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Stonelaw Mathematics Department
Blue Course
Revision Sheets
Block C
BC0
Negative Numbers 2.
BC 1 Special Numbers 1.
BC 2 Rounding.
BC 3 Fractions 2, Decimals and Percentages.
BC 4 Drawing Accurate 2D Shapes and Area (will not be examined).
Mixed Examples
BC0
Negative Numbers 2
BC0.1 I can add and subtract with negative numbers in abstract contexts in
preparation for use in algebra.
Write down the question then calculate,
a) 4 + (-11)
b) 2 - 12
c) (-6) + 16
d) -6 + (-9)
e) 7 - 15
f) (-6) - 7
g) (-50) + (-70)
h) (-42) + 42
i) (-11) + 4
j) 18 + (-22)
k) 13 - (-14)
l) 36 - (-14)
m) 9 - (-9)
n) 560 - (-840)
o) 3.4 - ( -2.6)
p) (-3) - ( -7)
q) (-9) - (-12)
r) -15 - (-15)
s) (-25x) - (-5x)
t) 9g - (-15g)
BC0.2 I understand the meaning of the term additive inverse add can give
the additive inverse of any integer (or algebraic term).
Write down the additive inverse of,
a) 6
b) 51
c) -83
d) 5k
e) -45j
BC0.3 I can multiply and divide with negative numbers in abstract contexts
in preparation for their use in algebra.
Write down the question then calculate,
a)
6 × (-6)
b) 7 × (-8)
c)
(-8) × 4
d) 15 × (-4)
e)
(-7) × 3
f)
(-40) ÷ 8
g) (-63) ÷ 9
h) 84 ÷ (-4)
i)
56 ÷ (-7)
j)
(-27) ÷ 3
k) (-5) × (-4)
l) (-9) × (-8)
m) (-3) × (-6)
n) (-4) × (-12)
o) (-10) × (-6)
p) (-48) ÷ (-8)
q)
r) (-81) ÷ (-9)
s)
t) (-36) ÷ (-12)
(-27) ÷ (-3)
u) 6 × (-7) ÷ 3
v) -8 × (-3) ÷ (-4)
(-63) ÷ (-7)
BC1
BC1.1
Special Numbers
I can list multiples of a given whole number and find the lowest
common multiple (LCM) of two or more numbers.
1.
List the first 5 multiples of 3.
2.
List all the multiples of 7 between 30 and 50.
3.
Find the LCM of,
a)
2 and 5
b) 3 and 7
c) 4 and 6
e)
13 and 3
f)
g) 3, 6 and 7
2, 3 and 5
d) 7 and 10
BC1.2 I can list all of the factors of a given whole number and find the
highest common factor (HCF) of two or more numbers.
1. Find the factors of,
a) 12
b) 24
c) 40
d) 70
e) 120
c) 15 and 36
d) 12 and 42
e) 14, 35 and 42
2. Find the HCF of,
a) 4 and 6
b) 9 and 27
BC1.3 I have investigated the importance of prime numbers in maths and
the wider world.
1. Write down the prime numbers from,
a) 14, 9, 38, 31, 21
b) 77, 81, 95, 47, 93
c) 78, 79 , 99, 63
BC1.4 I can deduce whether a whole number is prime or composite and
reduce any whole number to a product of prime factors (prime
decomposition).
2. Find the prime decomposition of,
a) 12
b) 45
c) 50
d) 98
e) 680
BC2
Rounding
BC2.1 I can round large numbers to the nearest 10, 100 and 1000.
1.
2.
3.
Round the following to the nearest 10:a) 79
b) 63
c) 59
d) 384
e) 273
f)
g) 449
h) 1 936
i)
j)
8
3 703
3 099
Round the following to the nearest 100:a) 541
b) 817
c) 479
d) 777
e) 3 084
f)
g) 455 700
h) 19 090
i)
j)
19 682
3 984
19 895
Round the following to the nearest 1000:a) 8 700
b) 16 400
c) 85 489
d) 2 063
e) 95 920
f)
g) 526 388
h) 355 900
i)
j)
89 975
357 806
799 656
BC2.2 I can use my knowledge of rounding to estimate answers.
