Q20-25 – copy from June 18 Higher Paper 2 Q1-Q6
Q1
Write \dfrac{3}{25} as a percentage.
Answer type: simple
Answer: 12 \%
Workings:
\dfrac{3}{25}=\dfrac{12}{100}=12\%1 mark
Q2
Write 4.93 correct to 1 decimal place.
Answer type: simple
Answer: 4.9
Workings:
The second decimal place has a value of 3, which is less than 5 so it rounds the answer down to 4.9
1 mark
Q3
Work out the value of 4^4
Answer type: simple
Answer: 256
Workings:
4\times4\times4\times4=2561 mark
Q4
Which of the following 6 digit numbers has a 7 as its thousands digit?
Answer type: multiple choice
Answer: 247983
Wrong Answers:
756700 576312 490071Workings:
The thousands digit is the third digit from the right.
1 mark
Q5
(a)
Change 3.5 m to cm
Answer type: simple
Answer: 350 cm
Workings:
1 m =100 cm so 3.5 m =350 cm
1 mark
(b)
Change 2.3 litres to millilitres
Answer type: simple
Answer: 2300 millilitres
Workings:
1 L = 1000 ml, so 2.3 L =2300 ml.
1 mark
(c)
Change 9500 grams to kilograms.
Answer type: simple
Answer: 9.5 kilograms
Workings:
1 kg = 1000 g, so 9500 g =9.5 kg.
1 mark
6
Denise is thinking of a number.
She says,
“My number is odd. It is a factor of 42 and a multiple of 7“
There are two possible numbers that Denise can be thinking of.
Give the values of these two numbers.
Answer type: multiple answers
Answers:
7
21
Workings:
The 7 times table is as follows:
7, 14, 21, 28, 35, 42The factor pairs of 42 are:
1\times42=42
2\times21=42
3\times14=42
6\times7=42
Hence, the only two odd numbers which appear in the seven times table and in the factors of 42 are 7 and 21
3 marks
Q7
Gunther has three cards, with the numbers 3, 6 and 9 on them.
He can combine the cards to make several three digit numbers.
List all the possible combinations, ranking them from largest to smallest.
Answer type: multiple answers
Answers:
Largest: 963
then: 936
then: 693
then: 639
then: 396
smallest: 369
2 marks
Q8
Keith buys 40 bags of crisps, 40 tubes of sweets, 40 biscuits and 40 cans of fizzy drink.
What is the total amount of money Keith spends?
Answer type: simple
Answer: £ 49.62
Workings:
Keith buys 40 bags of crisps, which can be bought in groups of 8 for £1.50. He buys 40\div 8 =5 groups. Therefore he spends 5\times £1.50=£7.50 on crisps.
He buys 40 tubes of sweets, which can be bought in groups of 5 for £0.99. He buys 40\div 5 =8 groups. Therefore he spends 8 \times £0.99 = £7.92 on sweets.
He buys 40 biscuits, which can be bought in groups of 10 for 55p. He buys 40\div10=4 groups. Therefore he spends 4\times £0.55 = £2.20 on biscuits.
He buys 40 cans of fizzy drink, which are 80p each. Therefore he spends 40\times£0.80 = £32 on fizzy drinks.
The total cost is therefore 7.50+7.92+2.20+32=49.62
5 marks
Q9
(a)
Sharon drives 184 miles in 4 hours.
What is her average speed?
Answer type: simple
Answer: 46 mph
Workings:
\text{speed} = \text{distance} \div \text{time}=\dfrac{184}{4}=46 mph
2 marks
(b)
Michelle drives at an average speed of 65 mph for 3 hours.
How many miles does Michelle drive?
Answer type: simple
Answer: 195 miles
Workings:
\text{distance} = \text{speed} \times \text{time}=65\times 3=195 mph
2 marks
Q10
(a)
Write down all the square numbers between 0 and 30
Answer type: multiple answers (any order)
Answers:
1
4
9
16
25
Workings:
1\times1=1
2\times2=4
3\times3=9
4\times4=16
5\times5=25
2 marks
(b)
Janice says,
“there are no square numbers which are also prime numbers”
Is Janice right?
Answer type: multiple choice
Answer: Yes
Wrong Answer: No
Workings:
A prime number has two factors , 1 and itself.
All square numbers except 1 have more than two factors.
Note: 1 is not a prime number – its has only one factor.
1 mark
Q11
(a)
Solve a+a+a+a-a=63
Answer type: simple
Answer:
a= 21
Workings:
3a=63
a=21
1 mark
(b)
Solve \dfrac{b}{8}=3
Answer type: simple
Answer:
b= 24
Workings:
b=3\times8=24
1 mark
(c)
Solve 6g-3=39
Answer type: simple
Answer:
g= 7
Workings:
6g=42
g=42\div6=7
1 mark
12
A group of students were asked to select a soft drink on a school trip.
The table below gives information about their answers.
Which of the following pie charts accurately represents this information?
