Paper 1 (non-calculator), Higher

Find the highest common factor and the lowest common multiple of 84 and 120.

Estimate the value of (49.7 × 3.12) ÷ 0.198. Show your rounding.

Work out 2 1/4 ÷ 1 1/2. Give your answer in its simplest form.

Work out (3 × 10^5) × (4 × 10^-2). Give your answer in standard form.

Simplify fully (a) 5^3 × 5^4 (b) (5^3)^2 (c) Evaluate 8^(2/3) × 4^(−1/2).

Solve 3(x + 4) = 5x − 6.

Solve x² + 2x − 15 = 0 by factorising.

Prove algebraically that the recurring decimal 0.272727… can be written as 3/11.

Amir and Beth share £240 in the ratio 5 : 3. Amir then gives Beth £30. 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 = 2, y = 12. Find y when x = 4.

A line passes through (1, 3) and (4, 9). (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 sin 30° × tan 60° + cos 45°.

A, B and C are points on a circle with centre O. Angle AOC = 128°. 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 30 students, 14 study French, 12 study Spanish and 5 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 5 red and 3 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 y = (3x + 2)/(x − 5).

Write x² + 6x + 2 in the form (x + p)² + q, and state the coordinates of the turning point of y = x² + 6x + 2.

Prove that the difference between the squares of any two consecutive odd numbers is a multiple of 8.

Describe fully the single transformation that maps the triangle with vertices (1, 1), (3, 1), (1, 2) onto the triangle with vertices (−1, 1), (−1, 3), (−2, 1).

Simplify fully (x² − 9)/(x² + x − 12).

Solve the simultaneous equations 3x + 2y = 16 5x − 2y = 0

Find the nth term of the quadratic sequence 4, 9, 18, 31, 48, …

OABC is a parallelogram with OA = a and OC = c. M is the midpoint of AB and N is the point on OB such that ON : NB = 2 : 1. Find CN and CM in terms of a and c, and hence show that C, N and M lie on a straight line.

Rationalise the denominator and simplify: 6/(√7 − 1).

Which of these is 0.000 47 written in standard form? (A) 4.7 × 10⁻⁴ (B) 4.7 × 10⁴ (C) 47 × 10⁻⁵ (D) 0.47 × 10⁻³

A regular polygon has 15 sides. Work out the size of each interior angle, and explain why regular polygons with interior angle 100° cannot exist.

Write 360 as a product of its prime factors. Give your answer in index form.