1.1
(a) Express 54 as a product of its prime factors.
(2)
(b) Find the Lowest Common Multiple (LCM) of 45 and 54
(2)
November 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q4
1.2
Find the Lowest Common Multiple (LCM) of 8 and 12
(Total for Question 5 is 2 marks)
November 2010 – Unit 2 (Modular) – Higher – Non-calculator – Q5
1.3
(a) Express 48 as a product of its prime factors.
(2)
Buses to Exeter leave a bus station every 20 minutes.
Buses to Plymouth leave the bus station every 16 minutes.
A bus to Exeter and a bus to Plymouth both leave the bus station at 8 a.m.
(b) When will buses to Exeter and Plymouth next leave the bus station at the same time?
(3)
June 2011 – Unit 2 (Modular) – Higher –Non- Calculator – Q3
1.4
Veena bought some food for a barbecue.
She is going to make some hot dogs.
She needs a bread roll and a sausage for each hot dog.
There are 40 bread rolls in a pack.
There are 24 sausages in a pack.
Veena bought exactly the same number of bread rolls and sausages.
(i) How many packs of bread rolls and packs of sausages did she buy?
...……………………………. packs of bread rolls
...…………………………… packs of sausages.
(ii) How many hot dogs can she make?
...……………………………. hot dogs
(Total for Question 4 is 5 marks)
March 2011 – Unit 2 (Modular) – Higher – Non-calculator – Q4
2.1
(a)
4.52
Work out
(2)
(b)
Write as a power of 4
(i)
45 × 47
(ii)
5 3
(1)
(4 )
(1)
(c)
1
9
Find the value of n.
3n 
[Grade A]
(1)
Practice Paper Set B – Unit 2 (Modular) – Higher – Non-calculator – Q2
2.2
(a) Simplify
54 × 56
(1)
(b) Simplify
75 ÷ 72
(1)
November 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q2
4.1
(a)
Work out
2 1

3 4
Work out
3
1
2 +5
4
2
(2)
(b)
(3)
Practice Paper Set A – Unit 2 (Modular) – Higher – Non-calculator – Q6
6.1
Last year, Jora spent
30% of his salary on rent
2
of his salary on entertainment
5
1
of his salary on living expenses.
4
He saved the rest of his salary.
Jora spent £3600 on living expenses.
Work out how much money he saved.
(Total for Question 15 is 5 marks)
November 2010 – Unit 2 (Modular) – Higher – Non-calculator – Q9
6.2
Mrs Jennings shares £770 between her two sons, Pete and Tim.
She shares the money in the ratio of her sons’ ages.
The combined age of her two sons is 66 years.
Pete is 6 years younger than Tim.
Work out how much money each son gets.
You must show all your working.
Pete £ ...............................
Tim £ ...............................
(Total for Question 10 is 5 marks)
November 2011 – Unit 2 (Modular) – Higher – Non-Calculator – Q10
*6.3 Edgar had a maths test and a science test.
He got 68% in the maths test.
He got 36 out of 55 in the science test.
Which test did Edgar get the better mark in, maths or science?
(3)
Mock paper – Unit 3 (Modular) – Higher – Calculator – Q5
6.4
A company sends every item of mail by second class post.
Each item of mail is either a letter or a packet.
The tables show information about the cost of sending a letter by second class post and the
cost of sending a packet by second class post.
Letter
Weight range
0 – 100 g
Packet
Weight range
0 – 100 g
101 – 250 g
251 – 500 g
501 – 750 g
751 – 1000 g
Second Class
32p
Second Class
£1.17
£1.51
£1.95
£2.36
£2.84
The company sent 420 items by second class post.
The ratio of the number of letters sent to the number of packets sent was 5 : 2
2
of the packets sent were in the weight range 0 – 100 g.
3
The other packets sent were in the weight range 101 – 250 g.
Work out the total cost of sending the 420 items by second class post.
(Total for Question 7 is 5 marks)
November 2010 – Unit 1 (Modular) – Higher – Calculator – Q7
6.5
Bill gives away £20 000 to help animals.
He gives 20% of the £20 000 to a donkey sanctuary.
He shares the rest of the £20 000 between a dogs’ home and a cats’ home in the ratio 3 : 2
How much money does Bill give to the cats’ home?
£..............................................
(Total for Question 6 is 4 marks)
March 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q6
7.1
A cooker costs £650 plus 20% VAT.
(a) Calculate the total cost of the cooker.
(3)
A washing machine has a price of £260
In a sale its price is reduced by £39
(b) Write the reduction as a percentage of the price.
.......................... %
(2)
3 kitchen chairs cost a total of £44.79
(c) Work out the total cost of 8 of these chairs.
(2)
June 2012 – Unit 3 (Modular) – Higher – Calculator – Q4
7.2
£500 is invested at a simple interest rate of 3% per year.
After how many years is the total interest £60?
(Total for Question 2 is 3 marks)
June 2012 – Unit 3 (Modular) – Higher – Calculator – Q2
7.3
John earns £30 000 each year.
He knows that 20% of his monthly pay is deducted each month.
Work out how much money John has left each month after this deduction.
£ ..............................................................
(3)
March 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q6
*7.4
Jim buys 6 trays of Cola for £9.99 a tray.
Each tray holds 24 cans of Cola.
Jim goes to the school fete to sell his Cola.
He sells 75 cans at 80p each.
He gives 10 cans to his friends.
He sells the rest at 50p each.
24 cans
£9.99 a tray
What is Jim’s percentage profit or loss?
Give your answer to 1 decimal place.
(Total for Question 9 is 5 marks)
Practice Paper Set B – Unit 3 (Modular) – Higher – Calculator – Q9
7.5
Petra booked a family holiday.
The total cost of the holiday was £3500 plus VAT at 20%.
Petra paid £900 of the total cost when she booked the holiday.
She paid the rest of the total cost in 6 equal monthly payments.
Work out the amount of each monthly payment.
