Algebra worksheet — GCSE Higher

1.Line L has equation y = 3x + 1. Which of these lines is perpendicular to L?

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

3.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

4.Simplify fully: (x + 2)/(3x) × 6x²/(x² − 4)

5.Factorise 6x² − 7x − 3.

6.Expand and simplify (x + 1)(x + 2)(x + 3).

7.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.

8.Solve 2x² − 32 = 0.

9.A bacteria colony doubles every 4 hours and its size is recorded only every 4 hours. The recorded population 20 hours after the start is 9,600. After how many hours did the recorded population first exceed 1,000?

10.A car's speed, in m/s, during a journey is: 0 at t = 0 s, 8 at t = 4 s, and 8 (constant) from t = 4 s to t = 10 s, increasing at a constant rate between t = 0 and t = 4. Estimate the total distance the car travels, using the areas of a triangle and a rectangle.

11.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?

12.The equation x³ − 3x − 4 = 0 has a root near x = 2. Four students each try a different iterative formula, all starting from x₀ = 2: xₙ₊₁ = ∛(3xₙ + 4); xₙ₊₁ = (xₙ³ − 4) ÷ 3; xₙ₊₁ = 4 ÷ (xₙ² − 3); xₙ₊₁ = xₙ³ − 2xₙ − 4. Only one of these formulas keeps producing values that settle near the root when it is repeated. Work out x₁, correct to 3 decimal places, for the formula that does this.

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

14.A caterer uses the formula C = 6p + 20 to work out the total cost, £C, of a buffet for p people, where £20 covers fixed costs. A customer is charged £92. Work out how many people, p, the buffet was for.

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