June 2018 GCSE Mathematics 1-9 Edexcel 1MA1 Paper 2 & 3 Revision Questions (HIGHER TIER) Remember: These questions are just a guide based on what hasn’t come up on Paper 1. There are no guarantees that these questions/topics will come up and there is nothing to say that topics that have already appeared on paper 1 won’t come up again! So, revise all you can before the calculator exams! Instructions Use black ink or ball-point pen. Answer all questions. Answer the questions in the spaces provided – there may be more space than you need You must show all your working Calculators may be used Diagrams are NOT accurately drawn, unless otherwise indicated Information The total mark for this paper is 125. The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question. Advice
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June 2018 GCSE Mathematics 1-9 Edexcel 1MA1Paper 2 & 3 Revision Questions (HIGHER TIER)
Remember: These questions are just a guide based on what hasn’t come up on Paper 1. There are no guarantees that these questions/topics will come up and
there is nothing to say that topics that have already appeared on paper 1 won’t come up again! So, revise all you can before the calculator exams!
Instructions
Use black ink or ball-point pen. Answer all questions. Answer the questions in the spaces provided
– there may be more space than you need
You must show all your working Calculators may be used Diagrams are NOT accurately drawn, unless otherwise indicated
Information
The total mark for this paper is 125. The marks for each question are shown in brackets
– use this as a guide as to how much time to spend on each question.
Advice Read each question carefully before you start to answer it. Keep an eye on time. Try to answer every question. Check your answers if you have time at the end.
1 Here is a Venn diagram.
(a) Write down the numbers that are in set
(i) A ∪ B
(ii) A ∩ B
One of the numbers in the diagram is chosen at random.
(b) Find the probability that the number is in set Aʹ
...........................................................
(Total for Question 1 is 3 marks)
2 The diagram shows a regular octagon and a regular hexagon.
Find the size of the angle marked x.You must show all your working.
...........................................................
(Total for Question 2 is 3 marks)
3.
ABC is a straight line.DEFG is a straight line.AC is parallel to DG.EF = BF.Angle BEF = 50°.
Work out the size of the angle marked x.Give reasons for your answer.
.............................................. °
(Total for Question 3 is 4 marks)4 f = 3g + 7h
(a) Work out the value of f when g = −5 and h = 2
(1)
(b) Factorise 3x + 6
(1)
(c) Expand and simplify 5(y − 2) + 2(y − 3)
(2)(d) Factorise completely 12 x3y – 18 xy2
(2)(e) Expand and simplify (2x – 3)(x + 4)
(2)
(Total for question 4 is 8 marks)
5 There are 80 singers in a choir.The cumulative frequency table gives information about the ages of the 80 singers.
Age (A) in years Cumulative frequency
20 < A 30 2
20 < A 40 15
20 < A 50 30
20 < A 60 52
20 < A 70 80
(a) On the grid on the next page, draw a cumulative frequency graph for this information.
(2)
(b) Use your cumulative frequency graph to find an estimate for
(i) the median age,
..............................................
(ii) the interquartile range.
..............................................(3)
(c) Find an estimate for the number of singers over 63 years old.
..............................................(2)
(Total for Question 5 is 7 marks)
___________________________________________________________________________6
Make k the subject of the formula.
...........................................................
(Total for question 6 is 3 marks)
7 Each student in a group of 32 students was asked the following question.
“Do you have a desktop computer (D), a laptop (L) or a tablet (T )?”
Their answers showed that
19 students have a desktop computer17 students have a laptop16 students have a tablet 9 students have both a desktop computer and a laptop11 students have both a desktop computer and a tablet 7 students have both a laptop and a tablet 5 students have all three.
(a) Using this information, complete the Venn diagram to show the number of students in each appropriate subset.
(3)
One of the students with both a desktop computer and a laptop is chosen at random.
(b) Find the probability that this student also has a tablet.
........................................................(1)
(Total for Question 7 is 4 marks)
8 The diagram shows a sector of a circle of radius 6.8 cm.
PQ is an arc of the sector.Angle PRQ = 100°.
Work out the perimeter of the sector.Give your answer correct to 3 significant figures.
.............................................................. cm
(Total for Question 8 is 3 marks)
9 ABC and ABD are two right-angled triangles.
Angle BAC = angle ADB = 90° AB = 13 cm DB = 5 cm
Work out the length of CB.
...........................................................
(Total for Question 9 is 4 marks)
10
The length of the rectangle is 35 cm correct to the nearest cm.The width of the rectangle is 26 cm correct to the nearest cm.
Calculate the upper bound for the area of the rectangle.Write down all the figures on your calculator display.
.................................................................cm2
(Total for Question 10 is 3 marks)
11
A rugby team played six games.The mean score for the six games is 14.5
The rugby team played one more game.The mean score for all seven games is 16
Work out the number of points the team scored in the seventh game.
.......................... points
(Total for Question 11 is 2 marks)
12
Rationalise the denominator
. . . . . . . . . . . . . . . . . . . . . .
(Total for Question 12 is 2 marks)
13
On the grid, enlarge the triangle by scale factor −1 , centre (0, 2).
. . . . . . . . . . . . . . . . . . . . . .