(Total for Question 7 is 5 marks)
June 2013 – Unit 3 (Modular) – Higher – Calculator – Q7
*8.1
Sam is going to paint his garden shed.
The paint is sold in two different shops.
Sam needs 7.5 litres of paint.
Sam wants to buy the cheapest paint.
He is going to buy the paint from one of these shops.
Which shop should he buy the paint from?
You must show your working.
(Total for Question 8 is 4 marks)
November 2012 – Unit 3 (Modular) – Higher – Calculator – Q8
*8.2
Debra and Mark are planning to go on a cruise.
They can travel with one of two companies, Caribbean Calypso or Royal European.
The table shows the cost per person to travel with each company.
Type of cabin
Cost per
person
Inside
Outside
Balcony
Suite
Caribbean Calypso
£1136
£1319
£1529
£2329
Royal European
£1043
£1263
£1484
£2147
Caribbean Calypso has a discount of 10% if you book online.
Royal European has a discount of 5% if you book online.
Debra and Mark are going to book a suite for their cruise.
They are going to book online.
Debra and Mark want to pay the lowest possible cost.
Which company should they choose?
You must show all your working.
(2)
March 2012 – Unit 1 (Modular) – Higher – Calculator – Q4
*8.3 Jon and Alice are planning a holiday.
They are going to stay at a hotel.
The table shows information about prices at the hotel.
Price per person per night (£)
Dinner(£)
Double room
Single room
per person per day
01 Nov – 29April
59.75
118.00
31.75
30 April – 08 July
74.25
147.00
31.00
09 July – 29 Aug
81.75
161.75
31.00
74.25
147.00
30 Aug – 31 Oct
Saver Prices
5 nights for the price of 4 nights from 1st May to 4th July.
3 nights for the price of 2 nights in November.
31.00
Jon and Alice will stay in a double room.
They will eat dinner at the hotel every day.
They can stay at the hotel for 3 nights in June or 4 nights in November.
Which of these holidays is cheaper?
(Total for Question 8 is 5 marks)
March 2011 – Unit 1 (Modular) – Higher – Calculator – Q8
8.4
The table shows the costs, per person, of a holiday at two different hotels.
It shows the cost for 5 nights and the cost for each extra night.
It also shows the discount for each child.
ParkPalace
Dubai Grand
5 nights
extra
night
5 nights
extra
night
01 Jan – 31 Mar
£1169
£150
£849
£86
01 Apr – 09 Apr
£1229
£150
£1219
£95
10 Apr – 15 Jul
£810
£80
£853
£53
16 Jul – 20 Aug
£810
£80
£854
£53
21 Aug – 10 Dec
£810
£80
£869
£94
Date holiday starts
Discount for each child
1
off
5
15% off
There are two adults and two children in the Smith family.
The family want a holiday for 7 nights, starting on 1st August.
One hotel will be cheaper for them than the other hotel.
Work out the cost of the cheaper holiday.
You must show all your working.
(Total for Question 8 is 6 marks)
March 2011 – Unit 2 (Modular) – Higher – Non-calculator – Q8
*8.5 Mr and Mrs Jones are planning a holiday to the Majestic Hotel in the Cape Verde Islands.
The table gives information about the prices of holidays to the Majestic Hotel.
MAJESTIC HOTEL, Cape VerdeIslands
Price per adult
Departures
7 nights
14 nights
1 Jan – 8 Jan
£694
£825
9 Jan – 28 Jan
£679
£804
29 Jan – 5 Feb
£687
£815
6 Feb – 18 Feb
£769
£835
19 Feb – 8 Mar
£714
£817
9 Mar – 31 Mar
£685
£805
1 Apr – 9 Apr
£788
£862
10 Apr – 30 Apr
£748
£802
Price per child: 95% of adult price for 7 nights or 85% of adult price for 14 nights.
Mr and Mrs Jones are thinking about going on holiday
on 20 February for 7 nights
or
on 10 April for 14 nights.
Mr and Mrs Jones have 2 children.
Compare the costs of these two holidays for the Jones family.
(Total for Question 2 is 5 marks)
November 2010 – Unit 1 (Modular) – Higher – Calculator – Q2
*8.6 Pete and Sue are going to take their children to France.
They will travel together on the same ferry.
They will travel with one of two ferry companies, Easy Ferry or Seawagon.
The tables give information about the costs for each adult and each child to travel with these
ferry companies.
Easy Ferry
July
August
Date
1 – 10
11 – 21
22 – 31
1 – 10
11 – 21
22 – 31
Adult
£32.00
£36.50
£39.50
£42.25
£42.25
£37.75
Child
£18.00
£20.25
£23.75
£25.85
£25.85
£21.00
Seawagon
July
August
Date
1 – 10
11 – 21
22 – 31
1 – 10
11 – 21
22 – 31
Adult
£33.50
£37.50
£40.25
£43.85
£44.95
£38.50
Child
£17.25
£19.75
£21.85
£24.65
£23.95
£19.95
The table below gives information about the discount they will get from each ferry company
if they book early.
Early booking discount
Easy Ferry
1
off
3
Seawagon
25% off
Pete and Sue have three children.
They will travel on 25 July.
They will book early.
Pete and Sue will travel with the cheaper ferry company.
Which ferry company?
You must show all your working.
(5)
June 2012 – Unit 1 (Modular) – Higher – Calculator – Q4
*8.7
Joan is planning a skiing holiday in Hinterglemm for herself and her two children.
They are going skiing for 6 days.
The table shows the costs of ski hire, of boot hire and of buying lift passes in two shops in
Hinterglemm.
All prices are in Euros.
Shop A
Adult
Child
Ski hire
Boot hire
Lift pass
6 days
111
53
236
13 days
168
90
314
6 days
78
52
165
13 days
122
87
210
Ski hire
Boot hire
Lift pass
6 days
108
54
242
13 days
170
89
324
6 days
68
48
160
13 days
118
85
205
Shop B
Adult
Child
Joan will use her own skis and her own boots.
