Algebra worksheet — GCSE Higher

1.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.

2.A circle has centre (0, 0) and equation x² + y² = 100. Work out which one of these points lies on the circle.

3.The graph of y = f(x) has a minimum turning point at (4, −5). The graph of y = f(x) + a has a minimum turning point whose minimum VALUE is 2. Work out the value of a, and state the coordinates of the minimum turning point of y = f(x) + a.

4.Solve the inequality 3x − 1 ≤ 11.

5.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?

6.Solve the inequality 5x − 3 > 2x + 9.

7.Factorise fully 12x² + 18x.

8.The equation x² − x − 6 = 0 has roots x = 3 and x = −2. It can be rearranged as xₙ₊₁ = xₙ² − 6. This formula is used with starting value x₀ = 2.9, close to the root x = 3. Work out what happens to the sequence of values as n increases.

9.Write y = x² + 12x + 40 in the form (x + a)² + b, and hence write down the minimum value of y.

10.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.

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

12.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

13.Solve 4x − (2x − 6) = 18

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

15.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.