Exam Structure Set A: Higher Paper 2

Question 1 [1 marks]

Pythagoras and Trigonometry

The diagram shows a right-angled triangle with the right angle marked. The sides are labelled p, q and r, where r is the side opposite the right angle. Diagram: right-angled triangle, right angle shown at the bottom-left corner, side p along the base, side q up the vertical side, side r as the slanted side joining the two ends.

Question 2 [2 marks]

Area, Volume and Measures

Grace is edging a circular flower bed with radius 3.5 m. Work out the length of edging she needs. Give your answer correct to 1 decimal place.

Question 3 [3 marks]

Number and Calculation

A car travels 150 miles, correct to the nearest 10 miles, in a time of 3 hours, correct to the nearest 0.5 hours. Work out the upper bound for the average speed of the car. Give your answer correct to 3 significant figures.

Question 4 [3 marks]

Angles and Geometrical Reasoning

Shape F has vertices at (2, 2), (4, 2) and (4, 3). Shape F is rotated 180 degrees about the point (1, 1) to give shape F'.

Question 5 [1 marks]

Linear Algebra

Simplify 5p + 4q - 2p + q.

Question 6 [1 marks]

Indices and Standard Form

Write 4 x 10^-1 as an ordinary number.

Question 7 [1 marks]

Graphs and Coordinates

The point (2, -1) lies on the graph y = f(x). Find the coordinates of the corresponding point on the graph y = f(x) + 4.

Question 8 [1 marks]

Angles and Geometrical Reasoning

Point N has coordinates (6, 4). Write down the coordinates of the image of N after an enlargement with scale factor 1/2, centre the origin.

Question 9 [1 marks]

Indices and Standard Form

Work out sqrt(121).

Question 10 [2 marks]

Area, Volume and Measures

The diagram shows a semicircle with diameter 26 cm. Work out the area of the semicircle. Give your answer correct to 1 decimal place.

Question 11 [2 marks]

Fractions, Decimals and Percentages

£2,500 is invested for 3 years at 3% per annum compound interest. Calculate the total value of the investment at the end of 3 years, to the nearest penny.

Question 12 [2 marks]

Area, Volume and Measures

A solid hemisphere has radius 9 cm. Calculate the volume of the hemisphere. Give your answer correct to 3 significant figures.

Question 13 [2 marks]

Fractions, Decimals and Percentages

Work out which is larger: 5/8 or 3/5. Give a reason for your answer.

Question 14 [3 marks]

Quadratics

Solve the inequality x^2 - 5x + 6 < x - 1. Give your answer in inequality form.

Question 15 [3 marks]

Statistics and Probability

The stem and leaf diagram shows the scores in a class test. Stem | Leaf 5 | 1 3 8 6 | 0 2 4 9 a) Write down the median score. b) Write down the mode of the scores.

Question 16 [3 marks]

Quadratics

The graph of y = x^2 - 4x + 3 is a parabola. On graph paper, sketch this parabola. On your sketch, clearly mark the vertex and the x- and y-intercepts.

Question 17 [3 marks]

Number and Calculation

Five different novels are placed in a row on a bookshelf. Work out the number of different ways the five novels can be arranged.

Question 18 [3 marks]

Quadratics

Write x^2 - 7x + 1 in the form (x + p)^2 + q.

Question 19 [4 marks]

Ratio and Proportion

A section of a map is drawn so that 1 cm on the map represents 250 m in real life. Two towns are 9 km apart in real life. Express this distance on the map in centimetres and give the answer in the ratio map:real.

Question 20 [4 marks]

Statistics and Probability

The universal set is E = {1, 2, 3, ..., 15}. A is the set of multiples of 3 in E. B is the set of multiples of 5 in E.

Write down the elements of set A.

Write down the elements of A intersect B.

List the elements of A union B.

Question 21 [4 marks]

Graphs and Coordinates

A taxi company charges a fare y (in pounds) according to the rule y = 1.5x + 2, where x is the distance in miles. Complete the table, plot the points and draw the straight line. Then estimate the distance when the fare is £11.50. x: 0, 2, 4, 6 y:

Complete the table and plot the points, then draw the straight line.

Estimate the distance x when the fare is £11.50, using your plotted line or the equation.

Question 22 [5 marks]

Sequences

Find the nth term of the sequence: 11, 18, 25, 32, ... Give your answer in the form an + b.

Question 23 [5 marks]

Area, Volume and Measures

The cross-section of a prism is a right-angled triangle. The hypotenuse of the triangle is 13 cm and one of the other two sides is 5 cm. The prism is 9 cm long. Diagram: right-angled triangle cross-section, hypotenuse 13 cm, one shorter side 5 cm, third side unmarked; prism length 9 cm. Work out the volume of the prism.

Question 24 [3 marks]

Linear Algebra

Solve the inequality 3(x - 2) >= 5(x + 4), giving your answer in the form x <= k, where k is an integer.

Question 25 [3 marks]

Indices and Standard Form

A pupil says that 0.00038 is equal to 38 x 10^-5 written in standard form. A second pupil says the first pupil is wrong, and that the correct standard form is 3.8 x 10^-4. By writing both expressions as ordinary numbers, determine which pupil (if either) is correct, and explain any error in the incorrect statement.

Question 26 [5 marks]

Ratio and Proportion

The resistance, R ohms, of a wire is directly proportional to its length, L metres, and inversely proportional to the square of its diameter, d millimetres. A wire of length 2 m and diameter 0.5 mm has a resistance of 8 ohms.

Find a formula for R in terms of L and d.

Find the resistance of a wire of the same material with length 5 m and diameter 1 mm.

Question 27 [5 marks]

Angles and Geometrical Reasoning

PA and PB are tangents to a circle with centre O, touching the circle at A and B. Angle AOB = 152 degrees. Diagram: circle, centre O, external point P, tangents PA and PB touching the circle at A and B, radii OA and OB, right angles marked at A and B, angle AOB = 152 degrees marked at O.

Work out the size of angle APB.

Work out the size of angle PAB.

Question 28 [5 marks]

Statistics and Probability

200 patients are tested for a medical condition. The two-way table shows the test result and whether each patient actually has the condition. Has condition No condition Total Tests positive 18 14 32 Tests negative 2 166 168 Total 20 180 200

One patient is chosen at random. Find the probability that they test positive.

Given that a patient tests positive, find the probability that they actually have the condition.

Given that a patient does not have the condition, find the probability that they test positive.