Stonelaw Mathematics Department
Blue Course
Revision Sheets
Block E
BE 0 Fractions and Percentages
BE 1 Algebra 2 (with negative numbers)
BE 2 Probability
BE 3 Statistics
BE 4 Special Numbers 2
Mixed Examples
BE0 Fractions and Percentages
BE0.1
I can convert between fractions and percentages (and vice
versa) with and without a calculator.
1.
Write down the percentage which is equivalent to each of the following
fractions
(a)
2.
1
(b)
2
3
4
(c)
1
10
(d)
2
3
Work out the percentage which is equivalent to each of the following
fractions. Show your working clearly.
(a)
3.
9
10
(b)
7
50
(c)
11
44
(d)
9
15
Write down the fraction which is equivalent to each of the following
percentages
(a) 25 %
4.
(b) 1 %
(c) 20 %
(d) 12½ %
Write each of the following percentages as a fraction in its simplest form.
Show your working clearly.
(a) 30 %
(b) 4 %
(c) 85 %
(d) 7·5 %
Section 2: Calculator Work (Round your answers to 1 decimal place)
5.
Work out the percentage which is equivalent to each of the following
fractions. Show your working clearly.
(a)
5
8
(b)
37
40
(c)
50
66
(d)
3
11
BE0.2
I can add and subtract any two fractions (including mixed
numbers) without a calculator.
Calculate
(a)
3
7
+
2
(b)
7
5
1
(e) 2 5 + 3 9
BE0.3
7
1
−
12
(c)
12
7
1
(f) 5 10 − 1 4
4
5
+
3
5
5
1
(d)
3
2
+
1
(g) 4 6 + 6 4
1
4
3
(h) 5 2 − 2 5
I can multiply and divide fractions (including mixed
numbers) by first “cancelling off” common multiples in the
numerators and denominators.
Calculate
1.
(a) 6 ×
3
(b)
4
1
1
(e) 2 2 × 1 3
2.
(a)
3
8
÷
3
1
3
×
1
3
(c)
4
2
1
5
8
×
2
(g) 3 6 ×
2
(c)
3
1
(f) 3 3 ÷ 1 3
4
9
÷
1
2
(d) 1 5 × 1 7
15
5
(f) 4 3 × 6
(b) 6 ÷
2
(e) 2 4 ÷ 1 2
3.
2
1
5
1
(h) 2 14 × 1 9
9
1
(d)
3
2
9
10
÷
3
5
1
(g) 9 ÷ 2 3
(h) 1 2 ÷ 6
1
1
Calculate the area of a rectangular floor which is 7 2 metres long and 5 3
metres wide.
4.
1
Pippa has a weekly piano lesson which lasts 1 4 hours. If she sat her first
examination after a total of 25 hours of piano lessons, how many lessons
had she needed?
BE1
BE1.1
Algebra 2 (with negative numbers)
I can multiply out brackets of the form
 ax(bx  cy ) .
1.
Multiply out these brackets
(a)
4(x + 4)
(b)
10(q – 5)
(c)
3(2t + 4)
(d)
2(8x – 1)
(e)
8(2 – 3y)
(f)
5(8 – y)
(g)
-6(2x + 5)
(h)
-3(3y – 7)
(i)
-7(4 – 5t)
(j)
11(x + y – z) (k)
2.
Multiply out these brackets
(a)
b(y – 3)
(b)
h(t + 10)
(c)
l(k – 4)
(d)
-z(p – 9)
(e)
-d(r + 2)
(f)
x(6 – a)
(g)
f(6 + 5t)
(h)
x(x + 1)
(i)
m(m – 2)
(j)
-s(4 – 7x)
(k)
c(3c + 2)
(l)
-w(8w – 5)
-9(a – 7b + c)
BE1.2
I can simplify expressions by adding, subtracting,
multiplying or dividing terms including expressions with
brackets.
