Edexcel GCSE Higher June 2017 Paper 2 (calculator)
23 questions · 80 marks. Every question from the paper, recreated, with the official mark scheme, an annotated worked solution and a shadow question (the same skill with new numbers). Open the paper in the Ultimate Exam Question Finder to present it, print it or build a set.
Question 1 (3 marks)
The table shows the probabilities that a biased dice will land on 2, on 3, on 4, on 5 and on 6
Number on dice Probability 1 2 0.17 3 0.18 4 0.09 5 0.15 6 0.1 Neymar rolls the biased dice 200 times.
Work out an estimate for the total number of times the dice will land on 1 or on 3
(3 marks)
Question 2 (5 marks)
On Saturday, some adults and some children were in a theatre.
The ratio of the number of adults to the number of children was 5 : 2
Each person had a seat in the Circle or had a seat in the Stalls.
3/4 of the children had seats in the Stalls.
117 children had seats in the Circle.There are exactly 2600 seats in the theatre.
On this Saturday, were there people on more than 60% of the seats?
You must show how you get your answer.(5 marks)
Question 3 (4 marks)
The diagram shows a prism with a cross section in the shape of a trapezium.
Diagram: A prism with a trapezium cross section, drawn in 3D. The trapezium at the front has a horizontal base 2 m, a vertical left side 2 m, a vertical right side 0.5 m and a sloping top 2.5 m. The prism is 1 m long. Arrows show the front (looking at the trapezium) and the side (looking from the right).
On the centimetre grid below, draw the front elevation and the side elevation of the prism.
Use a scale of 2 cm to 1 m.Diagram: A centimetre grid, 16 squares across and 11 squares up.
(4 marks)
Question 4 (5 marks)
Olly drove 56 km from Liverpool to Manchester.
He then drove 61 km from Manchester to Sheffield.Olly’s average speed from Liverpool to Manchester was 70 km/h.
Olly took 75 minutes to drive from Manchester to Sheffield.(a)
Work out Olly’s average speed for his total drive from Liverpool to Sheffield.
(4 marks)
(b)
Janie drove from Barnsley to York.
Janie’s average speed from Barnsley to Leeds was 80 km/h.
Her average speed from Leeds to York was 60 km/h.Janie says that the average speed from Barnsley to York can be found by working out the
mean of 80 km/h and 60 km/h.If Janie is correct, what does this tell you about the two parts of Janie’s journey?
(1 mark)
Question 5 (4 marks)
Diagram: Triangle AEC with E at the bottom left, C at the bottom right and A at the top. D is on EC and B is on AC. DB is parallel to EA (arrows).
ABC and EDC are straight lines.
EA is parallel to DB.EC = 8.1 cm.
DC = 5.4 cm.
DB = 2.6 cm.(a)
Work out the length of AE.
(2 marks)
(b)
AC = 6.15 cm.
Work out the length of AB.
(2 marks)
Question 6 (3 marks)
Anil wants to invest £25000 for 3 years in a bank.
Personal Bank Secure Bank Compound Interest Compound Interest 2% for each year 4.3% for the first year 0.9% for each extra year Which bank will give Anil the most interest at the end of 3 years?
You must show all your working.(3 marks)
Question 7 (2 marks)
A number, n, is rounded to 2 decimal places.
The result is 4.76Using inequalities, write down the error interval for n.
(2 marks)
Question 8 (2 marks)
The cumulative frequency graph shows some information about the heights, in cm,
of 60 students.Diagram: A cumulative frequency graph for the heights of 60 students. Height goes from 120 to 170 cm and cumulative frequency from 0 to 60. The curve starts at 130 cm with a cumulative frequency of 5, rises slowly to 150 cm, steeply to about 157 cm, and then less steeply to end at 170 cm with a cumulative frequency of 60.
Work out an estimate for the number of these students with a height greater than 160 cm.
(2 marks)
Question 9 (3 marks)
The diagram shows triangle A drawn on a grid.
Diagram: A grid with x and y from –5 to 5. Triangle A has corners at (3, 3), (4, 3) and (4, 1).
Kyle reflects triangle A in the x-axis to get triangle B.
He then reflects triangle B in the line y = x to get triangle C.Amy reflects triangle A in the line y = x to get triangle D.
She is then going to reflect triangle D in the x-axis to get triangle E.Amy says that triangle E should be in the same position as triangle C.
Is Amy correct?
You must show how you get your answer.(3 marks)
Question 10 (4 marks)
The table shows some information about eight planets.
Planet Distance from Earth (km) Mass (kg) Earth 0 5.97 × 10²⁴ Jupiter 6.29 × 10⁸ 1.898 × 10²⁷ Mars 7.83 × 10⁷ 6.42 × 10²³ Mercury 9.17 × 10⁷ 3.302 × 10²³ Neptune 4.35 × 10⁹ 1.024 × 10²⁶ Saturn 1.28 × 10⁹ 5.68 × 10²⁶ Uranus 2.72 × 10⁹ 8.683 × 10²⁵ Venus 4.14 × 10⁷ 4.869 × 10²⁴ (a)
Write down the name of the planet with the greatest mass.
(1 mark)
(b)
Find the difference between the mass of Venus and the mass of Mercury.
(1 mark)
(c)
Nishat says that Neptune is over a hundred times further away from Earth than Venus is.
Is Nishat right?
You must show how you get your answer.(2 marks)
Question 11 (4 marks)
Solve (3x – 2)/4 – (2x + 5)/3 = (1 – x)/6
(4 marks)
Question 12 (2 marks)
There are 30 students in Mr Lear’s class.
