Higher Core B

Question 1 [1 marks]

Statistics and Probability

Here are the shoe sizes of 10 dancers in a class: 4, 5, 4, 6, 7, 4, 8, 5, 4, 6 Write down the mode of the shoe sizes.

Question 2 [1 marks]

Ratio and Proportion

y is inversely proportional to x.

Question 3 [2 marks]

Quadratics

Factorise 2x^2 + 5x + 3

Question 4 [3 marks]

Linear Algebra

Make x the subject of each formula.

y = 4x

y = x/7

w = kx

Question 5 [1 marks]

Graphs and Coordinates

A vehicle travels at a constant velocity of 5 m/s for 6 seconds. Work out the distance travelled in that time.

Question 6 [1 marks]

Indices and Standard Form

Simplify p^5 * p^3.

Question 7 [1 marks]

Linear Algebra

Evaluate the expression 3x^2 - 2x + 5 when x = -1.

Question 8 [1 marks]

Statistics and Probability

A frequency table shows how long, in minutes, each customer waited in a queue at a post office in Cardiff. Waiting time (minutes): 0-5, 5-10, 10-15, 15-20 Frequency: 6, 9, 7, 3 Write down the width of the class 10-15.

Question 9 [1 marks]

Indices and Standard Form

Work out the value of 16^(1/2).

Question 10 [2 marks]

Angles and Geometrical Reasoning

The diagram shows a flat solid made from three 1 cm cubes on a 2 by 2 grid (one grid position is empty).

Which of these is the correct plan of the solid?

Even though the plan is an L-shape, the front elevation of this solid is a plain 2 cm by 1 cm rectangle, with no gap visible. Give a reason why.

Question 11 [2 marks]

Graphs and Coordinates

A point (4, -2) lies on y = f(x). Find the image of this point on the graph y = f(x - 3) - 5.

Question 12 [2 marks]

Linear Algebra

Solve 5x - 4 > 21 Show your working.

Question 13 [2 marks]

Ratio and Proportion

A model yacht club has 18 wooden hulls and 30 plastic hulls. The wooden:plastic ratio is 3 : n. Work out n.

Question 14 [4 marks]

Number and Calculation

Priya is making identical party bags for her birthday. She has 60 chocolate coins and 84 jelly sweets. She wants to put the sweets and coins into the greatest possible number of bags so that every bag has the same number of chocolate coins and the same number of jelly sweets, with none left over.

Find the greatest number of party bags Priya can make.

Work out how many chocolate coins and how many jelly sweets will be in each bag.

Question 15 [4 marks]

Indices and Standard Form

A single red blood cell has a volume of 9.0 x 10^-11 cm^3. An adult has approximately 2.5 x 10^13 red blood cells in their body. Work out the total volume of all the red blood cells in the adult's body. Give your answer, in cm^3, in standard form, correct to 2 significant figures.

Question 16 [5 marks]

Area, Volume and Measures

A sector of a circle has area 154 cm^2 and angle 100 degrees. Calculate the radius of the circle, giving your answer correct to 3 significant figures.

Question 17 [6 marks]

Sequences

A theatre has rows of seats. Row 1 has 18 seats. Each row after Row 1 has 4 more seats than the row before it.

Find an expression, in terms of n, for the number of seats in Row n.

Work out the number of seats in Row 15.

Show that Row 19 has 90 seats.

Question 18 [6 marks]

Area, Volume and Measures

A model car is built using a scale of 1:24 compared with the real car (every linear dimension of the real car is 24 times the corresponding dimension of the model). The model car has a volume of 90 cm^3 and a surface area of 220 cm^2.

Work out the volume of the real car. Give your answer in cm^3, in standard form correct to 3 significant figures.

Work out the surface area of the real car in m^2, correct to 3 significant figures.

Question 19 [7 marks]

Ratio and Proportion

V is directly proportional to L^3. When L = 2, V = 40.

Find a formula for V in terms of L.

Work out V when L = 5.

Work out the value of L when V = 200, giving your answer to 3 significant figures.

Question 20 [1 marks]

Quadratics

The equations y = x^2 - 1 and y = 2x + 2 are solved simultaneously. Which one of these points is a solution to both equations?

Question 21 [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 22 [1 marks]

Quadratics

x^2 - 14x + 51 can be written in the form (x - 7)^2 + k. What is the value of k?