Algebra worksheet — GCSE Higher

1.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

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

3.A cycle route is 84 km long. Freya sets off along it at a steady 14 km/h. Write down the function for the distance y, in kilometres, that is still to be cycled after x hours.

4.A photo printing service has two adverts for its price. Advert A: cost in pounds = 3(2n + 4) for n photos. Advert B: cost in pounds = 6n + 12. A customer says the two adverts always charge the same amount. Is the customer correct?

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

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

7.Work out the value of the discriminant b² − 4ac for the equation 2x² + 3x − 2 = 0.

8.Work out the smallest positive value of x, in degrees, for which y = tan x is undefined.

9.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.

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

11.For 0 ≤ x ≤ 360, the equation sin x = 0.5 has two solutions. What are they?

12.The point (−4, 3) lies on the circle x² + y² = 25, which has centre (0, 0). Work out the equation of the tangent to the circle at (−4, 3), giving your answer in the form y = mx + c.

13.Solve 5(x + 3) = 40

14.The equation x² = 5x − 3 is to be solved using iteration. Work out which of these iterative formulas comes from a correct rearrangement of the equation.

15.The point (3, 4) lies on the circle x² + y² = 25, which has centre (0, 0). Work out the gradient of the tangent to the circle at (3, 4).