Name: _______________________________________________
2016 Best Guess Booklet
Edexcel Higher
Date:
Time: 4 hours
Total marks available: 222
Total marks achieved: ______
Penketh High School
Questions
Q1.
Ali is planning a party.
He wants to buy some cakes and some sausage rolls.
The cakes are sold in boxes.
There are 12 cakes in each box.
Each box of cakes costs £2.50
The sausage rolls are sold in packs.
There are 8 sausage rolls in each pack.
Each pack of sausage rolls costs £1.20
Ali wants to buy more than 60 cakes and more than 60 sausage rolls.
He wants to buy exactly the same number of cakes as sausage rolls.
What is the least amount of money Ali will have to pay?
£...........................................................
(Total for Question is 5 marks)
Q2.
John buys some boxes of pencils and some packets of pens for people to use at a conference.
There are 40 pencils in a box.
There are 15 pens in a packet.
John gives one pencil and one pen to each person at the conference.
He has no pencils left.
He has no pens left.
How many boxes of pencils and how many packets of pens did John buy?
........................................................... boxes of pencils
........................................................... packets of pens
(Total for question = 3 marks)
Q3.
Build-a-mix makes concrete.
1 cubic metre of concrete has a weight of 2400 kg.
15% of the concrete is water.
The rest of the ingredients of concrete are cement, sand and stone.
The weights of these ingredients are in the ratio 1 : 2 : 5
(a) Work out the weight of cement, of sand and of stone in 1 cubic metre of concrete.
cement = . . . . . . . . . . . . . . . . . . . . . . kg
sand = . . . . . . . . . . . . . . . . . . . . . . kg
stone = . . . . . . . . . . . . . . . . . . . . . . kg
(4)
Build-a-mix needs to make 30 cubic metres of concrete.
Build-a-mix has only got 6.5 tonnes of cement.
* (b) Will this be enough cement for Build-a-mix to make 30 cubic metres of concrete?
You must show all of your working.
(3)
(Total for Question is 7 marks)
Q4.
*
In the UK, petrol cost £1.24 per litre.
In the USA, petrol cost 3.15 dollars per US gallon.
1 US gallon = 3.79 litres
£1 = 1.47 dollars
Was petrol cheaper in the UK or in the USA?
(Total for Question is 4 marks)
Q5.
Here are the ingredients needed to make 12 shortcakes.
Shortcakes
Makes 12 shortcakes 50 g of sugar
200 g of butter
200 g of flour
10 ml of milk
Liz makes some shortcakes.
She uses 25 ml of milk.
(a) How many shortcakes does Liz make?
..............................................................................................................................................
(2)
Robert has
500 g of sugar
1000 g of butter
1000 g of flour
500 ml of milk
(b) Work out the greatest number of shortcakes Robert can make.
..............................................................................................................................................
(2)
(Total for Question is 4 marks)
Q6.
Use your calculator to work out
Write down all the figures on your calculator display.
You must give your answer as a decimal.
..............................................................................................................................................
(Total for Question is 2 marks)
Q7.
* A supermarket has two special offers on lemonade.
The normal price of a 2.5 litre bottle of lemonade is £1.60
The normal price of a 0.33 litre can of lemonade is 28p.
Jerry is going to buy 4 bottles of the lemonade on special offer or 30 cans of the lemonade on special
offer.
Which special offer is the better value for money?
(Total for question = 5 marks)
Q8.
* Viv wants to invest £2000 for 2 years in the same bank.
At the end of 2 years, Viv wants to have as much money as possible.
Which bank should she invest her £2000 in?
(Total for Question is 4 marks)
Q9.
Claire is making a loaf of bread.
A loaf of bread loses 12% of its weight when it is baked.
Claire wants the baked loaf of bread to weigh 1.1 kg.
Work out the weight of the loaf of bread before it is baked.
........................................................... kg
(Total for question = 3 marks)
Q10.
Sasha drops a ball from a height of d metres onto the ground.
The time, t seconds, that the ball takes to reach the ground is given by
where g m/s2 is the acceleration due to gravity.
d = 35.6 correct to 3 significant figures.
g = 9.8 correct to 2 significant figures.
(a) Write down the lower bound of d.
..............................................................................................................................................
(1)
(b) Calculate the lower bound of t.
You must show all your working.
..............................................................................................................................................
(3)
(Total for Question is 4 marks)
Q11.
*
ABC, DEF and PQRS are parallel lines.