For 6 days she will need
to hire skis for each of her two children
to hire boots for each of her two children
and to buy lift passes for herself and each of her two children.
Shop A gives 5% off the total cost.
Shop B gives 3% off the total cost.
Joan wants to hire the skis and boots and buy the lift passes from the same shop.
She wants to get everything from the cheaper shop.
Which shop is cheaper for Joan?
You must show all your working.
(Total for Question 8 is 5 marks)
November 2012 – Unit 1 (Modular) – Higher – Calculator – Q8
*8.8 Ketchup is sold in three different sizes of bottle.
Small bottle
Medium bottle
Large bottle
A small bottle contains 342 g of ketchup and costs 88p.
A medium bottle contains 570 g of ketchup and costs £1.95.
A large bottle contains 1500 g of ketchup and costs £3.99.
Which bottle is the best value for money?
You must show your working.
(Total for Question 9 is 4 marks)
June 2013 – Unit 3 (Modular) – Higher – Calculator – Q9
9.1
Work out
1
3
3 4
3
4
(Total for Question 3 is 2 marks)
June 2012 – Unit 3 (Modular) – Higher – Calculator – Q3
9.2
Use your calculator to work out
67.92  13.9
3 .4  9 . 8
Write down all the figures from your calculator display.
You must give your answer as a decimal.
(Total for Question 2 is 2 marks)
Mock paper – Unit 3 (Modular) – Higher – Calculator – Q2
9.3
Use your calculator to work out
13.7  5.862
2.54  1.96
Write down all the figures on your calculator display.
You must give your answer as a decimal.
(Total for Question 6 is 2 marks)
Practice Paper Set B – Unit 3 (Modular) – Higher – Calculator – Q6
9.4
(a) Work out the value of
 30
2.5 2
Give your answer correct to 3 decimal places.
(2)
March 2013 – Unit 3 (Modular) – Higher – Calculator – Q9
9.5
Use your calculator to work out
40.96
.
7.1  2.48
Write down all the figures on your calculator display.
You must give your answer as a decimal.
(Total for Question 3 is 2 marks)
June 2013 – Unit 3 (Modular) – Higher – Calculator – Q3
10.1 (a) Simplify 3y + 2x – 4 + 5x + 7
(1)
(b) Factorise 2x2 – 4x (2)
(c) Expand and simplify 11 – 3(x + 2)
(2)
(d) Expand and simplify (x – 6)(3x + 7)
[Grade B]
(2)
June 2011 – Unit 2 (Modular) – Higher – Non-Calculator – Q2
10.2 (a) Simplify p3 × p5
h7
(b) Simplify 2 (1)
h
(1)
(c) Simplify (x2)3(1)
June 2011 – Unit 2 (Modular) – Higher –Non- Calculator – Q8
10.3 (a) Factorise
10a + 5
(1)
(b) Expand and simplify
5(x + 7) + 3(x – 2)
(c) Factorise completely
3a2b + 6ab2
(2)
[Grade B]
(2)
June 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q6
10.4
(a) Simplify 5f × 4g
(1)
9a + 3(8 – 2a)(2)
(b) Expand and simplify
(c) Simplify c2 × c6(1)
(d) Simplify (x5)3
(1)
(e) Factorise 7y + 21
10.5 (a) Factorise
(1)
November 2011 – Unit 2 (Modular) – Higher – Non-Calculator – Q2
3t + 12
(1)
(b) (i) Expand and simplify
7(2x + 1) + 6(x + 3)
(ii)Show that when x is a whole number
7(2x + 1) + 6(x + 3)
is always a multiple of 5
(3)
March 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q9
11.6 (a) Simplify 2e + 3f – e + 4f
(2)
(b) Expand 5(2c + 3d)
(1)
(c) Here are two straight lines, ABCDE and PQ.
In the diagrams all the lengths are in cm.
AE = 2PQ.
Find an expression, in terms of x, for the length of DE.
Give your answer in its simplest form.
.............................................. cm
(4)
November 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q7
3(2p – 5) = 21
11.1 (a) Solve
p = .............................................
(3)
9x – 11 = 5x + 7
(b) Solve
x = .............................................
(3)
November 2012 – Unit 3 (Modular) – Higher – Calculator – Q6
*11.2
The area of this shape is 38 cm².
All the measurements are in cm.
3x + 5
3
8
2x – 3
Find the length of the smallest side.
(Total for Question 8 is 4 marks)
Practice Paper Set B – Unit 3 (Modular) – Higher – Calculator – Q8
11.3 (a)
Solve
5x + 4 = 2(4x – 3)
x = ……………………..
(3)
(b)
Solve
2x  3 x  4

5
6
2
[Grade A]
x = …………………
(3)
Practice Paper Set B – Unit 3 (Modular) – Higher – Calculator – Q10
11.4 (a)
Solve
3x – 5 = 7x + 30
(2)
(b)
Solve
20  2 x
 2x  3
5
(3)
Practice Paper Set C – Unit 3 (Modular) – Higher – Calculator – Q10
11.5 (a) Solve
2x + 3 = x – 4
x = ..............................................
(2)
(b) Solve
4(x – 5) = 14
x = ..............................................
(2)
March 2013 – Unit 3 (Modular) – Higher – Calculator – Q12
11.6 Dan has some marbles.
Ellie has twice as many marbles as Dan.
Frank has 15 marbles.
Dan, Ellie and Frank have a total of 63 marbles.
How many marbles does Dan have?
(Total for Question 8 is 3 marks)
June 2013 – Unit 3 (Modular) – Higher – Calculator – Q8
*12.1
This formula is used to work out the body mass index, B, for a person of mass M kg and
height H metres.
B=
M
H2
A person with a body mass index between 25 and 30 is overweight.
Arthur has a mass of 96 kg.
He has a height of 2 metres.
Is Arthur overweight?
You must show all your working.
(Total for Question 14 is 3 marks)
November 2011 – Unit 2 (Modular) – Higher – Non-Calculator – Q6
12.2 R = 4(3y – 5)
R = 32
(a)
Work out the value of y.