In questions 1 to 3, multiply out the brackets, and collect the like terms
1 (a) 5(5a + 2) – 4a
(b) 6(7x – 4) + 13x
(c)
7(3g + 2) – 2
(d)
4(8k – 6) – 8k
(e) 4(6c – 3) + 6
(f)
3(9q + 5) – 11q
(g)
2(4t + 1) + 9
(h)
7(2y − 1) – 3
(i)
-3(5x + 4) + 16x
(j)
-5(5x + 4) + 6x
(k)
-7(2x – 3) + 16x
(l)
-4(4x – 1) + 5x
(m) -2(4x + 6) + 7
(n)
-8(3x + 5) + 4
(o)
-2(6x – 2) – 4
2(a) 6x + 2(5x + 2)
(b)
10 + 7(2e – 1)
(c)
5 + 4(k + 2)
(d)
(e)
4b + 3(6b – 8)
(f)
3r + 6(4r + 5)
(g) 7a – 3(2a + 3)
(h)
17n – 3(5n – 5)
(i)
15e – 6(6e + 3)
(j)
(k)
-2p – 3(4p + 5)
(l)
-5h – 2(2h – 7)
h + 5(3h – 4)
11b – 2(3b – 2)
3 (a) 7(p + 2) + 3(p + 4)
(b) 5(f + 2) + 2(f − 2)
(c) 5(3s − 3) + 3(2s + 4)
(d)
4(8w + 3) + 9(5w − 4)
(e) 3(3q − 2) + 5(2 – 4q)
(f) 8(4 – 5y) + 5(5 – 4y)
(g)
3(3t + 2) – 2(t − 2)
(h) 4(6w + 3) – 3(5w + 1)
(i) 6(5r − 4) – 7(4r + 5)
(j)
-3(2e + 1) – (2e − 9)
(k) -2(3x + 8) – 4(5x − 2)
(l) -4(7r + 2) – 4(3r + 2)
BE1.3
I can substitute any integer value into a formula or
expression.
1.
Find the value of each of the following expressions, given that
a = -3
b = -2
c = -1
d=0
w=2
x=3
y=5
a)
6c
b)
-5x
c)
-2a
d)
by
e)
ac
f)
4cw
g)
awx
h)
6b + 10w
i)
8d + 2b
j)
3a + 4c
k)
5c – 2a
l)
ab + cy
m)
wx – bw
n)
ad – xy + ac o)
2.
Evaluate the following expressions, given that
e = -3
g = -2
k = -1
h=0
p=2
ab + bc – cw p)
r=3
cwx – ay
t=5
a)
e2
b)
2g2
c)
4p2 + 5k2
d)
2t2 – 3c2
e)
8h2 – r2
f)
g3
g)
(3e)2
h)
(2k)3
3.
Evaluate the following expressions, given that
m=3
a)
e)
i)
𝑣
𝑛
5𝑚
𝑟
𝑟
𝑝
n=5
p=6
b)
f)
j)
q = -2
𝑝
𝑟
2𝑣
𝑞
𝑣2
𝑞
r = -3
c)
g)
k)
t = -6
v = -10
𝑡
d)
𝑟
𝑟𝑡
h)
𝑝
𝑚𝑛𝑟
𝑣
+𝑡
l)
𝑣
𝑛
𝑚𝑛𝑣
𝑡+𝑟−𝑝
𝑞3 −2𝑟
𝑛+𝑟
2
BE1.4
I can solve equations which contain brackets or fractions and
where the solution can be negative.
1.
Solve these equations
a)
5x = -15
b)
-3x = 30
c)
-14x = -28
d)
3x = -2
e)
7x – 11 = -4
f)
4x + 2 = -2
g)
2 – 6x = 1
h)
7x + 30 = x
2.
Solve these equations
a)
4(x + 3) = 28
b) 3(x + 5) = 9
d)
9(x + 3) = -27
e)
14 – x = 2 – 7x
c)
-6 = 2(x – 3)
f)
15 – 3(x + 2) = 5x + 1
3.
Solve these equations
a)
4(4 – x) = 3(5 – 2x)
b)
3(x + 2) – 5(x + 1) = x + 4
c)
– 2(2x + 3) = 2(5 – 2x) – 2x
d)
4(x + 1) + 2(3x – 2) = 5(x + 6)
4.
