Paper 1 (non-calculator), Higher

Write 252 as a product of its prime factors. Give your answer in index form.

Work out 3 1/3 ÷ 1 1/9. Give your answer in its simplest form.

Work out (6 × 10^4) × (5 × 10^3). Give your answer in standard form.

Simplify fully (a) 3^4 × 3^2 (b) (3^4)^3 (c) Evaluate 8^(2/3) × 4^(−1/2).

Estimate the value of (812 × 0.49) ÷ 19.6. Show your rounding.

Solve 4(x + 3) = 7x − 9.

Solve x² − 2x − 24 = 0 by factorising.

Prove algebraically that the recurring decimal 0.454545… can be written as 5/11.

Amir and Beth share £350 in the ratio 4 : 3. Amir then gives Beth £50. Work out the new ratio of Amir's money to Beth's money in its simplest form.

y is inversely proportional to x². When x = 3, y = 10. Find y when x = 6.

A line passes through (-1, 2) and (3, 14). (a) Find its equation in the form y = mx + c. (b) Find the gradient of a line perpendicular to it.

Work out the exact value of cos 60° + tan 45° × sin 60°.

A, B and C are points on a circle with centre O. Angle AOC = 114°. B is on the major arc. (a) Find angle ABC. (b) D is on the minor arc AC. Find angle ADC. Give a reason for each answer.

In a class of 40 students, 22 study French, 15 study Spanish and 7 study both. (a) Draw/describe a Venn diagram. (b) A student who studies French is chosen at random. Find the probability that they also study Spanish.

A bag contains 4 red and 6 blue counters. Two counters are taken at random without replacement. Work out the probability that they are the same colour.

Make x the subject of p = (2x − 7)/(x + 4).

Write x² − 8x + 5 in the form (x + p)² + q, and state the coordinates of the turning point of y = x² − 8x + 5.

Prove that the sum of the squares of any two consecutive integers is always odd.

Simplify fully (2x² + 7x + 3)/(x² − 9).

Solve the simultaneous equations 2x + 3y = 13 4x − y = 5

Find the nth term of the quadratic sequence 2, 8, 16, 26, 38, …

Rationalise the denominator and simplify: 10/(√6 − 1).

A regular polygon has 20 sides. Work out the size of each interior angle, and explain why regular polygons with interior angle 100° cannot exist.

A length is 4.7 m correct to 1 decimal place. Write down the error interval for the length L.

A café offers 4 starters, 6 main courses and 3 desserts. How many different three-course meals are possible?

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

Factorise fully 2x² − 5x − 12.