(2)
F = ma + b
(b)
Make m the subject of the formula.
m = ………………….
(2)
Practice Paper Set B – Unit 3 (Modular) – Higher – Calculator – Q1
13.1 The equation
x3 + 10x = 23
has a solution between 1 and 2
Use a trial and improvement method to find the solution.
Give your answer correct to one decimal place.
You must show all your working.
(Total for Question 7 is 4 marks)
June 2012 – Unit 3 (Modular) – Higher – Calculator – Q7
13.2 The equation
x3 – x = 32
has a solution between 3 and 4
Use a trial and improvement method to find this solution.
Give your solution correct to one decimal place.
You must show all your working.
x = .............................................
(Total for Question 11 is 4 marks)
November 2012 – Unit 3 (Modular) – Higher – Calculator – Q11
13.3 The equation x3 + 6x2 = 500 has a solution between 6 and 7
Use a trial and improvement method to find this solution.
Give your answer correct to one decimal place.
You must show all your working.
x = ..............................................
(Total for Question 10 is 4 marks)
Mock paper – Unit 3 (Modular) – Higher – Calculator – Q10
13.4 The equation
x3 – 6x = 84
has a solution between 4 and 5.
Use a trial and improvement method to find this solution.
Give your answer correct to one decimal place.
You must show all your working.
(Total for Question 11 is 4 marks)
June 2013 – Unit 3 (Modular) – Higher – Calculator – Q11
14.1 3x + 5 > 16
xis an integer.
Find the smallest value of x.
(Total for Question 1 is 5 marks)
November 2012 – Unit 3 (Modular) – Higher – Calculator – Q1
14.2 (a)
–5 <n 2
n is an integer
Write down all the possible values of n.
(b)
(2)
Here is an inequality, in x, shown on a number line.
x
–4 –3 –2 –1
0
1
2
3
4
5
Write down the inequality.
(2)
Practice Paper Set A – Unit 3 (Modular) – Higher – Calculator – Q6
14.3 (a)
–1 <y< 4
On the number line below mark the inequality
y
–4
–3
–2
–1
0
1
2
3
4
5
(1)
(b)
Here is an inequality, in x, shown on a number line.
x
–4 –3 –2 –1
Write down the inequality.
0
1
2
3
4
5
(2)
(c)
Solve the inequality
3t + 5 > 17
(2)
Practice Paper Set B – Unit 3 (Modular) – Higher – Calculator – Q2
14.4
–4 <n  1
n is an integer.
(a) Write down all the possible values of n.
(2)
(b) Write down the inequalities represented on the number line.
(2)
March 2013 – Unit 3 (Modular) – Higher – Calculator – Q4
15.1 The point A has coordinates (3, 8).
The point B has coordinates (7, 5).
M is the midpoint of the line segment AB.
Find the coordinates of M.
(2)
June 2011 – Unit 2 (Modular) – Higher –Non- Calculator – Q7
15.2
Find the coordinates of the midpoint of the line joining the points (1, 2) and (4, 0).
March 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q3
15.3. The graph shows information about the distances travelled by a car for different amounts of
petrol used.
(a) Find the gradient of the straight line.
(2)
(b) Write down an interpretation of this gradient.
(1)
June 2012 – Unit 3 (Modular) – Higher – Calculator – Q8
15.4 The straight line P has been drawn on a grid.
Find the gradient of the line P.
(Total for Question 7 is 2 marks)
June 2013 – Unit 1 (Modular) – Higher – Calculator – Q7
16.1 (a)
y = x² + x – 3
Complete the table of values for
x
–4
y
9
–3
–2
–1
–1
–3
0
1
2
(2)
(b)
On the grid below, draw the graph of y = x² + x – 3 for values of x from –4 to 2
y
10
8
6
4
2
–4
–3
–2
–1
O
1
2
–2
–4
–5
(2)
(c)
x² + x – 3 = 0
……………………….
(2)
Practice Paper Set C – Unit 3 (Modular) – Higher – Calculator – Q4
Use your graph to find estimates for the solutions of
[Grade B]
16.2 (a) Complete the table of values for y = 2x2 – 1
x
–2
y
7
–1
0
1
2
1
(2)
(b) On the grid below, draw the graph of y = 2x2 – 1 for values of x from x = –2 to x = 2
(2)
(c) Use your graph to write down estimates of the solutions of the equation 2x2 – 1 = 0
[Grade B]
....................................................................
(2)
June 2012 – Unit 3 (Modular) – Higher – Calculator – Q11
16.3 (a) Complete the table of values for y = x2 – 4
x
y
–3
–2
–1
0
–3
0
1
2
3
0
5
(2)
(b) On the grid, draw the graph of y = x2 – 4 for x = –3 to x = 3
(2)
(Total for Question 6 is 4 marks)
March 2013 – Unit 3 (Modular) – Higher – Calculator – Q6
15.4 Water flows out of a cylindrical tank at a constant rate.
The graph shows how the depth of water in the tank varies with time.
(a) Work out the gradient of the straight line.
(2)
(b) Write down a practical interpretation of the value you worked out in part (a).
(1)
November 2010 – Unit 1 (Modular) – Higher – Calculator – Q8
17.1 The graph shows the distance travelled by two trains.
(a) Work out the gradient of the line for train A.
(2)
(b) Which train is travelling at the greater speed?
You must explain your answer.
(1)
(c) After how many minutes has train A gone 10 miles further than train B?
....................................minutes
(1)
November 2011 – Unit 1 (Modular) – Higher – Calculator – Q7
17.2
You can use this formula to change a temperature C, in °C, to a temperature F,in °F.
F = 1.8C + 32
(a) Use the formula to change 20 °C into °F.
............................... °F
(2)
(b) On the grid below, draw a conversion graph that can be used to change between
temperatures in °C and temperatures in °F.
(3)
c)
Use your graph to change 100 °F into °C.
