National 4 Numeracy Revision Booklet Solutions
Page 1 - Ratio 1
Q1(a) 3 + 7 = 10
£50 ÷ 10 = £5
3 : 7
3 x £5 : 7 x £5
£15 : £35
Q1(a) £15 : £35 (b) 24kg : 56kg (c) £25 : £10 (d) 192g : 48g
Q2(a) Harry (£10) : James (£30) : Bill (£80) (b) Susan (£8) : Beth (£20) : Jill (£28)
Q3(a) Graeme (£1020) : Fred (£2380) (b) Graeme (£1860) : Fred (£4340)
Q4 15 girls
Q5(a) 16 g silver (b) Dave (£206) : Frank (£618)
Q6(a) 30 cows (b) 72 (c) Bill (27) : Dan (36) : George (9)
Page 2 - Percentages
10% = 10/100 = 1/10 = 0.1
20% = 20/100 = 1/5 = 0.2
25% = 25/100 = 1/4 = 0.25
50% = 50/100 = 1/2 = 0.5
75% = 75/100 = 3/4 = 0.75
Q1 (a) 0.32 (b) 0.87 (c) 0.20 (d) 0.08 (e) 0.03 (f) 0.90 (g) 0.07 (h) 0.125 (i) 0.035
Q2 (a) £8.64 (b) £1680 (c) £61.20 (d) £1.20 (e) £1.64 (f) £10 320 (g) £6.90
(h) £6.96 (i) £1.70 (j) £1.44 (k) £13 (l) £15
Q3 (a) £10.35 (b) £4.00 (c) £5.74 (d) £1.21 (e) £0.73 (f) £0.74 (g) £0.68
(h) £0.90 (i) £54.42 (j) £0.50 (k) £10.87 (l) £1.27 (m) £0.17 or 17p
(n) £0.11 or 11p
(o) £0.01 or 1p (p) £0.71 or 71p
Q4 Clock Radio = £31.50; Skate Board = £21.60; Yo Yo = £10.80;
Video Camera = £415.80; CD Player = £111.33; Cool Shades = £14.85
Q5 Clock Radio = £37.80; Skate Board = £25.92; Yo Yo = £12.96;
Video Camera = £498.96; CD Player = £133.60; Cool Shades = £17.82
Page 3 - Savings & Interest
Eg 4% of £600 OR 4% of £600
= 0.04 x £600
= 4/100 x £600
= £24
= £24
Page 4 - VAT
Eg 17.5% of £80
= 0.175 x £80
= £14
Q1 (a) £24 (b) £56 (c) £19.20 (d) £3.22
Q2 (a) (i) £45 (ii) £70.20 (iii) £16 (iv) £244.80 (b) £48 (£30 + £18)
Q3 (a) £33.60 (b) £22.60 (c) £2.20 (d) £65.61 (e) £5.75 (f) £8.40
Q4 £80
Q5 £80
Q1 (a) £14 (b) £22.75 (c) £1.40 (d) £14.35 (e) £11.90 (f) £112
Q2 Item
Camera Glasses
Ring
CD
Skate
(a) VAT
£10.50
£ 4.55
£40.25 £ 2.10 £ 8.40
(b) Total Cost £70.50 £30.55 £270.25 £14.10 £56.40
£
Q3 (a) 6 dozen nails @ £0.80 per doz. 4.80
5 tins of paint @ £4.60 per tin 23.00
10 rolls of wallpaper @ £6.80 per roll 68.00
Subtotal 95.80
+ VAT @ 171/2% 16.77
TOTAL = £112.57
Bike
DVD
£31.50 £25.90
£211.50 £173.90
£
(b) 8 starters @ £2.40 each 19.20
6 main courses @ £8.10 each 48.60
8 sweets @ £3.60 each 28.80
Subtotal 96.60
+ VAT @ 171/2% 16.91
TOTAL = £113.51
Q4 Boat 1: £16400 X 1.175 = £19270 & Boat 2: £19280  Boat 1 is cheaper by £10
Page 5 - Hire Purchase
Total Cost =
Deposit + Instalments
Maths Dept,
Millburn Academy
Q1
Item
(i) Hire Purchase
(ii) Difference
PC
Car
Bike
Printer
Camera Caravan
Earrings
