Higher Secure A

Question 1 [1 marks]

Angles and Geometrical Reasoning

Write down the sum of the exterior angles of any polygon.

Question 2 [2 marks]

Sequences

Here are the first five terms of a sequence. 2, 5, 7, 12, 19

Explain how each term of the sequence, after the first two, is found from the previous two terms.

Work out the next term in the sequence.

Question 3 [2 marks]

Ratio and Proportion

Priya is comparing two bags of rice. Bag A weighs 2 kg and costs £3.00. Bag B weighs 5 kg and costs £7.00. Show working to find the price per kg of each bag, then circle the bag which is better value.

Question 4 [4 marks]

Graphs and Coordinates

For each equation below, state whether its graph is linear, quadratic, cubic or reciprocal.

y = 4x - 3

y = x^2 + 5

y = x^3 - 6x

y = 10/x

Question 5 [1 marks]

Pythagoras and Trigonometry

Work out the length of the diagonal of a rectangle with sides 6 cm and 8 cm.

Question 6 [1 marks]

Statistics and Probability

Using the Venn diagram from Question 2, a student is chosen at random from the 30 students.

What is n(F union N)? A) 5 B) 13 C) 23 D) 30

Question 7 [1 marks]

Indices and Standard Form

Work out 9^2.

Question 8 [2 marks]

Area, Volume and Measures

A rectangle measures 10 cm by 6 cm. A small rectangle of size 3 cm by 2 cm has been removed from one corner. Work out the area of the remaining shape.

Question 9 [2 marks]

Statistics and Probability

A park ranger's bar chart shows how 220 visitors spent their time over a bank holiday weekend: Walking 85, Cycling 40, Other 15, and the rest were Picnicking. Work out the number of visitors who were picnicking.

Question 10 [3 marks]

Linear Algebra

Given f(t) = 4t^2 - 3t + 6,

Simplify f(t) - (t^2 + 2t - 1).

Evaluate your result from part (a) at t = 2.

Question 11 [3 marks]

Fractions, Decimals and Percentages

A charity shop sold 2/5 of the books that had been donated to it. This left 138 books unsold. Work out how many books had been donated to the shop in total.

Question 12 [3 marks]

Indices and Standard Form

Work out the value of 27^(-2/3). Give your answer as a fraction.

Question 13 [3 marks]

Statistics and Probability

A histogram has three classes 0-4, 4-9 and 9-14. The frequency density for 0-4 is 2 and for 9-14 is 3. The total number of observations is 40. Find the frequency density of the class 4-9.

Question 14 [4 marks]

Indices and Standard Form

Simplify each of the following.

p^-3 x p^5

q^2 / q^5

Question 15 [4 marks]

Quadratics

Solve algebraically the points of intersection between the parabola y = x^2 - x - 6 and the line y = 2x + 3. Give exact answers.

Question 16 [4 marks]

Angles and Geometrical Reasoning

A plane flies from airport A on a bearing of 205 to airport B, a distance of 150 km. Diagram: Point A is shown with a North arrow and a ray to B at a bearing of 205 degrees, between South and West.

Calculate how far south of A airport B is. Give your answer correct to 3 significant figures.

Calculate how far west of A airport B is. Give your answer correct to 3 significant figures.

Question 17 [4 marks]

Sequences

The sequence begins 10, 24, 44, 70, 102. (a) Find an expression for the nth term. (b) Hence find the value of n for which the term is 70.

Question 18 [5 marks]

Statistics and Probability

Zara works for a courier company. The table shows the mass, m kg, of each of 80 parcels she delivered in a week. Mass, m (kg) | Frequency 0 < m <= 2 | 8 2 < m <= 4 | 18 4 < m <= 6 | 26 6 < m <= 8 | 20 8 < m <= 10 | 8

Complete the cumulative frequency table below. Mass, m (kg) | Cumulative frequency m <= 2 | 8 m <= 4 | ... m <= 6 | ... m <= 8 | ... m <= 10 | 80

On the grid provided, draw a cumulative frequency graph for this data.

Use your graph to estimate the median mass of the parcels.

Question 19 [5 marks]

Ratio and Proportion

Freya is drawing a scale plan of her bedroom.

On the plan, one wall is drawn 8 cm long. The real wall is 20 m long. Find the scale of the drawing, giving your answer in the form 1 : n.

A different wall is drawn 11.4 cm long on the plan. Work out the real length of this wall, giving your answer in metres.

Question 20 [5 marks]

Linear Algebra

Two pens and three pencils cost £2.20 in total. One pen and one pencil cost £0.90 in total.

Using p for the cost of a pen in pounds and c for the cost of a pencil in pounds, write down a pair of simultaneous equations for this information.

Solve your equations to find the cost of a pen and the cost of a pencil.

Question 21 [1 marks]

Quadratics

An iteration formula is x_(n+1) = 3/(x_n - 2). Which of these values of x0 would make it impossible to calculate x1?

Question 22 [3 marks]

Statistics and Probability

A company's weekly sales figures, in GBP, for a product across all of its shops are shown on a box plot. The upper quartile is GBP 1200 and the maximum is GBP 2000. It is known that 18 shops had weekly sales between the upper quartile and the maximum.

Work out the total number of shops in the sample.

The lower quartile of weekly sales is GBP 700. A sales manager claims that 9 shops had weekly sales below this figure. State, with a reason, whether this claim is consistent with the box plot.

Question 23 [4 marks]

Linear Algebra

Solve the inequality x^2 - 5x - 6 > 0, giving your answer using set notation. Show your working.

Question 24 [4 marks]

Angles and Geometrical Reasoning

TA and TB are tangents from an external point T to a circle with centre O, touching the circle at A and B. C is a point on the major arc AB. Angle ATB = 40 degrees. Diagram: circle centre O, external point T with tangents TA, TB touching circle at A, B, radii OA, OB drawn forming quadrilateral OATB, C a separate point on the major arc AB, joined to A and B.

Calculate the size of angle AOB.

Hence calculate the size of angle ACB.

Question 25 [4 marks]

Area, Volume and Measures

A frustum is formed by cutting the top from a right cone. The lower radius is 6 cm, the upper radius is 2 cm and the height of the frustum is 9 cm. Calculate the volume of the frustum. Give your answer in terms of pi and then to 3 significant figures.

Question 26 [5 marks]

Graphs and Coordinates

The velocity-time graph shows the motion of a sprinter over 10 seconds. The sprinter accelerates uniformly from rest to a velocity of 9 m/s in the first 3 seconds, then runs at a constant velocity of 9 m/s for the remaining 7 seconds.

Calculate the distance travelled by the sprinter during the first 3 seconds.

Calculate the total distance travelled by the sprinter in the 10 seconds shown on the graph.