............................... °C
(1)
November 2010 – Unit 2 (Modular) – Higher – Non-calculator – Q7
17.3 You can use the graph opposite to find out how much Lethna has to pay for the units
ofelectricity she has used.
Lethna pays at one rate for the first 100 units of electricity she uses.
She pays at a different rate for all the other units of electricity she uses.
Lethna uses a total of 900 units of electricity.
Work out how much she must pay.
£.........................................................
(Total for Question 5 is 3 marks)
November 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q5
17.4 Water is leaking out of two containers.
The water started to leak out of the containers at the same time.
The straight line P shows information about the amount of water, in litres, in container P.
The straight line Q shows information about the amount of water, in litres, in container Q.
(a) Work out the gradient of line P.
(2)
One container will become empty first.
(b) (i) Which container?
You must explain your answer.
(ii) How much water is then left in the other container?
............................... litres
(2)
March 2012 – Unit 1 (Modular) – Higher – Calculator – Q6
*17.5 You can use this graph to convert between litres and gallons.
Jack buys 8 gallons of diesel.He pays £52.
Francoise buys 40 litres of diesel.She pays £58.
Who got the better value for their money, Jack or Francoise?
You must show your working.
(Total for Question 4 is 3 marks)
November 2013 – Unit 1 (Modular) – Higher – Calculator – Q4
*18.1
ABC is parallel to DEF.
EBP is a straight line.
AB = EB.
Angle PBC = 40°.
Angle AED= x°.
Work out the value of x.
Give a reason for each stage of your working.
(5)
March 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q10
19.1 The interior angle of a regular polygon is 160°.
(i) Write down the size of an exterior angle of the polygon.
(ii) Work out the number of sides of the polygon.
(Total for Question 6 is 3 marks)
March 2011 – Unit 2 (Modular) – Higher – Non-calculator – Q6
19.2
The diagram shows 3 sides of a regular polygon.
Each interior angle of the regular polygon is 140°.
Work out the number of sides of the regular polygon.
(Total for Question 6 is 3 marks)
November 2010 – Unit 2 (Modular) – Higher – Non-calculator – Q6
19.3 The diagram shows a regular hexagon and a regular octagon.
x
Find the size of the angle marked x.
You must show all the stages in your working.
Give the reasons for your answer.
(Total for Question 4 is 6 marks)
Practice Paper Set B – Unit 3 (Modular) – Higher – Calculator – Q4
19.5
ABCDE is a regular pentagon.
ABP is an equilateral triangle.
Work out the size of angle x.
.............................................. °
(Total for Question 8 is 4 marks)
March 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q8
20.1 Jake makes a picture frame from 4 identical pieces of card.
Each piece of card is in the shape of a trapezium.
The outer edge of the frame is a square of side 12 cm.
The inner edge of the frame is a square of side 8 cm.
Work out the area of each piece of card.
.............................................................. cm2
(Total for Question 16 is 4 marks)
November 2011 – Unit 2 (Modular) – Higher – Non-Calculator – Q4
20.2 A piece of card is in the shape of a trapezium.
A hole is cut in the card.
The hole is in the shape of a trapezium.
Work out the area of the shaded region.
.............................................................. cm2
(Total for Question 7 is 3 marks)
March 2011 – Unit 2 (Modular) – Higher – Non-calculator – Q7
20.3 Janice cuts a triangle from a rectangular piece of metal.
She uses the rest of the metal to make a name badge.
The rectangle has length 6 cm and width 3 cm.
The right-angled triangle has base 2 cm and height 3 cm.
Work out the area of the name badge.
20.4
(Total for Question 10 is 4 marks)
June 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q10
The diagram shows the plan of the floor of Mrs Phillips’ living room.
Mrs Phillips is going to cover the floor with floor boards.
One pack of floor boards will cover 2.5 m2.
How many packs of floor boards does she need?
You must show your working.
(4)
June 2011 – Unit 2 (Modular) – Higher – Non-Calculator - Q6
20.5
The diagram shows a wall in Neil’s house.
Neil is going to cover the wall completely with tiles.
Each tile has a width of 30 cm and a height of 40 cm.
The tiles are sold in packs.
There are 6 tiles in each pack.
Each pack costs £15
Work out the least amount of money Neil needs to pay for the tiles.
You must show all your working.
£ .............................................
(Total for Question 6 is 4 marks)
November 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q6
20.6
Mrs Kunal’s garden is in the shape of a rectangle.
Part of the garden is a patio in the shape of a triangle.
The rest of the garden is grass.
Mrs Kunal wants to spread fertiliser over all her grass.
One box of fertiliser is enough for 32 m2 of grass.
How many boxes of fertiliser will she need?
You must show your working.
(Total for Question 8 is 4 marks)
November 2010 – Unit 2 (Modular) – Higher – Non-calculator – Q8
*20.7 Amy has a field in the shape of a trapezium.
200 m
Diagram NOT
accurately drawn
125 m
100 m
275 m
She wants to sell the field.
Farmer Boyce offers her £1 per m²
Farmer Giles offers her £24 000
Which is the better offer?
You must show all your working.
(Total for Question 7 is 4 marks)
Practice Paper Set A – Unit 2 (Modular) – Higher – Non-calculator – Q7
*20.8
Kevin wants to tile two walls in his bathroom.
3.6 m
1.8 m
2.4 m
Tile
12 cm
15 cm
One wall is a rectangle with length 3.6 m by 2.4 m.
The other wall is a rectangle with length 2.1 m by 2.4 m.
The tiles that Kevin wants to use are 12 cm wide and 15 cm high.
There are 40 tiles in each box.
How many boxes of tiles does Kevin need to buy?
(Total for Question 6 is 6 marks)
Practice Paper Set B – Unit 2 (Modular) – Higher – Non-calculator – Q6
20.9 (b) Change 4.5 km2 to m2.
.............................................. m2
(2)
March 2013 – Unit 3 (Modular) – Higher – Calculator – Q9
21.
The diagram shows the region inside a running track.