BEQ is a straight line.
Angle ABE = 60°
Angle QER = 80°
Work out the size of the angle marked x.
Give reasons for each stage of your working.
(Total for question = 4 marks)
Q12.
ABCDEFGH is a regular octagon.
KLQFP and MNREQ are two identical regular pentagons.
Work out the size of the angle marked x.
You must show all your working.
...........................................................°
(Total for question = 4 marks)
Q13.
The diagram shows the front elevation and the side elevation of a prism.
(a) On the grid, draw a plan of this prism.
(2)
(b) In the space below, draw a sketch of this prism.
(2)
(Total for Question is 4 marks)
Q14.
A frustrum is made by removing a small cone from a similar large cone.
The height of the small cone is 20 cm.
The height of the large cone is 40 cm.
The diameter of the base of the large cone is 30 cm.
Work out the volume of the frustrum.
Give your answer correct to 3 significant figures.
. . . . . . . . . . . . . . . . . . . . . . . .cm3
(Total for Question is 4 marks)
Q15.
Sumeet has a pond in the shape of a prism.
The pond is completely full of water.
Sumeet wants to empty the pond so he can clean it.
Sumeet uses a pump to empty the pond.
The volume of water in the pond decreases at a constant rate.
The level of the water in the pond goes down by 20 cm in the first 30 minutes.
Work out how much more time Sumeet has to wait for the pump to empty the pond completely.
..............................................................................................................................................
(Total for Question is 6 marks)
Q16.
The diagram shows a pond.
The pond is in the shape of a sector of a circle.
Toby is going to put edging on the perimeter of the pond.
Edging is sold in lengths of 1.75 metres.
Each length of edging costs £3.49
Work out the total cost of edging Toby needs to buy.
£ ...........................................................
(Total for question = 5 marks)
Q17.
The diagram shows a quadrilateral ABCD.
Diagram NOT accurately
drawn
AB = 16 cm.
AD = 12 cm.
Angle BCD = 40°.
Angle ADB = angle CBD = 90°.
Calculate the length of CD.
Give your answer correct to 3 significant figures.
. . . . . . . . . . . . . . . . . . . . . . cm
(Total for Question is 5 marks)
Q18.
ABCD is a trapezium.
AD = 10 cm
AB = 9 cm
DC = 3 cm
Angle ABC = angle BCD = 90°
Calculate the length of AC.
Give your answer correct to 3 significant figures.
..............................................................................................................................................
(Total for Question is 5 marks)
Q19.
Diagram NOT accurately drawn
ABC is a triangle.
AB = 8.7 cm.
Angle ABC = 49°.
Angle ACB = 64°.
Calculate the area of triangle ABC.
Give your answer correct to 3 significant figures.
. . . . . . . . . . . . . . . . . . . . . cm2
(Total for Question is 5 marks)
Q20.
ABC is a triangle.
(a) Work out the area of triangle ABC.
Give your answer correct to 3 significant figures.
. . . . . . . . . . . . . . . . . . . . . . cm2
(2)
(b) Work out the length of the side AB.
Give your answer correct to 3 significant figures.
..............................................................................................................................................
(3)
(Total for Question is 5 marks)
Q21.
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 = 5 marks)
Q22.
Manchester airport is on a bearing of 330° from a London airport.
(a) Find the bearing of the London airport from Manchester airport.
...........................................................°
(2)
The London airport is 200 miles from Manchester airport.
A plane leaves Manchester airport at 10 am to fly to the London airport.
The plane flies at an average speed of 120 mph.
(b) What time does the plane arrive at the London airport?
...........................................................
(4)
(Total for question = 6 marks)
Q23.
A rectangle has an area of 4 m2.
Write this area in cm2.
........................................................... cm2
(Total for question = 2 marks)
Q24.
* Axel and Lethna are driving along a motorway.
They see a road sign.
The road sign shows the distance to Junction 8
It also shows the average time drivers will take to get to Junction 8
The speed limit on the motorway is 70 mph.
Lethna says,
'We will have to drive faster than the speed limit to go 30 miles in 26 minutes.'
Is Lethna right?
You must show how you got your answer.
(Total for Question is 3 marks)
Q25.
Liquid A has a density of 0.7 g/cm3.
Liquid B has a density of 1.6 g/cm3.
140 g of liquid A and 128 g of liquid B are mixed to make liquid C.
Work out the density of liquid C.
........................................................... g/cm3
(Total for question = 4 marks)
Q26.