£890
£110
£10 820
£1820
£826
£66
£390
£40
£742
£67
£225.90
£35.90
Q2 (a) £381.60 (b) £41.60
£7173
£723
National 4 Numeracy Revision Booklet Solutions
Page 6 - Holiday Travel
Currency (x Rate)
Back to £'s (÷ Rate)
Q1 (a) 2316 francs (b) 154 000 escudos
(c) 162 000 lire (d) 16 400 pesetas
(e) 1860 dollars (f) 245 marks
(g) 270.20 francs (h) 96 900 drachmas
(i) 2170 swiss fr (j) 5880 marks
Q2 (a) £60
(b) £43
(c) £5
(d) £390
(e) £420
(f) £200
(g) £124.35
(h) £49.41
(i) £38.18
(j) £22.86
Q3 (a) 13 510 francs (b) £180
Q4 (a) John 2 025 000 lire & Graeme 1 836 000 lire (b) John £729 & Graeme £671.50
Q5 Spain - £950 & Switzerland - £980  Cheaper in Spain by £30
Q6 £65 x 9.80 = 637 fr; 637 ÷ 9.98 = £63.83  lost £1.17
Q7 (a) £0.75/litre (b) £3.43/gallon
Page 7 - Distance
D
S
T
Q1 (a) 200 km (b) 390 miles
(c) 217.5 km (d) 12 km
(e) 24 miles
Q2 (a) 3220 km (b) yes
Method 1: Yes, as he can travel 13 x 460 = 5980 km in 13 hrs > 5900 km
Method 2: Yes, as 5900/460 = 12.826 < 13 hrs so he can complete the journey on time
Q3 (a) 91 km (b) 28km + 126 km + 21 km = 175 km (2 x 14 = 28; 4.5 x 28 = 126; 3 x 7 = 21)
Page 8 - Angles
CARE to read
correct scale on
Protractor
Q1(a)∠ABC = 25 o (±2o) (b)∠PQR = 95 o (±2o) (c)∠DEF = 115 o (±2o) (d)∠KLM = 235 o (±2o)
Q2 (a)∠BAC = 90 o (±1o) (b)∠HFG = 140 o (±1o) (c)∠JKL = 300 o (±1o) (d)∠MWN = 27 o (±1o)
Q3 (a) 135O (b) 65 O (c) 120O (d) 70O (e) 50 O (f) 37O (g) 122O (h) 50 O (i) 72O
Pages 9 to 12 - Scales
Remember to
write down
units too
Q1 250g
Q2 150g
Q3 100g
Q4 300g
Q5 50g
Q6 130g
Q7 340g
Q8 170g
Q9 40g
Q10 130g Q11 260g
Q12 310g
Q13 4 cm; 18 cm; 27 cm; 17.5 cm
Q14 (a)(i) 2kg (ii) 2000g
(b) (i) 1.5 kg (ii) 1500g
(c) (i) 5.5 kg (ii) 5500g
Q15 (a)(i) 1400ml (ii) 1.4 L (b)(i) 800ml (ii) 0.8 L
(c)(i) 1000ml (ii) 1 L
Q16 (a) L = 1200 ml ; R = 800 ml (b) L = 800 ml ; R = 1200 ml (c) L = 500 ml ; R = 1500 ml
Q17 NOT LEGIBLE AS LINES FADED
Q18 (a) -5oC (b) 2oC (c) -8oC (d) 7oC (e) -1oC
Q19 (a) 9oC (b) 29oC (c) -9oC (d) -39oC (e) - 3oC *** CARE: Q19 is NOT exactly on
line so accept (±1 oC)
Pages 13/14 - Perimeter and Area
Perimeter is 1D 
Units are cm, m, etc
Area is 2D  Units2
(eg cm2, m2, mm2, etc)
Maths Dept,
Millburn Academy
Q1 42 cm Q2 70 mm
Q3 72 cm
Q4 22 m
2
Q5 (a)(i) 38 cm (ii) 48 cm
(b) (i) 18 cm (ii) 22 cm2
Q6 1.08 m2 (or 10 800 cm2)
Q7 (a) 14 cm (b) 10 cm (c) 140 cm2 (d) 88 cm
Q8 (a) 780 m (b) 16 rolls (c) £40 (***In Q8 £250 per roll intended so very cheap!)