This region is in the shape of a rectangle with a semi-circle at both ends.
The rectangle has a length of 105 m.
It has a width of 64 m.
The semi-circles each have a diameter of 64 m.
The groundsman is going to cover this region with grass seed.
One sack of grass seed will cover 250 m2.
How many sacks of grass seed does the groundsman need?
You must show all your working.
(Total for Question 9 is 4 marks)
Mock paper – Unit 3 (Modular) – Higher – Calculator – Q9
22.1
Calculate the length of AB.
Give your answer correct to 1 decimal place.
............................................. cm
(Total for Question 7 is 3 marks)
November 2012 – Unit 3 (Modular) – Higher – Calculator – Q7
22.2 The diagram shows the marking on a school playing field.
The diagram shows a rectangle and its diagonals.
Work out the total length of the four sides of the rectangle and its diagonals.
(Total for Question 9 is 5 marks)
June 2012 – Unit 3 (Modular) – Higher – Calculator – Q9
*23.1 Marc drives a truck.
The truck pulls a container.
The container is a cuboid 10 m by 4 m by 5 m.
Diagram NOT
accurately drawn
Marc fills the container with boxes.
Each box is a cuboid 50 cm by 40 cm by 20 cm.
Show that Marc can put no more than 5000 boxes into the container.
(Total for Question 4 is 4 marks)
March 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q4
23.2 The diagram shows a prism.
Work out the volume of the prism.
........................................cm3
(Total for Question 8 is 4 marks)
Mock paper – Unit 3 (Modular) – Higher – Calculator – Q8
23.3
Work out the total surface area of this triangular prism.
(Total for Question 5 is 4 marks)
March 2011 – Unit 2 (Modular) – Higher – Non-calculator – Q5
23.4 This diagram, drawn on a centimetre grid, is an accurate net of a triangular prism.
Work out the volume of the prism.
(Total for Question 7 is 4 marks)
November 2011 – Unit 2 (Modular) – Higher – Non-Calculator – Q7
23.5 The diagram shows an L-shaped prism.
Calculate the volume of the prism.
............................................. cm3
(Total for Question 9 is 3 marks)
November 2012 – Unit 3 (Modular) – Higher – Calculator – Q9
23.6
Terry fills a carton with boxes.
Each box is a cube of side 10 cm.
The carton is a cuboid with
length 60 cm
width 50 cm
height 30 cm
Work out the number of boxes Terry needs to fill one carton completely.
(Total for Question 7 is 3 marks)
June 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q7
23.7
Work out the volume of the triangular prism.
.............................................. cm3
(Total for Question 9 is 2 marks)
June 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q9
23.8 Here is the cross section of a steel girder.
The cross section has two lines of symmetry.
The girder is a prism.
The length of the girder is 200 cm.
Work out the volume of the girder.
.............................................. cm3
(Total for Question 11 is 5 marks)
November 2013 – Unit 2 (Modular) – Higher – Non-Calculator – Q11
24.1 The diagram shows an accurate scale drawing of two towns, Middleton and Newtown.
Scale: 1 cm to 2 km
A new shopping centre is going to be built.
The shopping centre will be
less than 12 km from Middleton and
less than 15 km from Newtown.
On the diagram, shade the region where the shopping centre can be built.
(Total for Question 6 is 3 marks)
Mock paper – Unit 3 (Modular) – Higher – Calculator – Q6
24.2 The diagram represents a triangular garden ABC.
The scale of the diagram is 1 cm represents 1 m.
A tree is to be planted in the garden so that it is
nearer to AB than to AC,
within 5 m of point A.
On the diagram, shade the region where the tree may be planted.
B
A
C
(Total 3 marks)
Practice Paper Set C – Unit 3 (Modular) – Higher – Calculator – Q7
24.3 Here is a scale drawing of Gilda’s garden.
Scale: 1 cm represents 1 m
Gilda is going to plant an elm tree in the garden.
She must plant the elm tree at least 4 metres from the oak tree.
On the diagram, show by shading the region where Gilda can plant the elm tree.
(Total for Question 3 is 2 marks)
March 2013 – Unit 3 (Modular) – Higher – Calculator – Q3
24.4 The map shows the positions of two schools, Alford and Bancroft.
Scale 1 cm represents 1 km
A new school is going to be built.
The new school will be less than 5 kilometres from Alford.
It will be nearer to Bancroft than to Alford.
Shade the region on the map where the new school can be built.
(Total for Question 7 is 3 marks)
November 2013 – Unit 3 (Modular) – Higher – Calculator – Q7
25.1
Caroline is driving her car in France.
She sees this road sign.
Caroline is going to Rennes on the N12
She stops driving 10 miles from the road sign.
Work out how much further Caroline has to drive to get to Rennes
..............................................................
(Total for Question 7 is 3 marks)
March 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q7
25.2 Here is a list of ingredients for making apple crumble for 2 people.
Apple Crumble
for 2 people
10 ounces apples
4 ounces flour
2 ounces sugar
1 ounce butter
1 tablespoon water
1 teaspoon baking powder
1 ounce = 28 grams
1 tablespoon = 15 ml
1 teaspoon = 5 ml
Anne is going to make apple crumble for 5 people.
(a) Work out how much flour she needs.
Give your answer in grams.
............................................. grams
(3)
David is making an apple crumble.
He uses 140 grams of butter.
(b) Work out how many people he is making apple crumble for.
(2)
November 2012 – Unit 2 (Modular) – Higher – Non-Calculator – Q2
25.3. Jonty is going to completely fill an empty tank with water.
The tank holds 2 m3.
How many litres of water does he need?
……………………. litres
(Total for Question 8 is 3 marks)
Practice Paper Set A – Unit 3 (Modular) – Higher – Calculator – Q8
*25.4 Rodney bought some old railway track at an auction.
Each piece of track was 20 metres long.
Each piece of track weighed 40 kg per metre length.
Rodney has a lorry that can carry a maximum of 45 tonnes.