Solve these equations
a)
d)
5.
a)
c)
6.
a)
𝑥
5
1
4
= 10
b)
𝑥−6=1
e)
6
𝑥
= −2
𝑥
c)
2
10 + 3 𝑥 = −8
−6
3
f)
5
=
3
2
𝑥 =𝑥−4
Solve these equations
2
3
1
3
1
𝑥−1= 𝑥+3
b)
3
1
2
1
𝑥−1= 𝑥−4
5
1
(𝑥 + 2) = 1 + 𝑥
4
Solve these equations
𝑥
2
𝑥
− =7
3
b)
𝑥+1
3
=
𝑥−1
4
c)
6+3𝑥
7
=
2+𝑥
5
BE1.5
I can factorise expressions using common factor.
1.
Factorise each of the following expressions
a)
3x + 27
b)
10e – 50k
c)
30 – 5b
d)
16c + 4r
e)
4p – 6
f)
6g + 9a
g)
25 + 10d
h)
28k – 16m
2.
Factorise each of the following expressions
a)
pq + 4p
b)
5ab – 2bd
c)
10gh + 3h
d)
xy2 – 2y
e)
8tv + 7t2
f)
m2n – 6m
g)
5eg + g2
h)
9st – 11s
3.
Factorise each of the following expressions
a)
7xy + 21x
b)
16ab – 12b
c) 10m + 25mn
d) 30g2 + 2gh
e)
6st – 27s2
f)
8pqr + 32qrs
g) 12bz + 18bq
h) 30v2w – 20ew2
BE1.6
I can solve inequalities and describe the solution using set
notation.
1.
Solve the following inequations. Describe your answers using set
notation, choosing from the set of integers, {…, -2, -1, 0, 1, 2, …}
(a)
x+4<9
b)
x–2>3
c)
y+7<5
d)
a–2≤4
e)
t + 3 ≥ -2
f)
p – 7 < -3
g)
y – 5 > -8
h)
7+x<1
i)
-2 + x ≥ 10
j)
p+7<7
k)
k+7≥7
l)
x + 100 > 101
2.
Solve the following inequations. Describe your answers using set
notation, choosing from the set of integers, {…, -2, -1, 0, 1, 2, …}
a)
2x > 12
b)
7y < 14
c)
5x ≤ 15
d)
3a ≥ 21
e)
4x < -20
f)
16 < 8m
g)
-6 ≤ 3x
h)
30 > 6q
i)
-4 ≥ 2x
j)
4y ≥ 10
k)
6x < 9
l)
5t ≤ -12
3.
Solve the following inequations. Describe your answers using set
notation, choosing from the set of integers, {…, -2, -1, 0, 1, 2, …}
a)
6x + 4 < 3x + 7
b)
7t + 5 ≥ 2t + 30
c)
7x + 11 > 5x – 9
d)
10m – 3 ≤ m + 6
e)
3y – 11 > 2y + 5
f)
5p – 9 < 2p
g)
14 + 8c ≥ c
h)
3a + 2 ≤ a + 2
i)
9q – 1 > 2q – 1
BE2 Probability
BE2.3
I can express the probability of simple events as a fraction.
A ten sided spinner, numbered 1 to 10, is spun.
8
7
9
10
1
2
3
6
5
4
Work out each of the following probabilities.
BE2.4
(a) The probability that the spinner will land on an odd number.
(2)
(b) The probability that the spinner will land on a square number.
(2)
(c) The probability that the spinner will land on a prime number.
(2)
I can express the probability of combined events as a
fraction.
Two dice are thrown. What is the probability that:
(a) The probability that the sum of the two dice is 7.
(b) The probability that the difference is 2.
(c) The probability of the product being a multiple of 5.
BE3
Statistics
BC3.1 I can carry out calculations involving the Mean, Median, Mode
and the Range.
1.
A group of 18 year old boys and girls were surveyed about how old they were
when they went out on their first date. The results of the survey are shown below.