Answer type: multiple choice
Answer:
Wrong Answers:
Workings:
The total number of students is 36
Using the data from the table, the angle for each option can be calculated as follows,
Lemonade: \dfrac{12}{36}\times360=120\degree
Cola: \dfrac{16}{36}\times360=160\degree
Orange Juice: \dfrac{8}{36}\times360=80\degree
Hence the correct option is the pie chart in which the largest angle is cola, and the angle for orange juice is less than 90\degree
3 marks
Q13
There are 253 sweets in a large jar.
42 of the sweets are strawberry flavoured.
A sweet is taken at random from the jar.
Find the probability that the sweet is not strawberry flavoured.
Give your answer as a fraction
Answer type: fraction
Answer: 211/253
Workings:
The number of sweets that are not strawberry is 253-42=211
The probability a sweet is not strawberry is therefore \dfrac{211}{253}
2 mark
Q14
A running club has two groups, over 50s and under 50s.
25 of the 70 members are over 50.
22 of the 31 members who are female are under 50.
Which of the following tree diagrams is a correct representation of this information?
Answer type: multiple choice
Answer:
Wrong Answers:
Workings:
There are 70 members in total, 25 are over fifty, so 70-25=45 are under fifty.
22 of the under fifties are female
3 marks
15
(a)
Saleem needs to work out the size of angle x in this diagram.
He writes,
x=45\degree because each angle is half a right angle.
Saleem is wrong.
Give the correct value of the angle x
Answer type: simple
Answer: x= 60 \degree
Workings:
Triangle ABC is an equilateral triangle, so the internal angles are all equal to 60\degree.
1 mark
(b)
Graeme needs to work out the size of the angle y in this diagram.
Graeme writes,
One of Graeme’s reasons is wrong.
Which of the following is the correct reason?
Answer type: multiple choice
Answer: because corresponding angles are equal
Wrong Answers:
because co-interior angles are equal
because alternate angles are equal
because angles around a point add up to 360\degree
Workings:
Angles DEI and FGI are corresponding angles, so they are equal.
1 mark
Q16
Martha buys some bags of chocolate counters.
There are 15 counters, 16 counters, 17 counters or 18 counters in each bag.
The table gives some information about the number of counters in each bag.
The total number of counters is 295
How many bags contained 18 counters?
Answer type: simple
Answer: 3
Workings:
3\times15=45
8\times16=128
4\times17=68
The total from bags with 15, 16 and 17 counters is 45+128+68=241
The total number of counters in bags with 18 counters is 295-241=54
54\div18=3
3 marks
Q17
Here is a list of ingredients for making 12 pancakes
Dougal has the following ingredients
1100 g plain flour
1800 ml milk
20 eggs
100 ml vegetable oil
What is the greatest number of pancakes Dougal can make?
Answer type: simple
Answer: 36
Workings:
Flour: 1100\div200=5.5
Milk: 1800\div600 = 3
Eggs: 20\div4=5
Vegetable oil: 100\div30=3.33
The ingredient in the shortest supply is milk, so Dougal can make 3 batches of 12 pancakes,
Total = 3\times12=36
3 marks
Q18
Which of the following fully describes the single transformation that maps shape A onto shape B?
Answer type: multiple choice
Answer: translation by the vector \begin{pmatrix} 0 \\ -5 \end{pmatrix}
Wrong Answers:
rotation 180\degree about the point (2,1)
reflection in the x axis
enlargement by a scale factor of 1 about the point (3,1)
Workings:
Shape A has been moved down 5 squares without moving left or right. This is a translation by the vector \begin{pmatrix} 0 \\ -5 \end{pmatrix}
2 marks
Q19
A local council has an area of unused space in the shape of a circle.
The council hires a local turf company to cover the unused space with grass.
The cost breakdown is as follows:
It takes the turf company four days to complete the work.
Work out the total cost.
Give your answer to the nearest pound (£).
Answer type: simple
Answer: £ 3010
Workings:
The total area, A, to be covered is,
A=\pi r^2 = \pi \times 12.5^2=490.87... m^2
The cost for the grass is therefore,
490.87... \times 4.91 = £2410.19The total cost for the labour is,
£150 \times 4 = £600The total cost is therefore,
£2410.19+£600=£3010.19 or £3010 to the nearest pound.
5 marks
Q26
Here is a triangular prism.
Work out the volume of the prism.
Give your answer to correct to 3 significant figures.
Answer type: simple
Answer: 296 cm^3
Workings:
The height, h of the prism can be calculated using Pythagoras’ theorem,
\begin{aligned}h^2 + 6.4^2 &= 12.1^2 \\ h^2 + 40.96 &= 146.41 \\ h^2 &= 105.45 \\ h &= 10.268... \end{aligned}The volume of the prism is given by the area of the cross section \times the depth
The area of the cross section, A = \dfrac{1}{2} \times b \times h where b is the width of the base
Thus, the volume of the prism, V, is,
V=\dfrac{1}{2}\times6.4\times10.268...\times9=295.74.. cm^3, which is 296 cm ^3 to three significant figures.
5 marks