Exam Structure Set B: Higher Paper 2

Question 1 [1 marks]

Statistics and Probability

State one feature of a good line of best fit drawn on a scatter graph.

Question 2 [1 marks]

Angles and Geometrical Reasoning

A bearing of 315 degrees represents which compass direction?

Question 3 [2 marks]

Sequences

Here are the first four terms of a sequence. 2, 6, 10, 14

Write down the next two terms of the sequence.

Describe, in words, the term-to-term rule for the sequence.

Question 4 [2 marks]

Area, Volume and Measures

The diagram shows a rectangle.

Question 5 [3 marks]

Graphs and Coordinates

Complete the table of values for y = x^3 - 1. x : -2 , -1 , 0 , 1 , 2 y : -9 , _ , _ , _ , 7

Question 6 [1 marks]

Indices and Standard Form

Simplify sqrt(32) fully.

Question 7 [1 marks]

Ratio and Proportion

Which is cheaper per litre: a 750 ml bottle for £1.20 or a 1.5 litre bottle for £2.50? Give the cheaper option and the price per litre.

Question 8 [1 marks]

Fractions, Decimals and Percentages

Write 175% as a fraction in its simplest form.

Question 9 [1 marks]

Indices and Standard Form

Write the number 0.000000083 in standard form.

Question 10 [2 marks]

Fractions, Decimals and Percentages

Priya ate 2/5 of a cake. The part she ate weighed 160 g. Work out the weight of the whole cake in grams.

Question 11 [2 marks]

Area, Volume and Measures

A cylindrical candle has radius 3.5 cm and height 9 cm. Calculate the volume of wax needed to make the candle. Give your answer correct to 3 significant figures.

Question 12 [2 marks]

Graphs and Coordinates

Find the gradient of the line joining the points A(2, 5) and B(6, 13).

Question 13 [2 marks]

Quadratics

Factorise 5x^2 - 13x - 6

Question 14 [3 marks]

Number and Calculation

A combination lock has 3 dials. Each dial can be set to any digit from 0 to 9, and digits may repeat across dials. Work out the number of different combinations possible.

Question 15 [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 16 [3 marks]

Angles and Geometrical Reasoning

A chord PQ of a circle with centre O has length 24 cm. The radius of the circle is 13 cm. M is the midpoint of PQ, and OM is drawn perpendicular to PQ. Diagram: circle, centre O, chord PQ = 24 cm, M marked as the midpoint of PQ, OM drawn perpendicular to PQ from the centre, radius OP = 13 cm marked.

Explain why PM = 12 cm.

Work out the length OM.

Question 17 [4 marks]

Ratio and Proportion

Salma and Tom share some money in the ratio 3:4. Salma receives £27.

Write Tom's share as a fraction of Salma's share.

Work out the total amount of money shared between Salma and Tom.

Question 18 [4 marks]

Quadratics

Write 5x^2 + 20x + 3 in the form a(x + p)^2 + q, stating the values of a, p and q.

Question 19 [5 marks]

Linear Algebra

Solve the simultaneous equations: 3x + 2y = 16 2x + 3y = 19

Question 20 [5 marks]

Pythagoras and Trigonometry

A circle has centre O and a chord AB of length 14 cm. The perpendicular from O to AB meets AB at M and OM = 6 cm. Find the radius of the circle.

Question 21 [5 marks]

Linear Algebra

Two mobile phone companies charge for calls as follows. Company A: a fixed monthly charge of £15 plus 5p per minute of calls. Company B: a fixed monthly charge of £9 plus 8p per minute of calls. Let C = the total monthly cost in pounds and m = the number of minutes of calls used in a month.

Write down an equation for C in terms of m for each company.

Find the number of minutes of calls, m, for which both companies charge the same monthly amount, and state this common cost.

Question 22 [6 marks]

Quadratics

A rectangle has length (x + 5) cm and width x cm. The area of the rectangle is 84 cm^2.

Show that x^2 + 5x - 84 = 0

Solve the equation to find the value of x, given that x > 0

Hence find the length of the rectangle

Question 23 [1 marks]

Pythagoras and Trigonometry

In triangle ABC, angle A and sides a and b are given (side a is opposite angle A). Which condition guarantees that the ambiguous case (two possible triangles) cannot occur?

Question 24 [2 marks]

Indices and Standard Form

Show that sqrt(3^5) = 3^(5/2).

Question 25 [5 marks]

Area, Volume and Measures

A factory makes solid rubber doorstops in the shape of a triangular prism. Each doorstop has a cross-section that is a right-angled triangle with base 6 cm and perpendicular height 4 cm, and the prism length is 11 cm.

Show that the volume of one doorstop is 132 cm^3.

The factory has a block of rubber with volume 3.168 m^3. Work out the maximum number of complete doorstops that can be made from this block of rubber, assuming there is no wastage.

Question 26 [6 marks]

Angles and Geometrical Reasoning

PAQ is a straight tangent line touching a circle at A. B and C are points on the circle, with chords AB and AC drawn, and BC also drawn to complete triangle ABC. Angle QAB = 47 degrees and angle PAC = 65 degrees (the angles between the tangent and each chord). Diagram: circle with straight tangent line PAQ touching at A, chords AB and AC drawn to points B and C on either side, chord BC also drawn, angle QAB = 47 degrees and angle PAC = 65 degrees marked between tangent and each chord.

State the size of angle ACB, giving a reason for your answer.

State the size of angle ABC, giving a reason for your answer.

Calculate the size of angle BAC.

Question 27 [7 marks]

Area, Volume and Measures

A sector-shaped garden ornament is cut from a sheet of metal. The sector has radius 18 cm. Its perimeter (the two straight edges plus the curved arc) is 54 cm. The metal costs £0.09 per cm^2.

Show that the arc length of the sector is 18 cm.

Find the angle of the sector, giving your answer correct to 1 decimal place.

Find the area of the sector, giving your answer correct to 3 significant figures.

Calculate the cost of the metal needed for the ornament.