Mathematics Standard Level Textbook Answers
ANSWERS
Worked solutions: Chapter 1
© Oxford University Press 2012: this may be reproduced for class use solely for the purchaser's institute
WORKED SOLUTIONS
1
Answers
Skills check
a
y
4 3 2 1 –2 –3 –1 –4
A C F D E
0
x
–4 –3 –2 –1 2 1 3 5 4
B
b
A
(0, 2),
B
(1, 0),
C
(−1, 0),
D
(0, 0),
E
(2, 1),
F
(−2, −2),
G
(3, −1),
H
(−1, 1)
a
4
x
+ 3
y
= 4(4) + 3(6)
=
16 + 18
=
34
b
z
2
− 3
y
= (−10)
2
− 3(6)
=
100 − 18
=
82
c
y
−
z
= 6 − (−10)
=
6 + 10
=
16
d
2 5
x yz
=
2(4) 5 6 ( 10)
=
−
8 5 60
=
−
13 60
a
3
x
− 6 = 6
3
x
= 12
x
= 4
b
5
x
+ 7 = −3
5
x
= −3 − 7 = −10
x
= −2
c
2
x
+ 6 = 11
x
+ 12
= 22
x
= 10
a
–1 1
y x
1 2 4 3 –2 –3 –4 –1 2 4 3 –4 –3 –2 7 6 5 0
Functions
1
b
–1 1
y x
2 4 6 8 10 12 14 16 2 4 3 –2 5 0
c
–1 –2 –3 1 2 3
y
–2 –4 0
x
2 4 6
a
(
x
+ 4)(
x
+ 5) =
x
2
+ 5
x
+ 4
x
+ 20
=
x
2
+ 9
x
+ 20
b
(
x
− 1)(
x
− 3) =
x
2
− 3
x
−
x
+ 3
=
x
2
− 4
x
+ 3
c
(
x
+ 5)(
x
− 4) =
x
2
− 4
x
+ 5
x
− 20
=
x
2
+
x
− 20
Investigation
– handshakes
Represents one person. Represents one handshake
a
So 4 people require 6 handshakes.
b
Number of peopleNumber of handshakes
2 1 3 3 4 6 5 10 6 15 7 21 8 28 9 36 10 45
Worked solutions: Chapter 1
© Oxford University Press 2012: this may be reproduced for class use solely for the purchaser's institute
WORKED SOLUTIONS
2
c
y
0
x
246810 5 15 25 35 45 Number of people
N u m b e r o f h a n d s h a k e s
d
H
=
1 2
n
(
n
– 1)
Exercise 1A
a
Function. All
x
values are different
b
Function. All
x
values are different
c
Relation. The domain contains more than one 4
d
Relation. The domain contains two ones
e
Relation. The domain contains two – 4s and two –3s
f
Function. All
x
values are different.
a
The domain is {0, 1, 2, 3, 4} The range is {0, 1, 2} It is a function because the domain has exactly one of each value.
b
The domain is {–1, 0, 1, 2, 3} The range is {–1, 0, 1, 2} Not a function as domain contains two −1s.
It is a function because the domain has exactly one of each value.
Exercise 1B
a
y x
0
Function. Crosses only once
b
y x
0
Function. Crosses only once
c
y
–1 –2 0
x
–1 –2 1 2 3 4 2 3 4 1
Relation. Crosses twice
d
y x
0
Function. Crosses only once
e
y
–2 0
x
2 1 2 1 –1
Relation. Crosses twice
f
y
0
x
Function. Crosses only once
g
y
–2 –1 1 0
x
2 1 3 5 4 2
Relation. Crosses twice
h
y
–1 –2 0
x
–1 –2 –3 –4 –5 1 2 3 2 3 1
Function. Crosses only once
Mathematics Standard Level Textbook Answers
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