National 4 Numeracy Revision Booklet Solutions
Page 15 - Integers
+++
+--+-
--+
Page 16/17 - Integers
Addition & Subtraction
Q1 12
Q9 -18
Q17 6
Q2 26
Q10 24
Q18 22
Q3 -10
Q11 25
Q19 27
Q4 -22
Q12 -1
Q20 15
Q5
-8
Q13 -4
Q21 -66
Q6 -12
Q14 -57
Q22 -17
Q3 -9
Q11 -10
Q19 9
Q4 -6
Q12 -9
Q20 -4
Q5 -6
Q13 -49
Q21 -10
Q6 -72
Q14 -27
Q22 -16
Q2 -11
Q10 0
Q18 -40
Q3 1
Q11 -15
Q19 7
Q4 10
Q12 -21
Q20 20
Q5 -25
Q13 41
Q21 -5
Q6 -12
Q14 -8
Q22 1
Q25 140 Q26 -61
Q27 48
Q28 12
Q29 -11
Q30 -33
Q7 19
Q8 -4
Q15 -71 Q16 22
Q23 -31 Q24 8
Multiplication & Division
Q1 -6
Q9 -9
Q17 1
Q2 -9
Q10 -48
Q18 -90
Q7 4
Q15 49
Q23 -25
Q8 -10
Q16 -10
Q24 8
Mixed
Q1 -20
Q9 78
Q17 -42
Q7 -9
Q15 0
Q23 24
Q8 48
Q16 -9
Q24 -31
Temperature Problems
Q1 10oC Q2 3oC
Q7a) Moscow (-14oC)
e) 13oC
Page 18/19 - Pie Charts
Pie Chart Calculations
Number = Angle x Total
360
OR
EQUIVALENT FRACTIONS
144 = ? .
360 720
Q3 4oC Q4 6oC Q5 1oC Q6 -2oC
b) Bangkok and Dubai (both the hottest at 29oC)
f) 28oC
g) 27oC
Q1 a) Comedy (Most)  A b) Science (Least)  C c) News  B
Q2 a)
Mode of Transport
Eurotunnel
Hovercraft
Ferry
Number of Degrees
144o
90 o
108 o
144
90
108
People = Angle/360 x 720
/360 x 720
/360 x 720
/360 x 720
Number of People
288
180
216
Q2 b) (i) Hovercraft = 90/360 = 1/4
(ii) Ferry = 108/360 = 12/40 = 3/10
c) 32oC
d) 24oC
Plane
18 o
18
/360 x 720
36
(iii) Flew = 18/360 = 1/20
Q3 a) 5% of 240 mins = 1/20 of 240 = 12 mins
[May find it easier to find 10% first:
1
b) 20% of 240 mins = /5 of 240 = 48 mins
10% of 240 mins = 1/10 of 240 = 24 mins]
c) 45% = (5% + 20% + 20%) = 12 mins + 48 mins + 48 mins = 1 hr 48 mins
Q4
Activity
(a) Angle
(b) Number of People
90
(i) Swimming
90o
/360 x 180 = 45
o
120
(ii) Keep Fit
120
/360 x 180 = 60
o
45
(iii) Dance
45
/360 x 180 = 22.5 ~ 23
105
Court Games
105o
/360 x 180 = 52.5
o
TOTAL =
360
= 180
[**Q5b) Should read: Which two networks are the least popular?]