What is the maximum number of railway tracks that Rodney can fit onto the lorry?
(Total for Question 10 is 6 marks)
Practice Paper Set B – Unit 2 (Modular) – Higher – Non-Calculator – Q10
25.5 Sam has a swimming pool.
There are 60 000 litres of water in the swimming pool.
Sam wants to put chlorine powder in the water.
She needs 0.75 mg of chlorine powder for each litre of water.
Work out the total amount of chlorine powder Sam needs.
Give your answer in grams.
........................................ g
(Total for Question 11 is 3 marks)
March 2013 – Unit 3 (Modular) – Higher – Calculator – Q11
26.1 The diagram shows the position of town A.
Town B is 64 km from town A on a bearing of 070°.
Mark the position of town B, with a cross (×).
Use a scale of 1 cm represents 10 km.
(Total for Question 5 is 2 marks)
November 2012 – Unit 3 (Modular) – Higher – Calculator – Q5
26.2
N
A
Diagram NOT
accurately drawn
63º
138º
P
B
Work out the bearing of
(i)
B from P,
…………………º
(ii)
P from A.
………………….º
(Total for Question 7 is 4 marks)
Practice Paper Set C – Unit 3 (Modular) – Higher – Calculator – Q7
26.3 The diagram shows the position of two ports, P and Q.
A ship sails from port P to port Q.
N
N
Q
P
Scale: 1 cm represents 20 km
(a)
Find the bearing of port P from port Q
(1)
(b)
Work out the real distance between port P and port Q.
Use the scale 1 cm represents 20 km.
.................................. km(2)
Port R is 120 km on a bearing of 120 from port Q.
(c)
On the diagram, mark port R with a cross ().
Label it R.
(2)
Practice Paper Set B – Unit 3 (Modular) – Higher – Calculator – Q3
26.4 The diagram shows the position of two boats, B and C.
Boat T is on a bearing of 060° from boat B.
Boat T is on a bearing of 285° from boat C.
In the space above, draw an accurate diagram to show the position of boat T.
Mark the position of boat T with a cross (×).
Label it T.
(Total for Question 6 is 3 marks)
June 2013 – Unit 3 (Modular) – Higher – Calculator – Q6
27.1
Mr Smith drives 24 miles to work.
On Monday his journey to work takes 30 minutes.
On Tuesday the average speed of his journey to work is 56 km/h.
Did Mr Smith drive more quickly to work on Monday or Tuesday?
You must show all your working.
(4)
June 2011 – Unit 2 (Modular) – Higher –Non- Calculator – Q9
27.2 A plane takes 30 seconds to fly a distance of 8 kilometres.
Work out the average speed of the plane, in miles per hour.
.............................................................. miles per hour
(Total for Question 9 is 3 marks)
March 2011 – Unit 2 (Modular) – Higher – Non-calculator – Q9
*27.3 Lisa cycles to work.
The travel graph shows information about her journey to work on Tuesday.
Martin also cycles to work.
On Tuesday his average speed was 16 km per hour.
Who has the greater average speed, Lisa or Martin?
You must show all your working.
(Total for Question 9 is 4 marks)
November 2011 – Unit 2 (Modular) – Higher – Non-Calculator – Q9
28.1 Dishwasher tablets are sold in two sizes of box.
A small box contains 15 tablets and costs £3.95
A large box contains 22 tablets and costs £6.15
*(a) Which size of box gives the better value for money?
You must show all your working. (4)
The weight of the large box is 357 grams, to the nearest gram.
(b) (i) What is the minimum possible weight of the box?
........................................ grams
(ii) What is the maximum possible weight of the box?
........................................ grams (2)
November 2011 – Unit 1 (Modular) – Higher – Calculator – Q6
28.2 Sonia measures the length of her pencil case as 15cm to the nearest cm.
(a)
Write down the greatest length this could be.
………….………….cm
(1)
(b)
Write down the least length this could be.
……………………..
(1)
Practice Paper Set A – Unit 1 (Modular) – Higher – Calculator – Q8
28.3 A piece of wood has a length of 65 centimetres to the nearest centimetre.
(a) What is the least possible length of the piece of wood?
.............................................. cm
(1)
(b) What is the greatest possible length of the piece of wood?
.............................................. cm
(1)
March 2013 – Unit 1 (Modular) – Higher – Calculator – Q7
29.1 Gulam and Alexi measured the heights of some wild grasses.
Here are their results
Height (h cm)
(a)
Frequency
0h5
3
5  h  10
6
10  h  15
5
15  h  20
7
20  h  25
3
25  h  30
1
On the grid below draw a frequency polygon to show this information.
10
8
frequency
6
4
2
0
0
5
10
15
height (cm)
20
25
30
(2)
(b)
In which group does the median height lie?
…………………………
(1)
Practice Paper Set C – Unit 1 (Modular) – Higher – Calculator – Q8
29.2 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.
Length of time (t minutes)
Frequency
0 <t ≤ 10
6
10 <t ≤ 20
9
20 <t ≤ 30
8
30 <t ≤ 40
7
40 <t ≤ 50
5
On the grid below, draw a frequency polygon for this information.
(Total for Question 5 is 2 marks)
June 2013 – Unit 1 (Modular) – Higher – Calculator – Q5
31.1 The table gives information about the speeds of 75 cars on a road.
Speed (s km/h)
Frequency
30 s < 40
7
40 s < 50
22
50 s < 60
34
60 s < 70
12
Work out an estimate for the mean speed.
....................................................... km/h(4)
June 2012 – Unit 1 (Modular) – Higher – Calculator – Q6
31.2 Faisel weighed 50 pumpkins.
The grouped frequency table gives some information about the weights of the pumpkins.
Weight (w kilograms)
Frequency
0 <w 4
11
4<w 8
23
8<w  12
14
12<w  16
2
Work out an estimate for the mean weight.
............................................. kg
(4)
November 2012 – Unit 1 (Modular) – Higher – Calculator – Q3
31.3
The table shows information about midday temperatures.