16 of the students are boys.Two students from the class are chosen at random.
Mr Lear draws this probability tree diagram for this information.
Diagram: A probability tree diagram. 1st student: boy 16/30, girl 14/30. 2nd student after a boy: boy 15/30, girl 14/30. After a girl: boy 16/30, girl 13/30.
(a)
Write down one thing that is wrong with the probabilities in the probability tree diagram.
(1 mark)
(b)
Owen and Wasim play for the school football team.
The probability that Owen will score a goal in the next match is 0.4
The probability that Wasim will score a goal in the next match is 0.25Mr Slater says,
“The probability that both boys will score a goal in the next match is 0.4 + 0.25”
Is Mr Slater right?
Give a reason for your answer.(1 mark)
Question 13 (3 marks)
The histogram shows some information about the ages of the 134 members of a sports club.
Diagram: A histogram. Age in years across from 0 to 100, frequency density up from 0 to 3. Bars: 0 to 10 at height 1.1, 10 to 20 at height 2.8, 20 to 40 at height 2.3, 40 to 60 at height 1.4, 60 to 90 at height 0.7.
20% of the members of the sports club who are over 50 years of age are female.
Work out an estimate for the number of female members who are over 50 years of age.
(3 marks)
Question 14 (3 marks)
Here are some graphs.
Graph A
Diagram: Graph A: a curve close to the x-axis on the left, crossing the y-axis above O and rising more and more steeply to the right.
Graph B
Diagram: Graph B: two curves, top left and bottom right, never touching the axes.
Graph C
Diagram: Graph C: a wave through O, rising through O to a peak on the right and falling to a trough on the left.
Graph D
Diagram: Graph D: a wave with its peak on the y-axis, above O, falling to a trough on each side.
Graph E
Diagram: Graph E: a U-shaped curve with its lowest point on the y-axis, below O.
Graph F
Diagram: Graph F: a curve through O, rising from bottom left to top right all the way, flattening a little at O.
Graph G
Diagram: Graph G: an upside-down U-shaped curve with its highest point at O.
Graph H
Diagram: Graph H: two curves, top right and bottom left, never touching the axes.
Graph I
Diagram: Graph I: a curve falling from top left, crossing the y-axis above O and getting closer and closer to the x-axis on the right.
In the table below, match each equation with the letter of its graph.
Equation Graph y = sin x y = x³ + 4x y = 2^(x) y = 4/x (3 marks)
Question 15 (3 marks)
A, B, C and D are four points on the circumference of a circle.
Diagram: A circle with four points on it: A at the top left, B on the right, C at the bottom right and D at the bottom left. The chords AB, BC, CD and DA are drawn, and the lines AC and BD cross at E inside the circle.
AEC and BED are straight lines.
Prove that triangle ABE and triangle DCE are similar.
You must give reasons for each stage of your working.(3 marks)
Question 16 (3 marks)
Using algebra, prove that 0.13̇6̇ × 0.2̇ is equal in value to 1/33
(3 marks)
Question 17 (5 marks)
Diagram: A sector ONQ of a circle with centre O: OQ goes left from O along the bottom and ON goes up to the left, with the arc from Q up to N. A is on ON and B is on OQ, and AB is drawn so that AOB is an equilateral triangle. The region between AB and the arc is shaded.
ONQ is a sector of a circle with centre O and radius 11 cm.
A is the point on ON and B is the point on OQ such that AOB
is an equilateral triangle of side 7 cm.Calculate the area of the shaded region as a percentage of the area of the sector ONQ.
Give your answer correct to 1 decimal place.(5 marks)
Question 18 (3 marks)
16^(1/5) × 2^x = 8^(3/4)
Work out the exact value of x.
(3 marks)
Question 19 (4 marks)
2 – (x + 2)/(x – 3) – (x – 6)/(x + 3) can be written as a single fraction in the form (ax + b)/(x² – 9)
where a and b are integers.Work out the value of a and the value of b.
(4 marks)
Question 20 (5 marks)
The diagram shows part of the graph of y = x² – 2x + 3
Diagram: A graph with x from –4 to 6 and y from –1 to 11. The U-shaped curve y = x squared – 2x + 3 comes down from (–2, 11), crosses the y-axis at 3, has its lowest point at (1, 2), and rises to (4, 11).
(a)
By drawing a suitable straight line, use your graph to find estimates for the solutions
of x² – 3x – 1 = 0(2 marks)
(b)
P is the point on the graph of y = x² – 2x + 3 where x = 2
Calculate an estimate for the gradient of the graph at the point P.
(3 marks)
Question 21 (4 marks)
The diagram shows 3 identical circles inside a rectangle.
Each circle touches the other two circles and the sides of the rectangle, as shown in
the diagram.Diagram: A rectangle containing three equal circles: two side by side along the top, touching each other, and one below, touching both of them. The circles touch the sides of the rectangle. The centre of each circle is marked with a dot.
The radius of each circle is 24 mm.
Work out the area of the rectangle.
Give your answer correct to 3 significant figures.(4 marks)
Question 22 (3 marks)
Here are the first five terms of a sequence.
4 11 22 37 56
Find an expression, in terms of n, for the nth term of this sequence.
(3 marks)
Question 23 (3 marks)
L is the circle with equation x² + y² = 4
P(3/2, dfrac√72) is a point on L.
Find an equation of the tangent to L at the point P.
(3 marks)
Questions © Pearson Education, recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.