Note: Questions 19-26 are copied from November 17 Higher Paper 3 Questions 1-8.
Question 1
(1 mark)
Write 249 correct to the nearest 100
Answer Type: Simple Text
Answer: 200
Question 2
(1 mark)
Simplify 6x+4x-5x
Answer Type: Multiple choice type 1
Answer: 5x
Wrong answers:
15x
6x
7x
Question 3
(2 marks)
Not including 1 and 24, what are all the factors of 24?
Answer Type: Multiple choice type 1
Answer: 2, 3, 4, 6, 8, 12
Wrong answers:
3, 4, 6, 8, 12
2, 3, 4, 5, 6, 8, 12
2, 3, 4, 6, 8, 12, 18
Question 4
The table below gives information about the prices for entry to a zoo.
Mr and Mrs Davies and their 2 children go to the zoo.
4(a)
(3 marks)
How much cheaper is it for them to get a family ticket compared to individual tickets?
Answer Type: Simple Text
Answer: £7.10
WORKING:
Cost of individual tickets =2\times£12.50+2\times8.65=£42.30
£42.30-£35.20=£7.104(b)
(2 marks)
One of the children times how long they are at the zoo for.
She records that they were there for 255 minutes.
If they got to the zoo at 1:30 pm, did they leave before 5:30 pm?
Answer Type: Multiple Choice
Answer: No
Wrong Answer: Yes
WORKING:
255 minutes =4 hours 15 minutes.
4 hours 15 minutes after 1:30 pm is 5:45 pm, so they didn’t leave before 5:30 pm.
Question 5
(3 marks)
Jeremy makes a jug of lemonade.
There are 3 litres of lemonade in this jug.
Jeremy has some small glasses that can be filled with 240 ml of lemonade.
How many glasses can be filled completely with lemonade from the jug?
Answer Type: Simple Text
Answer: 12
WORKING:
First we need to convert 240 ml into litres
240 ml =0.24 litres
3\div0.24=12.5
So 12 glasses can be completely filled.
Question 6
(3 marks)
The pictogram below with an incomplete key, shows the information about the number of ice creams sold from an ice cream van on Monday, Tuesday, Wednesday, Thursday and Friday.
The total number of ice creams sold in these five days was 123
6(a)
(2 marks)
Complete the key for this pictogram.
Answer Type: Simple Text
Answer: 1 ice cream symbol = 6 ice creams
WORKING:
There are 20\frac{1}{2} ice cream symbols.
123\div20.5=6So 1 ice cream symbol = 6 ice creams.
6(b)
(1 mark)
How many ice creams were sold on Wednesday?
Answer Type: Simple Text
Answer: 21
WORKING:
6\times3.5=21Question 7
The diagram below shows the triangle ABC and the straight line ACD.
7(a)
(3 marks)
What is angle ABC?
Answer Type: Simple Text
Answer: 68\degree
WORKING:
As ACD is a straight line, we know that \angle ACB+112\degree =180\degree,
so \angle ACB = 180\degree - 112\degree = 68\degree
Angles in a triangle add up to 180\degree,
so \angle ABC = 180\degree - 44\degree - 68\degree =68\degree
7(b)
(1 mark)
What type of triangle is triangle ABC?
Answer Type: Multiple Choice
Answer: Isosceles
Wrong Answers:
Equilateral
Right-angled
Scalene
WORKING:
Triangle ABC is an isosceles triangle because it has two equal angles.
Question 8
(2 marks)
The distance from Manchester to London is 336.1 km.
The distance from Manchester to Sydney is approximately 51 times greater than distance of Manchester to London.
Work out the distance from Manchester to Sydney in miles, given 1 km =0.62 miles.
Give your Answer to 1 decimal place.
Answer Type: Simple Text
Answer: 10627.5 miles
WORKING:
Distance from Manchester to Sydney =336.1 km \times 51=17141.1 km
17141.1 km = 10627.5 miles (to 1 decimal place)
Question 9
(2 marks)
Jasmine writes down two prime numbers, a and b, where a<b<30
She subtracts a from b.
Her answer is an square number.
What is the largest possible number a could be?
