Higher Core A

Question 1 [1 marks]

Indices and Standard Form

Write 9.1 x 10^4 as an ordinary number.

Question 2 [1 marks]

Fractions, Decimals and Percentages

Work out 3/8 + 2/8. Give your answer in its simplest form.

Question 3 [5 marks]

Statistics and Probability

Freya Sinclair organised a charity bake sale where 90 cakes were sold, either Sponge or Chocolate, in the morning or the afternoon. Some of the results are shown in the two-way table below.

Question 4 [2 marks]

Linear Algebra

Solve 2(x + 3) = 16 Show your working.

Question 5 [2 marks]

Graphs and Coordinates

The graphs of x = 3 and y = 2x - 4 are drawn on the grid. Write down the solution of the simultaneous equations x = 3 and y = 2x - 4.

Question 6 [2 marks]

Ratio and Proportion

A cyclist travels at a constant speed of 20 m/s. Work out this speed in km/h.

Question 7 [2 marks]

Area, Volume and Measures

Shape 1 has sides of length 4.5 cm and 6 cm. Shape 2 is mathematically similar to shape 1. The side on shape 2 corresponding to the 4.5 cm side has length 3 cm.

Question 8 [2 marks]

Linear Algebra

Show that the equation 4(2x - 3) = 2(x + 9) simplifies to x = 5

Question 9 [4 marks]

Quadratics

A student attempts to solve 3x^2 + 4x - 2 = 0 using the quadratic formula. Their working is shown below: x = (-4 +/- sqrt(4^2 - 4x3x(-2))) / (2x3) x = (-4 +/- sqrt(16 - 24)) / 6 Identify the error made by the student, and find the correct solutions to the equation, giving your answers correct to 2 decimal places.

Question 10 [5 marks]

Sequences

Here are the first four terms of a sequence. 50, 44, 38, 32

Write down the next term of the sequence.

Find an expression, in terms of n, for the nth term of the sequence.

Explain whether 0 is a term of the sequence.

Question 11 [6 marks]

Pythagoras and Trigonometry

A surveyor stands at point A and measures the angle of elevation to the top of a tower as 31 degrees. She then walks 48 m closer to the tower along the level ground to point B and measures the angle of elevation as 46 degrees. Work out the height of the tower to the nearest metre.

Find the height of the tower to the nearest metre.

Question 12 [6 marks]

Angles and Geometrical Reasoning

Two points A(-5, 0) and B(5, 0) are 10 cm apart on a coordinate grid (1 unit = 1 cm). (a) Describe the locus of points that are equidistant from A and B, and give its equation. (b) A circle has centre A and radius 13 cm. Find the coordinates of the points where this circle meets the locus from part (a). Show your working.

Describe the geometric locus in words and give its equation.

Find the coordinates of the points where the circle centre A radius 13 cm meets the locus x = 0. Show your working.

Question 13 [7 marks]

Graphs and Coordinates

Tom walks 3 km from home to the park in 40 minutes. He then jogs 5 km from the park to the leisure centre in 25 minutes.

Calculate Tom's average speed while walking, in km/h.

Calculate Tom's average speed while jogging, in km/h.

Calculate Tom's average speed for the whole journey from home to the leisure centre, in km/h. Give your answer correct to 1 decimal place.

Question 14 [3 marks]

Angles and Geometrical Reasoning

A search and rescue team searches a triangular area defined by three points X, Y and Z. XY = 12 km, XZ = 9 km, and the angle YXZ (the angle between the bearings from X to Y and from X to Z) is 105 degrees. Diagram: Point X is shown with a North arrow and two rays to Y (12 km) and Z (9 km), with angle YXZ marked 105 degrees.

Question 15 [4 marks]

Graphs and Coordinates

Each equation below is a transformation of y = sin x. Match each equation to the letter of the description that correctly describes its transformation. A) Translation by vector (-90, 0) B) Stretch, scale factor 4, parallel to the y-axis C) Translation by vector (0, -3) D) Stretch, scale factor 2, parallel to the x-axis

y = sin x - 3

y = sin(x + 90)

y = 4 sin x

y = sin(x/2)

Question 16 [8 marks]

Statistics and Probability

A bag contains 3 red counters and n blue counters only, where n > 0. Two counters are taken from the bag at random, one after another, without replacement.

Show that the probability that both counters are red is 6 / ((n+3)(n+2)).

Given that the probability that both counters are red is 1/5, show that n^2 + 5n - 24 = 0.

Hence find the number of blue counters in the bag.