1.
Round the numbers to 1 figure accuracy before multiplying. Use your answer to
decide which of the three given answers is most likely to be the correct one:a)
2.
Choice of
{359.6, 3 596 or 35 996}
b) 297 × 21
Choice of
{6 237, 9 237 or 62 237}
c)
Choice of
{3 423, 34 232 or 342 232}
d) 493 × 108
Choice of
{5 244, 23 244 or 53 244}
e)
Choice of
{23 000, 2 030 or 203}
389 × 88
79 982 ÷ 394
Round each number to 1 figure accuracy, then give an estimate to:a) 62 × 47
b) 88 × 19
c) 72 × 103
d) 596 × 42
e) 306 × 78
f)
798 × 190
g) 889 ÷ 29
h) 4 125 ÷ 38
i)
j)
59 566 ÷ 599
k) 17 745 ÷ 888
l)
BC2.3
1.
62 × 58
4 227 ÷ 219
91 299 ÷ 2 787
I can round to a given number of decimal places.
When each of the following numbers is rounded to 1 decimal place, which of the two
values in the brackets is the correct answer:a)
5·48
(5·4 or 5·5)?
b) 7·73
(7·7 or 7·8)?
c)
4·05
(4·0 or 4·1)?
d) 0·87
(0·8 or 0·9)?
e)
18·85
(18·8 or 18·9)?
f)
3·98
(3·9 or 4·0)?
g) 11·03
(11·0 or 11·1)?
h) 0·08
(0·0 or 0·1)?
i)
(12·9 or 13·0)?
j)
(8·5 or 8·6)?
12·99
8·55
2.
2.
3.
Round the following numbers to 1 decimal place:a)
6·79
b) 8·43
c) 3·26
d) 121·48
e)
11·48
f)
2·37
g) 18·87634
h) 29·2536
i)
49·26511
j)
71·23476
k) 0·0914
l)
0·7821
m) 0·9546
n) 0·89516
o) 17·4517
p) 86·9572
q) 31·554
r)
s)
t)
0·0814
0.03999
10.0503
Round the following numbers to 2 decimal places:a)
14·739
b) 21·276
c) 78·937
d) 92·476
e)
31·213
f)
0·456
g) 0·215
h) 3·024
i)
41·765
j)
99·1967
k) 86·35969
l)
63·42537
m) 33·7248
n) 52·31643
o) 29·0672
p) 0·00567
q) 7·51723
r)
s)
t)
101·9764
29.99543
0.00499
Round the following numbers to the decimal place(s) shown in the brackets:a)
16·347 (1)
b) 141·8257 (2)
c) 2·376 (2)
d) 0·0491 (2)
e)
8·7654 (2)
f)
87·3946 (1)
g) 56·99 (1)
h) 7·2964 (2)
i)
0·0954 (2)
j)
84·6932 (1)
k) 3·6745 (2)
l)
172·576 (1)
m) 249·432 (2)
n) 7·634 (1)
o) 0·594 (2)
p) 746·995 (2)
q) 17·635 (1)
r)
s)
t)
0·5692 (2)
152·303 (1)
0·05052 (1)
BC2.4 I can round to a given number of Significant Figures.
1.
2.
Write down the number of significant figures for each of the following values:a)
3·6
b) 6·4
c) 7·9
d) 3·4
e)
11·7
f)
13·5
g) 4·0
h) 23·0
i)
117·5
j)
10 000·00
k) 1 412·900
l)
16·000
m) 3 124·890
n) 0·0049
o) 0·000370
p) 0·02090
q) 0·0004700
r)
s)
t)
0·819000
10·00100
820 000
Round the following numbers to three significant figures:a)
358·215
b) 726·209
c) 8·00973
d) 4 901·82
e)
300·1862
f)
1 821·591
g) 1 689·139
h) 438·593
i)
2 561·843
j)
38·01102
k) 5·20213
l)
0·6371904
m) 0·03879
n) 0·09346
o) 0·0081162
p) 1 276
q) 2 408
r)
s)
t)
u) 20 678
v) 10 676
w) 39 058
x) 309 495
y) 540·1
z) 273·06
aa) 41 300·01
bb) 0·0030774
6 987
6 209
17 840
3.