Answer Type: Simple Text
Answer: 19
WORKING:
If b is 29, then the only possible value of a is 13, as 29-13=16=4^2
If b is 23 then a must equal 19 or 7, as 29-19=4=2^2 and 23-7=16=4^2
Because the only prime numbers that are greater than 19 and less than 30 are 29 and 23, we know that the greatest number that a can be is 19
Question 10
(2 marks)
Pam thinks of a number.
\dfrac{3}{5} of Pam’s number is 36
Work out \dfrac{11}{12} of her number.
Answer Type: Simple Text
Answer: 55
WORKING:
Let Pam’s number be x
Then:
\dfrac{3}{5}\times x=36
x=36\times\dfrac{5}{3}=60
\dfrac{11}{12}\times x=\dfrac{11}{12}\times 60 =55
Question 11
(3 marks)
A new video streaming service has just come out, with a standard monthly fee of £7.99
Lucy receives two emails containing two different offers for the service.
If Lucy wants to use the streaming service for 6 months, which offer should she choose to use, assuming she can only use one?
Answer Type: Multiple Choice
Answer: Offer 2
Wrong Answer: Offer 1
WORKING:
Cost of 6 months with offer 1:
1 month free +5\times £7.99=£39.95
Cost of 6 months with offer 2:
6\times £7.99=£47.94
0.8\times £47.94=£38.35
So offer 2 is better for 6 months.
Question 12
(2 marks)
300 g of pick and mix sweets costs £2.55
Work out the cost of 500 g of pick and mix sweets.
Answer Type: Simple Text
Answer: £4.25
WORKING:
Price per 100 g = £2.55\div 3 = £0.85
Price for 500 g = 5\times £0.85 = £4.25
Question 13
(5 marks)
13(a)
(2 marks)
Complete the table of values for y=2-\dfrac{3}{2}x
Answer Type: Multiple Answer
Answer:
a=3.5
b=2
c=-1
d=-2.5
WORKING:
Substitute the x values from the table into the equation to find the corresponding y values:
13(b)
(2 marks)
Which of the following is the correct graph of y=2-\dfrac{3}{2}?
Answer Type: Multiple Choice
Answer:
Wrong Answers:
13(c)
(1 mark)
Use the graph to find the value of x when y=1.1
Answer Type: Simple Text
Answer: 0.6
WORKING:
Question 14
(2 marks)
(2 marks)
Which of the following describes the single transformation that maps shape A onto shape B?
Answer Type: Multiple Choice
Answer: Rotation clockwise by 90\degree
Wrong Answers:
Rotation Anti-clockwise by 90\degree
Reflection in the x-axis
Reflection in the y-axis
Question 15
(3 marks)
The ratio of the cost for a one hour session with one personal trainer compared to another is 3:4
Complete the table of costs.
Answer Type: Multiple Answer
Answer:
a = £132
b = £165
c = £264
d = £88
e = £176
f = £220
g = £352
WORKING:
To work out how much personal trainer 1 charges per hour we need to divide £66 by 2
£66\div2=£33Then to calculate what personal trainer 2 charges per hour we do:
£33\div3=£11
£11\times4=£44
Question 16
(5 marks)
Kelly is going to use her spare bedroom to store some identical boxes.
Each box is a cuboid, 50 cm by 35 cm by 45 cm.
The space in her spare bedroom for boxes has:
Maximum length of 2.5 m
Maximum width of 2.8 m
Maximum height of 2.7 m
The space for boxes in her spare bedroom is currently empty.
Kelly wants to put as many boxes as possible into the room.
She can put 4 boxes into the room in one minute.
Assume that the space for boxes is in the shape of a cuboid.
16(a)
(4 marks)
Calculate how many minutes it should take Kelly to put as many boxes as possible into the spare bedroom.
Answer Type: Simple Text
Answer: 60 minutes
WORKING:
Amount of boxes that will fit along the length of the space:
2.5\div 0.5 = 5
Amount of boxes that will fit along the width of the space:
2.8 \div 0.35 = 8
Amount of boxes that can be stacked to the height of the space:
2.7\div 0.45=6
Therefore, 5\times8\times6=240 boxes can fit in the space.
So it will take Kelly 240 \div 4 = 60 minutes to put as many boxes as possible into the room.