On the grid, enlarge the triangle by scale factor − , centre (0, −2).
(Total for Question is 2 marks)
Q27.
Describe fully the single transformation which maps triangle A onto triangle B.
....................................................................................
...............
....................................................................................
...............
(Total for Question is 3 marks)
Q28.
Describe the single transformation that maps triangle A onto triangle B.
.............................................................................................................................................
.............................................................................................................................................
(Total for Question is 2 marks)
Q29.
P and Q are two triangular prisms that are mathematically similar.
Prism P has triangle ABC as its cross section.
Prism Q has triangle DEF as its cross section.
AC = 6 cm
DF = 12 cm
The area of the cross section of prism P is 10 cm2.
The length of prism P is 15 cm.
Work out the volume of prism Q.
..............................................................................................................................................
(Total for Question is 4 marks)
Q30.
Ali has two solid cones made from the same type of metal.
Diagram NOT accurately drawn
The two solid cones are mathematically similar.
The base of cone A is a circle with diameter 80 cm.
The base of cone B is a circle with diameter 160 cm.
Ali uses 80 ml of paint to paint cone A.
Ali is going to paint cone B.
(a) Work out how much paint, in ml, he will need.
. . . . . . . . . . . . . . . . . . . . . . ml
(2)
The volume of cone A is 171 700 cm3.
(b) Work out the volume of cone B.
. . . . . . . . . . . . . . . . . . . . . . cm3
(3)
(Total for Question is 5 marks)
Q31.
PQR and PTS are straight lines.
Angle PTQ = Angle PSR = 90°
QT = 4 cm
RS = 12 cm
TS = 10 cm
(a) Work out the area of the trapezium QRST.
. . . . . . . . . . . . . . . . . . . . . cm2
(2)
(b) Work out the length of PT.
. . . . . . . . . . . . . . . . . . . . . cm
(3)
(Total for Question is 5 marks)
Q32.
(a) Complete the table of values for y = 2x + 2
x
−2
y
−2
−1
0
1
2
3
4
6
(2)
(b) On the grid, draw the graph of y = 2x + 2
(2)
(Total for Question is 4 marks)
Q33.
The straight line L has equation y = 2x − 5
Find an equation of the straight line perpendicular to L which passes through (−2, 3).
...........................................................
(Total for Question is 3 marks)
Q34.
The diagram shows part of the curve with equation y = f(x).
The coordinates of the maximum point of the curve are (3, 5).
(a) 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)
(............................................. , .............................................)
(3)
The curve with equation y = f(x) is transformed to give the curve with equation y = f(x) − 4
(b) Describe the transformation.
.............................................................................................................................................
(1)
(Total for question = 4 marks)
Q35.
Here is the graph of y = sin x° for –180 ≤ x ≤ 180
(a) On the grid above, sketch the graph of y = sin x° + 2 for –180 ≤ x ≤ 180
(2)
Here is the graph of y = cos x° for –180 ≤ x ≤ 180
(b) On the grid above, sketch the graph of y = –2 cos x° for –180 ≤ x ≤ 180
(Total for question = 4 marks)
Q36.
Simon went for a cycle ride.
He left home at 2 pm.
The travel graph represents part of Simon's cycle ride.
At 3 pm Simon stopped for a rest.
(a) How many minutes did he rest?
. . . . . . . . . . . . . . . . . . minutes
(1)
(b) How far was Simon from home at 5 pm?
. . . . . . . . . . . . . . . . . . km
(1)
At 5 pm Simon stopped for 30 minutes.
Then he cycled home at a steady speed.
It took him 1 hour 30 minutes to get home.
(c) Complete the travel graph.
(2)
(Total for Question is 4 marks)
Q37.
Here are the first four terms of an arithmetic sequence.
(a) Find, in terms of n, an expression for the nth term of this arithmetic sequence.
...........................................................
(2)
(b) Is 121 a term of this arithmetic sequence?
You must explain your answer.
.............................................................................................................................................
.............................................................................................................................................
.............................................................................................................................................
(2)
(Total for question = 4 marks)
Q38.
The diagram shows a cube and a cuboid.
All the measurements are in cm.
The volume of the cube is 100 cm3 more than the volume of the cuboid.
(a) Show that x3 – 10x = 100
(2)
(b) Use a trial and improvement method to find the value of x.
Give your answer correct to 1 decimal place.
You must show all your working.
x=......................
(4)
(Total for Question is 6 marks)
Q39.