Q5 a) Vodafone
b) Tesco & 3 c) 1/4 of 720 = 180 people
d) 144/360 x 720 = 288
Q6 a) Water events
b) Cycling
c) 13/65 = 1/5 = 1/5 of 360 = 72o
Q7 a) Eden Court
b) Ironworks = 72/360 x 135 = 2/10 x 135 = 1/5 x 135 = 27 pupils
Page 20 - Probability
Maths Dept,
Millburn Academy
Q1
0
0.1
0.2 0.25 0.3
0.4
0.5
0.6
0.7 0.75 0.8
0.9
1
Impossible
Unlikely
Evens
Very likely
Certain
Q2 a)(i) 3 (ii) 6 (iii) Prob(Odd) = 3/6 = 1/2 or 0.5 b) Prob(6) = 1/6
Q3 a) Prob(1) = 2/6 = 1/3
b) Prob(2) = 2/6 = 1/3
c) Prob(3) = 2/6 = 1/3
d) Prob(4) = 0 = Impossible e) Prob(> 3) = 0 = Impossible
Q4 a)(i) 150
(ii) 20
(iii) Prob(Sci-Fi) = 20/150 = 2/15
40
b)(i) Prob(Romance) = /150 = 4/15 (ii) Prob(Romance) = 40/150 = 4/15
Q5 a) Prob(Electrical) = 27/113 b) Prob(Timing) = 25/113 c) Prob(Gearbox) = 18/113
National 4 Numeracy Revision Booklet Solutions
Page 21 - Probability Q6 Prob(Male) = 8/20 = 2/5
Q7 a) Prob(Mazda 2) = 38/100 = 19/50 or 0.38
b) Prob(Female & Focus RS) = 8/100 = 2/25 or 0.08
Q8 a) Prob(Face) = 12/52 = 3/13 b) Prob(Not Face) = (1 - 3/13) = 10/13 c) Prob(King of Hearts) = 1/52
Q9 a) Prob(6) = 1/8 b) Prob(Odd) = 4/8 = 1/2 b) Prob(9) = 0 Impossible!
d) Prob(Prime) = 4/8 = 1/2 e) Prob(Square) = 2/8 = 1/4 f) Prob(1,2,3,4,5,6,7,8) = 1 Certain!
b) There are far more 2's and only one 5  biased
This may imply the dice is weighted and more
rolls are necessary to clarify if this is the case.
Q10 a) Prob(1) = 6/30 = 1/5
Prob(2) = 8/30 = 4/15
Prob(3) = 7/30
Prob(4) = 4/30 = 2/15
Prob(5) = 1/30
Prob(6) = 4/30 = 2/15
Page 22 - Bar Graphs
Q1b) 5 + 2 + 6 + 7 + 10 = 30 trees
Q1c) Rowans = 10/30 = 1/3
Q1a)
Trees Types in the Public Park
10
9
8
7
6
5
4
3
2
1
0
Oak
Elm
Beech
Birch
Rowan
Q2 a)
Lounge
Bedroom
8
7
6
5
4
3
2
1
0
8
10
7
6
No. of Tins
No. of Tins
No. of Tins
Kitchen
5
4
3
2
1
0
6
4
2
0
Green
Colour of Paint
8
Blue
Lemon
Red
White
White
Cream
L Blue
L Pink
Colour of Paint
Colour of Paint
Q2 b) White = 4 + 2 + 8 = 14 tins (** Off-White is not bought as white and mixed)
No. of People
No of People
24
25
12
11
10
9
8
7
6
5
4
3
2
1
0
17
20
12
15
10
5
2
0
None
A
B
C
A & B A & C B & C ALL
STATIONS PICKED UP
Q3 b) (i) 2 (ii) 17 (iii) 24 (iv) 12
Maths Dept,
Millburn Academy
Listeners
Listeners
Q3 a)
NONE
ONE
TWO
THREE
Number of Stations Picked Up
L Green
National 4 Numeracy Revision Booklet Solutions
Page 23 - IH Probs 1
Q1 a)(i) Boys on Monday = 4
(ii) Boys on Friday = 8
Q1b) The boys absence figures grow/rise/increase over the week
Q1c)
 With the exception of Thursday, the girls absence figures also rise over the week
 However overall the girls attendance is better than the boys.
Q2 a) White loaves on Wednesday = 30
b) 60 - 20 = 40 more brown than white on Thursday
c) White loaves sales decrease/fall/drop over the week
d) Brown loaves were on sale (as there is a dramatic rise in brown and drop in white sales)
 special offer had a huge impact on buying habits.
Q3 a) There has been a fall/decrease in customers using leaded petrol at the service station
since 1987, which has levelled off to 20 customers (as some people still drive older cars)
b) 1993
c) White loaves sales decrease/fall/drop over the week
d) 4 years (1994, 1995, 1996 & 1997)
~ End of Answers for National 4 Revision Booklet ~
Maths Dept,
Millburn Academy