16(b)
(1 mark)
The space in the room might not be a cuboid.
Would this affect the time it would take Kelly to fill the room with boxes?
Answer Type: Multiple Choice
Answer: Yes
Wrong Answer: No
WORKING:
It could take her more time as she would have to arrange the boxes in a different way.
Question 17
17(a)
(1 mark)
Find a and b such that, 8p+24=a(p+b)
Answer Type: Multiple Answer
Answer:
a=8
b=3
WORKING:
The common factor of 8p and 24 is 8, so we can factorise this out.
Giving us the factorised form 8(a+3)
17(b)
(2 marks)
Which of the following statements is true?
Answer Type: Multiple Choice
Answer:
2y is a term in the equation 2y=5+3x
Wrong Answers:
2y is a multiple in the equation 2y=5+3x
2y is an identity in the expression 2y=5+3x
2y is a factor in the identity 2y=5+3x
WORKING:
2y=5+3x is an equation because it is states that two expressions are equal.
Thus, 2y is a term in this equation.
Question 18
Below is a sequence of patterns made with sweets.
18(a)
(2 marks)
Which of the following expressions represents the number of sweets in pattern number n?
Answer Type: Multiple Choice
Answer: 5n-2
Wrong Answers:
3n+5
5n+3
5n
WORKING:
The amount of sweets increases by 5 from one pattern to the next.
So we know that the expression will be of the form 5n+a, for some number a
To find a, we can substitute n=1 into the expression.
This gives us 5+a
We can see that there are 3 sweets when n=1, giving us the equation 5+a=3
So, a=3-5=-2
Therefore the correct expression is 5n-2
18(b)
(2 marks)
Henry has 70 sweets.
Can he make a pattern in this sequence using all 70 of his sweets?
Answer Type: Multiple Choice
Answer: No
Wrong Answer: Yes
WORKING:
If we let 5n-2=70,
5n = 72
n=\dfrac{72}{5}=14.4
So there is no pattern number where 70 sweets are used, because n has to a whole number.
Question 19
(3 marks)
The table below shows information about the heights of 90 children.
19(a)
Find the class interval that contains the median.
(1 mark)
Answer: Multiple Choice
Answer: 155<h\le 160
Wrong Answers:
150<h\le 155
160<h\le 165
145<h\le 150
WORKING:
The median of a set of 90 numbers is half way between the 45th and 46th number.
The 45th and 46th number both lie in the interval 155<h\le 160.
19(b)
Select which frequency polygon represents the information in the table.
(2 marks)
Answer type: Multiple Choice
Answer:
Wrong Answers:
WORKING:
To draw a frequency polygon we first need to find the midpoints of the intervals.
These are: 142.5, 147.5, 152.5, 157.5, 162.5
Then plot these against their respective frequencies.
So we plot the points: (142.5, 9), (147.5, 13), (152.5, 17), (157.5, 28), (162.5, 23).
We then connect these points with straight lines to give us a frequency polygon.
Question 20
(3 marks)
In Dublin, 1 litre of petrol costs 125 cents.
In Washington DC, 1 gallon of petrol costs \$2.62.
1 US gallon = 3.785 litres.
€1 = \$1.22.
In which city is petrol better value for Money?
Answer type: Multiple Choice
Answer: Washington DC
Wrong Answer: Dublin
WORKING:
First we find the price of petrol per gallon in Dublin.
Dublin: 3.785\times1.25= €4.73 per gallon.
4.73\times1.22=\$5.77 per gallon.
We can clearly see that this is more expensive in Dublin compared to Washington DC.
Question 21
(3 marks)
A silver bar has a mass of 4.5 kg.
The density of silver is 10.49 g/cm^3.
Work out the volume of the silver bar, giving your answer to 3 significant figures.
Answer type: Simple text
Answer: 429 cm^3
WORKING:
The formula for density is:
Density = \dfrac{\text{Mass}}{\text{Volume}}
We can rearrange this to give us the formula for volume:
Volume = \dfrac{\text{Mass}}{\text{Density}}
Volume = \dfrac{4.5\times1000}{10.49}=429 cm^3 (to 3 significant figures).
Question 22
(3 marks)
There are only yellow, blue and white counters in a bag.
