H
Mathematics
Stonelaw High School
Home Learning
Blue Course
Homework 1 – BH1.3
Find the size of the shaded angles in each diagram.
(O is the centre of each circle, PS and PT are tangents)
1.
2.
3.
62
o
48o
57o
O
O
O
4.
5.
6.
43o
O
O
41o
P
P
S
S
7.
40o
O
T
8.
88o
59o
O
O
36o
S
Calculate the size of angle x in each diagram below.
9.
10.
11.
x
x
O
O
O
80o
65o
x
P
Homework 2 – BH1.4
1.
2.
3.
4.
Homework 3 – BH2.6
Calculators must not be used for the following questions. Show all necessary
working.
Calculate the gradient of the line joining each pair of points
1.
a)
2.
Write down the gradient and y – intercept of the following lines
a) y = 3x – 2
b)
y=x+4
c)
y = 4x
d)
3.
b)
X ( -1 , 1 )
Y ( 5 , 13 )
c)
R ( -2 , -5 )
S ( 2 , -7 )
y = - 2x – 1
Rearrange these equations in the form y = mx + c and then write down the
gradient and y – intercept :
a)
4.
A ( 2 , -1 )
B(4,7)
y – 2x = 3
b) y – x + 3 = 0
Write down the equation of the line with :
a) gradient 2 and y-intercept -1
b)gradient -3 and passing through the origin
5.
In which pairs are the lines parallel – give reason for your answer
a)
y = 2x – 5
y = 2x + 1
b)
y = 3x + 6
y = 6x + 6
c)
y–x=3
y–x=0
Homework 4 – BH2.9
Calculators may be used for the following questions. Show all necessary working.
A tank which holds 100 litres of water has a leak.
After 150 minutes, there is no water left in the tank.
v
100
litres
O
minutes
150
t
The above graph represents the volume of water (v litres) against time (t minutes).
(a) Find the equation of the line in terms of v and t.
(b) How many minutes does it take for the container to lose 30 litres of water?
Homework 5 – BH2.11
Question 1
Question 2
Question 3
Question 4
Question 5
Homework 6 – BH3.2
Calculators must not be used for the following questions.
Show all necessary working.
1
.
x + y = 12
x–y=4
2.
x+y=5
x–y=2
3
.
2x + 4y = 7
4x – 3y = 3
4.
2x + 5y = 16
x–y =1
5
.
x+y =0
4x + 3y = 3
6.
2x – 5y = 1
4x – 3y = 9
7
.
x+y =2
2x – y = 2
8.
2x – y = 5
x – 2y = 4
9
.
2x + 3y = 8
3x + 2y = 17
10.
3x + 4y = -7
2x + y = -3
Homework 7 – BH3.3
Show all necessary working.
1
Alloys are made by mixing metals. Two different alloys are made using iron
and lead.
To make the first alloy 3 cubic centimetres of iron and 4 cubic centimetres of
lead are used . This alloy weighs 65 grams.
a) Let x be the weight of 1 cubic centimetre of iron and y be the weight of 1
cubic centimetre of lead – write an equation using x and y which satisfies
this condition.
To make the second alloy 5 cubic centimetres of iron and 7 cubic centimetres of
lead are used. This alloy weighs 112 grams.
b) Write an equation using x and y which satisfies this condition.
c) Find the weight of 1 cubic centimetre of iron and 1 cubic centimetre of lead.
2.
(a) 4 peaches and 3 grapefruits cost £1.30.
Write down an algebraic equation to illustrate this.
(b) 2 peaches and 4 grapefruits cost £1.20.
Write down an algebraic equation to illustrate this.
(c) Find the cost of 3 peaches and 2 grapefruits.
3.
The tickets for a Sports Club disco cost £2 for members and £3 for nonmembers.
(a) The total ticket money collected was £580.
x tickets were sold to members and y tickets were sold to non-members.
Use this information to write down an equation involving x and y.
(b) 250 people bought tickets for the disco.
Write down another equation involving x and y.
(c) How many tickets were sold to members?
Homework 8 – BH4.3
1.
Simplify
a)
2.
2𝑥
(𝑝−3)(𝑝+2)
𝑝+2
𝑥 2 −1
b)
𝑥 2 −7𝑥+6
3𝑥 2 +7𝑥+2
5𝑥+10
Simplify
a)
4.
b)
Factorise fully and simplify
a)
3.
6𝑥𝑦 2
4
5𝑥
+
1
b)
2𝑦
4𝑘+5
9
−
3𝑘−4
÷
9𝑣
6
Simplify
a)
2𝑞3
𝑟
×
5𝑟
b)
2𝑞4
18𝑣 3
𝑤
𝑤2
Homework 9 – BH5
1.
Express each of the following in its simplest form
(a) √8
(b) √12
(c) √27
(d) √20
(e) √50
(f) √28
(g) √18
(h) √24
(i) √200
(j) √75
(k) √45
(l) √72
(o) √54
(p) 7√8
(q) 5√32
(r) 6√40
(m) √300 (n) √147