4.
5.
Round the following numbers to two significant figures:a)
53·8914
b) 76·8215
c) 0·02738
d) 0·088181
e)
46·7529
f)
0·06384
g) 0·008619
h) 17·082
i)
42·69163
j)
0·029964
k) 3·0982
l)
2·02815
m) 0·0012912
n) 30·2391
o) 13 752
p) 0·03291
q) 3·05141
r)
s)
t)
u) 27 283 300
v) 15 900
w) 1·986
x) 29 651
y) 601 951
z) 735 049
aa) 8 131 900
bb) 5 059 908
348 000
8·034
38 700 000
Round the following numbers to one significant figure:a)
93·835
b) 19·728
c) 729
d) 857
e)
1 396
f)
3 820
g) 17 800
h) 36 900
i)
489·563
j)
11 842
k) 0·00793
l)
0·0077
m) 0·00731
n) 0·00893
o) 0·0643
p) 375 600
q) 5 025 860
r)
s)
t)
2 378 000
19·0089
5 870 000
Round the following numbers to the significant figure(s) shown in the brackets:a)
3 828 (2)
b) 51 980 (3)
c) 73 198 (4)
d) 0·06104 (3)
e)
3·503 (3)
f)
g) 0·921 (2)
h) 3 714 (1)
0·20111 (4)
BC3
Fractions 2, Decimals and Percentages
BC3.1 I can apply my knowledge of lowest common multiples and
equivalent fractions to help me add or subtract fractions (proper
fractions or whole number answers only).
1.
2.
Copy each of the following and complete:a)
1
5
+5
b)
3
8
+8
c)
e)
1
+4
5
1
f)
1
+2
3
1
i)
1
+9
2
1
j)
1
m)
1
3
n)
4
3
+7
1
5
9
24
+ 24
d)
g)
1
1
+3
4
1
k)
1
2
2
n)
5
+7
7
9
20
+ 20
h)
1
1
+ 24
10
9
l)
1
3
3
+8
5
o)
5
+8
5
10
+ 10
2
+8
3
7
7
12
+ 18
Copy each of the following and complete:a)
3
e)
1
i)
4
5
− 10
m)
1
1
7
2
2
b)
−7
1
8
2
d)
14
− 14
g)
5
1
h)
5
1
k)
3
l)
2
n)
16
o)
7
− 15
c)
−4
1
2
−5
f)
2
3
j)
7
n)
11
− 15
12
− 12
11
12
15
3
9
−3
8
− 15
20
7
9
4
−2
11
− 20
8
− 15
21
7
3
9
−4
5
−8
3
− 16
12
BC3.2 I can perform calculations involving multiplication and division of
fractions (proper fractions or whole number answers only).
1.
Copy each of the following and complete:a)
1
e)
1
i)
m)
2.
2
5
×3
1
b)
3
×2
f)
2
j)
7
5
4
12
15
16
×5
24
× 25
n)
5
7
8
7
2
3
×8
c)
×3
g) 4 × 20
16
× 21
7
24
18
× 35
3
d)
×4
3
k)
n)
2
5
7
×8
8
39
4
7
2
×9
3
h) 7 × 28
l)
6
7
2
×3
× 56
o)
45
13
49
× 81
28
4
Copy each of the following and complete:a)
1
÷2
9
1
b)
2
÷8
7
3
c)
3
÷8
5
5
d)
5
e)
1
÷3
2
f)
1
3
g)
2
5
h)
4
i)
2
8
j)
l)
22
m)
78
2
3
÷9
99
39
÷ 44
n)
4
÷5
9
16
4
27
3
÷4
k)
÷5
n)
7
÷6
8
16
15
3
4
÷ 25
÷6
o)
÷5
7
9
2
÷3
27
7
12
44
÷ 45
÷7
𝑎
BC3.3 I understand the term reciprocal and know that
1.
2.