Solve the simultaneous equations
3x + 4y = 5
2x − 3y = 9
x = ...........................................................
y = ...........................................................
(Total for Question is 4 marks)
Q40.
Solve the simultaneous equations
x2 + y2 = 25
y = 2x + 5
x = . . . . . . . . . . . . . . and y = . . . . . . . . . . . . . .
or
x = . . . . . . . . . . . . . . and y = . . . . . . . . . . . . . .
(Total for Question is 6 marks)
Q41.
Simplify
..............................................................................................................................................
(Total for Question is 3 marks)
Q42.
* Prove algebraically that the difference between the squares of any two consecutive integers is equal to
the sum of these two integers.
(Total for Question is 4 marks)
Q43.
(a) Simplify fully
..............................................................................................................................................
(3)
(b) Write
as a single fraction in its simplest form.
..............................................................................................................................................
(3)
(Total for Question is 6 marks)
Q44.
On the grid below, show by shading, the region defined by the inequalities
x+y<6
Mark this region with the letter R.
x>−1
y>2
(Total for Question is 4 marks)
Q45.
Make p the subject of the formula
y = 3p2 – 4
......................
(Total for Question is 3 marks)
Q46.
Make a the subject of the formula
...........................................................
(Total for question = 4 marks)
Q47.
The expression x2 − 8x + 6 can be written in the form (x − p)2 + q for all values of x.
(a) Find the value of p and the value of q.
p = ...........................................................
q = ...........................................................
(3)
The graph of y = x2 − 8x + 6 has a minimum point.
(b) Write down the coordinates of this point.
(............................. , .............................)
(1)
(Total for question = 4 marks)
Q48.
148 students went to Brighton.
Each student went to the Aquarium or the Brighton Wheel or the Royal Pavilion.
The table gives information about these students.
The teacher takes a sample of 40 of these students.
The sample is stratified by gender and by place visited.
Work out the number of students in the sample who are female and went to the Brighton Wheel.
...........................................................
(Total for question = 2 marks)
Q49.
The table shows some information about the weights, in grams, of 60 eggs.
Weight (w grams)
Frequency
0 < w ≤ 30
30 < w ≤ 50
50 < w ≤ 60
60 < w ≤ 70
70 < w ≤ 100
0
14
16
21
9
(a) Calculate an estimate for the mean weight of an egg.
......................g
(4)
(b) Complete the cumulative frequency table.
Weight (w grams)
0 < w ≤ 30
0 < w ≤ 50
0 < w ≤ 60
0 < w ≤ 70
0 < w ≤ 100
Cumulative
frequency
0
(1)
(c) On the grid, draw a cumulative frequency graph for your table.
(2)
(d) Use your graph to find an estimate for the number of eggs with a weight greater than 63 grams.
..............................................................................................................................................
(2)
(Total for Question is 9 marks)
Q50.
The table gives information about the time it took each of 80 children to do a jigsaw puzzle.
Work out the mean time for all 80 children.
........................................................... minutes
(Total for Question is 3 marks)
Q51.
Jim went on a fishing holiday.
The histogram shows some information about the weights of the fish he caught.
(a) Use the histogram to complete the frequency table.
(2)
Jim kept all the fish he caught with a weight greater than 2000 g.
(b) Find the ratio of the number of fish Jim kept to the total number of fish he caught.
..............................................................................................................................................
(c) Use the histogram to find an estimate of the median.
..............................................................................................................................................
(2)
(Total for Question is 6 marks)
Q52.
Carlos has a cafe in Clacton.
Each day, he records the maximum temperature in degrees Celsius (°C) in Clacton and the number of hot
chocolate drinks sold.
The scatter graph shows this information.
On another day the maximum temperature was 6 °C and 35 hot chocolate drinks were sold.
(a) Show this information on the scatter graph.
(1)
(b) Describe the relationship between the maximum temperature and the number of hot chocolate drinks
sold.
.............................................................................................................................................
.............................................................................................................................................
(1)
(c) Draw a line of best fit on the scatter diagram.
One day the maximum temperature was 8 °C.
(d) Use your line of best fit to estimate how many hot chocolate drinks were sold.
..........................
(1)
(Total for Question is 4 marks)
Q53.
Helen went on 35 flights in a hot air balloon last year.
The table gives some information about the length of time, t minutes, of each flight.
On the grid below, draw a frequency polygon for this information.
(Total for Question is 2 marks)
Mark Scheme
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