Temperature (t °C)
10 t <15
15 t <20
20 t <25
25 t <30
30 t <35
35 t <40
Number of days
6
4
24
44
10
4
(a) Write down the modal class interval.
(1)
(b) Work out an estimate for the mean midday temperature.
Give your answer correct to 3 significant figures
.............................................................. °C
(4)
(c) On the grid opposite, draw a cumulative frequency graph for the information from the table
about the midday temperatures.[Grade B]
d) Find estimates for the median and the interquartile range of these midday temperatures.
[Grade B]
Median .............................................................. °C
Interquartile range .............................................................. °C
(3)
June 2011 – Unit 1 (Modular) – Higher – Calculator – Q8
32.1 23 girls have a mean height of 153 cm.
17 boys have a mean height of 165 cm.
Work out the mean height of all 40 children.
.............................................................. cm (3)
June 2012 – Unit 1 (Modular)– Higher – Calculator – Q8
32.2 5 female giraffes have a mean weight of x kg.
7 male giraffes have a mean weight of y kg.
Write down an expression, in terms of x and y, for the mean weight of all 12 giraffes.
(Total for Question 10 is 2 marks)
November 2012 – Unit 1 (Modular) – Higher – Calculator – Q10
32.3 Susie has to deliver some packages and some parcels.
The total number of packages is 4 times the number of parcels.
The total number of packages and parcels is 40
Each parcel has a weight of 1.5 kg.
The total weight of the packages and parcels is 37.6 kg.
Each of the packages has the same weight.
Work out the weight of each package.
(Total for Question 10 is 4 marks)
June 2012 – Unit 3 (Modular) – Higher – Calculator – Q10
32.4 Daniela works in a shop.
Daniela served 50 customers in the morning.
She served 75 customers in the afternoon.
The mean time to serve 50 customers in the morning was 48.7 seconds.
The mean time to serve all 125 customers was 50.2 seconds.
(a) Work out the mean time to serve the 75 customers in the afternoon.
.............................................................. seconds (3)
For the 75 customers served in the afternoon
the least time was 18 seconds
the greatest time was 96 seconds
the median time was 56 seconds
the lower quartile was 32 seconds
the upper quartile was 72 seconds
(b) On the grid, draw a box plot for this information.
[Grade B]
(3)
March 2012 – Unit 1 (Modular)– Higher – Calculator - Q10
32.5 The table gives information about the time it took each of 80 children to do a jigsaw
puzzle.
Boys
Number of children
Mean time (minutes)
32
32.4
48
Girls
Work out the mean time for all 80 children.
28.4
.............................................. minutes
(Total for Question 10 is 3 marks)
November 2013 – Unit 1 (Modular) – Higher – Calculator – Q10
*33.1 Zoe recorded the heart rates, in beats per minute, of each of 15 people.
Zoe then asked the 15 people to walk up some stairs.
She recorded their heart rates again.
She showed her results in a back-to-back stem and leaf diagram.
Compare the heart rates of the people before they walked up the stairswith their heart rates
after they walked up the stairs.
(Total for Question 4 is 6 marks)
November 2010 – Unit 1 (Modular) – Higher – Calculator – Q4
33.2 Jamal plays 15 games of ten-pin bowling.
Here are his scores.
72
59
75
66
79
75
66
63
89
76
65
79
77
71
83
(a) Draw an ordered stem and leaf diagram to show Jamal’s scores.
(3)
Gill plays 15 games of ten-pin bowling.
The table gives some information about her scores.
Highest score
95
Lowest score
75
Mean score
80
*(b) Compare the distribution of Jamal’s scores and the distribution of Gill’s scores.
(5)
June 2012 – Unit 1 (Modular) – Higher – Calculator – Q5
33.3
There are 25 students in a class.
12 of the students are girls.
Here are the heights, in cm, of the 12 girls.
160
173
148
154
152
164
179
164
162
174
168
170
(a) Show this information in an ordered stem and leaf diagram.
(3)
There are 13 boys in the class.
Here are the heights, in cm, of the 13 boys.
157
159
162
166
168
169
170
173
174
176
176
181
184
* (b) Compare the heights of the boys with the heights of the girls. (3)
June 2011 – Unit 1 (Modular)– Higher – Calculator – Q4
34.1 The probability that a seed will grow into a flower is 0.85
Loren plants 800 seeds.
Work out an estimate for the number of these seeds that will grow into flowers.
(Total for Question 5 is 2 marks)
March 2011 – Unit 1 (Modular) – Higher – Calculator – Q5
34.2 Here is a four-sided spinner.
The sides of the spinner are labelled A, B, C and D.
The table shows the probability that the spinner will land on A or on B or on D.
Letter
Probability
A
B
0.12
0.39
Amber spins the spinner once.
(a) Work out the probability that the spinner will land on C.
C
D
0.18
(2)
Lucy is going to spin the spinner 50 times.
(b) Work out an estimate for the number of times the spinner will land on A. (2)
November 2012 – Unit 1 (Modular) – Higher – Calculator – Q2
34.3 Denzil has a 4-sided spinner.
The sides of the spinner are numbered 1, 2, 3 and 4
The spinner is biased.
The table shows each of the probabilities that the spinner will land on 1, on 3 and on 4
The probability that the spinner will land on 3 is x.
Number
Probability
1
0.3
2
3
4
x
0.1
(a) Find an expression, in terms of x, for the probability that the spinner will land on 2.
Give your answer in its simplest form.
(2)
Denzil spins the spinner 300 times.
(b) Write down an expression, in terms of x, for the number of times the spinner is likely to
land on 3.
(1)
June 2011 – Unit 1 (Modular) – Higher – Calculator – Q5
34.4 The probability that a pea plant will grow from a seed is 93%.
Sarah plants 800 seeds.
Work out an estimate for the number of seeds that will grow into pea plants.
(Total for Question 2 is 2 marks)
March 2013 – Unit 1 (Modular) – Higher – Calculator – Q2