𝑏
𝑏
×𝑎 =1.
What is the value of each letter:a)
𝑎
×8= 1
6
6
b)
1
×𝑏 =1
4
c)
3
×3=1
5
d)
×3=1
10
e)
𝑒
8
f)
25
g)
20
h)
ℎ
8
× 13 = 1
𝑓
4
12
× 25 = 1
𝑔
𝑐
3
× 20 = 1
3
7
𝑑
𝑖
× 28 = 1
Write down the reciprocal for each of the following:a)
3
f)
4
5
b)
1
g)
1
4
8
c)
8
h)
3
7
4
d) 8
e)
3
9
j)
1
i)
2
7
21
BC3.4 I can convert comfortably between (common) fractions, decimals
fractions and percentages.
1. Write each of the following as a fraction and as a decimal fraction (simplify),
a) 13%
b) 24%
c) 99%
d) 56%
e) 25%
f) 83%
g) 10%
h) 80%
i) 75%
j) 16%
k) 5%
l) 3%
m) 7.2%
n) 35%
o) 1%
2. Change each fraction into a percentage (calculator),
18
4
c) 10
49
h) 8
a) 100
b) 5
1
g) 50
f) 4
7
d) 25
17
5
i) 40
27
19
e) 20
6
j) 75
BC3.5 I can comfortably convert between mixed numbers and improper
fractions.
1. Change each of the following to mixed numbers and simplify where possible,
a)
16
f)
33
6
9
b)
22
g)
265
34
d) 15
55
e) 20
58
i)
180
j) 10
c) 10
4
h)
50
8
66
88
40
2. Change each of the following to improper fractions,
a) 3
5
6
2
b) 5 3
2
c) 2 4
3
d) 7 5
3
e) 7 7
2
h) 6 2
1
i) 10 4
1
j) 6 8
g) 1 5
f) 8 9
6
5
BC3.6 I can use mixed numbers in problems involving the four operations.
1. Copy, complete and simplify,
4
8
5
3
a)3 9 - 2 6
b) 1 9 + 1 4
f) 5 3 + 6 2
2
1
g) 8 12 - 4 4
2
1
l) 9 11 + 5 4
k) 6 5 - 3 2
7
7
5
2
2
5
e) 6 5 + 2 6
5
j) 8 10 - 2 6
5
o) 10 5 + 8 6
d) 3 7 - 1 6
c) 3 7 - 2 9
3
h) 4 6 + 2 12
5
i) 2 3 + 4 9
1
m) 5 5 + 3 9
1
5
n) 3 4 - 2 8
1
1
1
4
5
7
5
4
1
2. Copy, complete and simplify,
1
1
a)2 2 × 1 5
1
f) 7 2 ÷
1
1
b) 6 2 × 1 5
1
4
c) 4 3 ÷ 7 2
2
5
h) 5 8 × 8 8
g) 5 3 ÷ 5 6
5
10
k) 9 2 ÷ 6 11
7
1
8
5
l) 2 × 6
9
9
2
1
d) 2 11 × 3 10
7
1
i) 9 2 ÷ 14 9
1
1
1
2
11
m) 9 × 2
1
8
2
n) 2 2 ÷ 10 3
2
1
3
4
e) 1 3 ÷ 12 2
j) 5 5 × 17 7
o) 10
4
11
×4
1
2
Mixed Examples
1.
A piece of wood is 318 inches wide.
What would be the width of 12 of these pieces of wood placed side by
side.
2.
John was born on the 5th of September 2001 or 5/9/1.
John’s wee brother was born on a date which can be made from the
prime factors of 66.
Give a possible date of John’s wee brother’s birth.
3.
Callum walks 513 miles in 116 hours.
Use the formula
𝑨𝒗𝒆𝒓𝒂𝒈𝒆 𝑺𝒑𝒆𝒆𝒆𝒅 =
𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆
𝒕𝒊𝒎𝒆
,
to find his average speed.
4.
John travelled 234 miles to the market, then 523 miles back to the farm.
a) How far did John travel altogether?
b) What is the difference in distance between the two journeys?
5.