(Total for Question 13 is 2 marks)
14 Write x2 + 2x – 8 in the form (x + m)2 + n where m and n are integers.
. . . . . . . . . . . . . . . . . . . . . .
(Total for Question 14 is 2 marks)
15
Alex and Ben go to a cafe with some friends.
Alex buys 4 cups of coffee and 3 cups of tea.He pays a total of £6.95
Ben buys 5 cups of coffee and 2 cups of tea.He pays a total of £7.20
Work out the cost of each cup of coffee and the cost of each cup of tea.
Cup of coffee.............................................
Cup of tea.............................................
(Total for Question 15 is 5 marks)
16
(a) Show that the equation 3x2 – x3 + 3 = 0 can be rearranged to give x = 3 +
(b) Using xn+1 = 3 + with x0 = 3.2, find the values of x1, x2 and x3
. . . . . . . . . . . . . . . . . . . . . .
(Total for Question 16 is 5 marks)
17 On the grid, shade the region that satisfies all these inequalities.
x + y < 4 y > x – 1 y < 3x
Label the region R.
. . . . . . . . . . . . . . . . . . . . . .
(Total for Question 17 is 4 marks)
18 The diagram shows a trapezium.
All measurements on the diagram are in centimetres.
The area of the trapezium is 119 cm2
(i) Show that 2x2 – x – 120 = 0
(ii) Find the value of x.Show your working clearly.
x = .......................................................
(Total for Question 18 is 6 marks)
19 Clive wants to estimate the number of bees in a beehive.
Clive catches 50 bees from the beehive.He marks each bee with a dye.He then lets the bees go.
The next day, Clive catches 40 bees from the beehive.8 of these bees have been marked with the dye.
(i) Work out an estimate for the number of bees in the beehive.
.............................................. bees
(ii) Write down any assumptions you have made.
......................................................................................................................................................
......................................................................................................................................................
(Total for Question 19 is 4 marks)
20 Nomusa has 30 sweets.
She has18 fruit sweets7 aniseed sweets5 mint sweets
Nomusa is going to take at random two sweets.
Work out the probability that the two sweets will not be the same type of sweet.You must show all your working.
..............................................
(Total for Question 20 is 4 marks)
21 The histogram shows information about the lifetime of some electrical components.
Lifetime (years)
Work out the proportion of the components with a lifetime of between 1 and 6 years.
..............................................................
(Total for Question 21 is 4 marks)
22
OAB is a triangle.
O⃗A = a
O⃗B = b
(a) Find the vector A⃗B in terms of a and b.
A⃗B = ........................................(1)
P is the point on AB such that AP : PB = 3 : 2
(b) Show that O⃗P =
15 (2a + 3b)
(3)(Total for Question 22 is 4 marks)
23 Here is a speed-time graph for a car.
(a) Work out an estimate for the distance the car travelled in the first 10 seconds.Use 5 strips of equal width.
(b) Is your answer to (a) an underestimate or an overestimate of the actual distance?Give a reason for your answer.
. . . . . . . . . . . . . . . . . . . . . .
(Total for Question 23 is 4 marks)
24 ABC is a triangle. D is a point on AB.
Work out the area of triangle BCD. Give your answer correct to 3 significant figures.
. . . . . . . . . . . . . . . . . . . . . .
(Total for Question 24 is 5 marks)
25 The diagram shows an oil tank in the shape of a prism.
The cross section of the prism is a trapezium.
The tank is empty. Oil flows into the tank.After one minute there are 300 litres of oil in the tank.Assume that oil continues to flow into the tank at this rate.
Work out how many more minutes it takes for the tank to be 85% full of oil.(1 m3 = 1000 litres)
. . . . . . . . . . . . . . . . . . . . . .
(Total for Question 25 is 5 marks)26
ABC is a triangle. D is a point on AC. Angle BAD = 45° Angle ADB = 80° AB = 7.4 cm DC = 5.8 cm
Work out the length of BC. Give your answer correct to 3 significant figures.
........................................................... cm
(Total for question 26 is 5 marks)
27 f is the function f(x) = 2x + 5.
(a) Find f(3).
................................(1)
(b) Express the inverse function f–1 in the form f–1(x) =
f–1(x) = ................................................................(2)
g is the function g(x) = x2 – 25.
(c) Find g(–3).
................................(1)
(d) (i) Find gf(x).Give your answer as simply as possible.
gf(x) = ................................................................
(ii) Solve gf(x) = 0.
................................................................(5)
(Total for Question 27 is 9 marks)
28
The diagram shows part of the curve with equation y = f(x). The coordinates of the maximum point of the curve are (3, 5).
Write down the coordinates of the maximum point of the curve with equation
(i) y = f(x + 3)
(.............. , ............)
(ii) y = 2f(x)
(.............. , ............)
(iii) y = f(3x)
(.............. , ............)
(Total for Question 28 is 3 marks)
29 Solve + = 1
...........................................(Total for Question 29 is 5 marks)
30
In the space below, use ruler and compasses to construct an equilateral triangle with sides of length 6 centimetres. You must show all your construction lines.
(Total for question 30 is 3 marks)
END OF QUESTIONS
GOOD LUCK with the Calculator Papers!
@mrcollinsmaths
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