation x² + y² = 36. Work out the coordinates of the two points where the circle crosses the y-axis.

4.Work out the value of 3a − 2b when a = 5 and b = 4

5.The curve y = x² − 1 and the line y = 3x − 3 meet at two points. Work out the x-coordinates of those two points.

6.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

7.Which of these is a formula, rather than an expression, an equation, or an identity?

8.Expand and simplify 2(a + 6) − 2(a − 7)

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

10.f(x) = x + 3 and g(x) = 2x. Work out fg(x).

11.A region S consists of every point that lies on or above the line y = 2, on or below the line y = x, and on or to the left of the line x = 6. Which of these is the system of inequalities that defines S?

12.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.

13.Describe the single transformation that maps the graph of y = x² onto the graph of y = x² + 3.

14.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

15.The first four terms of a sequence are 2, 2√3, 6, 6√3, ... Work out the next term.