The ratio of the number of yellow counters to blue counters is 1:3.
The ratio of the number of blue counters to white counters is 7:5.
There are less than 130 counters in the bag.
What is the greatest possible number of white counters in the bag?
Answer type: Simple text
Answer: 45
WORKING:
We first need to convert the two ratios we have into one ratio.
To do this we see that blue counters are in both ratios, so we can combine the ratios by finding the lowest common multiple of 3 and 7, which is 21.
Ratio of yellow to blue is 1:3=7:21
Ratio of blue to white is 7:5=21:15
Thus, the ratio of yellow to blue to white is 7:21:15.
7+21+15=43=43
\dfrac{130-1}{43}=3
15\times3=45 white counters.
Question 23
(3 marks)
23(a)
Find the reciprocal of 1.25.
Give your answer as a decimal.
(1 mark)
Answer type: Simple Text
Answer: 0.8
WORKING:
1\div1.25=1\div\dfrac{5}{4}=1\times\dfrac{4}{5}=0.823(b)
(2 marks)
Kate rounds a number, x, to one decimal place.
The result is 8.7
Write down the error interval for x
Answer type : Multiple Answer
Answer:
x \ge 8.65
x < 8.75
Question 24
(5 marks)
Here is a rectangle.
The length of the rectangle is 9 cm longer than the width of the rectangle.
4 of these rectangles are used to make this 8-sided shape.
The perimeter of the 8-sided shape is 104 cm.
Work out the area of the 8-sided shape.
Answer type: Simple Text
Answer: 280 cm^2.
WORKING:
If we represent the width of the rectangle by x, the length of the rectangle =x+9.
As shown by the diagram below the perimeter of the 8-sided shape =x+9+x+x+x+9+x+x+9+x+x+9+9+9+2x=10x+54.
10x+54=104
10x=50
x=5
So, we can work out the area of one rectangle: (x+9)\times x=14\times5=70 cm^2.
Area of 4 rectangles joined together: 70\times4=280 cm^2.
Question 25
(2 marks)
Work out (12.7\times10^6)\times(4.9\times10^{-11})
Give your answer as an ordinary number.
Answer: Simple Text
Answer: 0.0006223
WORKING:
(12.7\times10^6)\times(4.9\times10^{-11})=6.223\times10^{-4}=0.0006223.
Question 26
(3 marks)
When a drawing pin is dropped it can land point down or point up.
Sarah, Jack and Mike each dropped the drawing pin a number of times.
The table below shows the number of times the drawing pin landed point down and the number of times the drawing pin landed point up for each person.
Emma is going to drop the drawing pin once.
26(a) Whose results will give the best estimate for the probability that the drawing pin will land point up?
(1 mark)
Answer: Multiple Choice
Answer: Jack
Wrong Answers:
Sarah
Mike
WORKING:
Jack’s results will give the best probability that the drawing pin will land point up because he drops the pin the most times.
26(b) (2 marks)
Oliver is going to drop the drawing pin twice.
Use all the results in the table to work out an estimate for the probability that the drawing pin will land point down the first time and point up the second time.
Answer type: Multiple Choice
Answer: \dfrac{2}{9}
Wrong Answers:
\dfrac{1}{3}
\dfrac{2}{5}
\dfrac{1}{4}
WORKING:
Total number of drops =27+58+15+17+23+10=150.
Number of times pin landed point down =27+58+15=100.
Number of times pin landed point up =17+23+10=50.
Estimate for the probability that the drawing pin will land point down the first time and point up the second time:
=\dfrac{100}{150}\times\dfrac{50}{150}=\dfrac{2}{9}Question 27
(3 marks)
Solve the simultaneous equations:
3x+y=12
2x-8y=21
Answer Type: Multiple Answer
Answer:
x=4.5
y=-1.5
WORKING:
3x+y=12 (1)
2x-8y=21 (2)
We can rearrange (1) to get an expression for y:
3x+y=12
y=12-3x (3)
We can then substitute this into (2), which gives us:
2x-8(12-3x)=21
2x-96+24x=21
26x=117
x=4.5
We can then substitute this value for x into (3), to give us y:
y=12-3(4.5)=-1.5