14
12
10
Frequency
8
6
Boys
4
Girls
2
0
13
14
15
16
17
Age at first date
2.
(a)
How many boys took part in the survey?
(b)
What was the modal age for the girls?
(c)
What was the range of ages for the boys?
(d)
Can you draw any conclusions about the dating ages of the boys and girls
who took this survey?
The following list of numbers represents the number of goals scored by
Manchester United in the 2010/11 Champions League.
0
1
1
3
1
1
2
1
2
2
4
1
0
(a)
What was the mean number of goals scored? (answer to 2 d.p’s)
(b)
What was the modal number of goals scored?
(c)
What was the median number of goals scored?
(d)
What was the range of goals scored?
3.
Twenty five S1 pupils at Calderglen sit their first maths test and obtain the following
percentages:
55
34
94
35
35
62
89
57
97
50
73
36
68
53
68
72
45
44
78
39
81
31
72
31
74
(a) Construct an ordered stem and leaf diagram to display these results.
(b) Work out the median score from your diagram.
4.
Shona and David record the length of their phone calls over a two week period. Here
are the lengths of calls to the nearest minute.
8
8
7
8
8
9
10
6
9
7
10
7
9
7
6
8
7
5
8
6
9
11
Construct a dotplot from the above data, comment on the distribution of the data
and state the modal phone call length.
BC3.2 I can construct a frequency table and calculate the mean from a
frequency table.
1.
John and Sarah love to cycle together on a Saturday. They record the number of
miles they travel each time they cycle.
The last 30 distances (to the nearest mile) are shown below.
20
24
22
27
19
22
22
23
25
21
20
24
23
23
26
21
23
24
21
20
22
22
23
23
22
22
23
24
20
24
(a)
Construct a frequency table from John and Sarah’s data.
No. of miles travelled
Tally
Frequency
(b)
On how many days did John and Sarah cycle 24 miles?
(c)
Calculate the mean number of miles cycled.
BC3.3 I can find the median from a cumulative frequency table.
Terry is a car salesman.
Terry records the number of cars he sells in the 1st week of June.
Day
Frequency
Mon
3
Tue
2
Wed
5
Thur
6
Fri
4
Sat
10
(a)
Copy the frequency table and add a cumulative frequency column.
(b)
Calculate the median from your frequency table.
BE4 Special Numbers 2
BE4.1
I am able to calculate simple whole number powers mentally.
Do NOT use a calculator. Find the values of :(a) 52
BE4.2
(b) 102
(c) 32 + 22
(d) 62 - 42
2 2
(e) (3)
I am able to use a calculator to find larger whole number
powers.
1.
Use a calculator to find the values of :-
(a)
132
2.
Calculate the area of the following squares using the formula;
(b) 212
(c) 342
(d) 3002
(e) 422 - 202
Area = (length)2
A = l2
(a)
(b)
(c)
10m
6c
m
1cm
6c
m
BE4.3
I have researched the importance of whole number powers.
A chessboard has 64 squares.
If we are going to place £1 in the first square, £2 in the second square, £4 in the third
square, so that the amount keeps doubling, how much money do we need to fill all the
64 squares?
BE4.4
I can find the square root of Square Numbers and the square
root of any other positive number.
1.
Do NOT use a calculator. Find the values of :-
(a) √16
2.
(b) √25
(c) √64
(d) √81
(e) √100
Use a calculator to find the values of the following, round your answers to 2
decimal places.
(a) √65
(b) √3
(c) √16
(d) √24
(e) √2
3.
A square has an area of 36cm2. Find the length of one of its sides.
4.
A square has an area of 49cm2. Find the length of one of its sides.
BE4.5
I am aware that the square root of a real number can be
expressed as a positive AND a negative number.
Find all square roots of the following:(a)
BE4.6
√9
(b) √25
(c) √121
(d) √1
(e) √169
Working with others I have investigated the square root of
negative numbers.
Find the square roots of the following:(a) √(−9)
(b) √(−6)
(c) √(−12)
(d) √(−1)
(e) √(−200)