86202831-International-Mathematics-4

Challenge Worksheet

5:03 Algebraic Expressions and
Indices

Name: Class:

Examples

1 Write each of the following without using negative or fractional indices.

a (x + 1)−2 b (x + 1)–2-1- c 2−x

= [(x + 1)2]−1 [ ]= (x + 1)12-- −1 = (2x)−1

= ---------1---------- = ----------1---------- = --1--
(x + 1)2 (x + 1) 2x

2 Write each of the following in index form.

a ------1------- b ---------1---------- c --------1---------
(2x)3 (x + 3)3 ex + 1

Let p = 2x Let p = x + 3 Let p = ex + 1

------1------- = --1-- ---------1---------- = --1-- --------1--------- = --1--
(2x)3 p3 (x + 3)3 p3 ex + 1 p 21--

= p−3 = p−3 = p–-21-
= (2x)−3 = (x + 3)−3 = (ex + 1)–2-1-

Exercise

1 Write each of the following without using negative or fractional indices.

a (x + 2)−3 b (x + 2)2-1- c (x + 2)–-12-

d 3−x e 3−2x f e−x
g (ex + 2)−1 h (ex + 2)−1 i (ex + 2)21--

2 Write each of the following in index form.

a 2x + 1 b x2 + 1 c ex
d --1----
e ---------1---------- f -------1--------
x (x + 2)2 x+2

g x x+1 h -------x-------- i ----x---2----
x+1 x+1

Answers can be found in the Interactive Student CD. 2 Copyright © Pearson Australia 2009
(a division of Pearson Australia Group Pty Ltd)
INTERNATIONAL MATHEMATICS 4 CHALLENGE WORKSHEETS This page may be photocopied for classroom use.

9:03 Challenge Worksheet

Solving Three Simultaneous
Equations

Name: Class:

Example If we have three unknown pronumerals,
we can find them provided we have three
equations we can solve simultaneously.

Find a, b and c if: a + 2b + 3c = 4 1
2a − b + 2c = 14 2
3
3a + b − c = 12

Firstly, eliminate one pronumeral from two different pairs of the equations.

Taking 1 + 2 × 2 , eliminate b. Taking 1 − 2 × 3 , eliminate b.

a + 2b + 3c = 4 a + 2b + 3c = 4
4a − 2b + 4c = 28 6a + 2b − 2c = 24

5a + 7c = 32 4 −5a + 5c = −20 5

The new equations formed, 4 and 5 , are two equations, with two unknown pronumerals.
Now solve these equations. Taking 4 + 5 , eliminate a.

5a + 7c = 32
−5a + 5c = −20

12c = 12
c=1

When you have found the value of one pronumeral, substitute back to find the others.
If c = 1, substitute into either 4 or 5 to find a, giving a = 5.

If a = 5 and c = 1, substitute into either 1 , 2 or 3 to find b, giving b = −2.

The solution is a = 5, b = −2, c = 1.

Exercise

1 Solve the following sets of simultaneous equations.

a a+b+c=6 b 2m + n + p = 3 c 5x + 2y + z = 0
3x + 4y + 2z = 14
2a + b − c = 13 m + 3n + 2p = 0 2x + 5y − 4z = 21

a + 2b + 3c = 7 m − 2n − p = 3

2 Find the cost of each drink, ice-cream and lolly if the cost of:
5 drinks, 3 ice-creams and 4 lollies is $25
4 drinks, 5 ice-creams and 2 lollies is $26
8 drinks, 6 ice-creams and 6 lollies is $43.

Answers can be found in the Interactive Student CD. 3 Copyright © Pearson Australia 2009
(a division of Pearson Australia Group Pty Ltd)
INTERNATIONAL MATHEMATICS 4 CHALLENGE WORKSHEETS This page may be photocopied for classroom use.

Challenge Worksheet

11:02 Regular Polygons and
Tessellations

Name: Class:

When a tessellation (tiling pattern) is made up of regular polygons of only one shape, it is said to
be a regular tessellation.

In Investigation 5:02C it was found that there are only three types of regular tessellations.
Semi-regular tessellations are formed by using one or more types of regular polygons in such a
way that the order of polygons at each vertex is the same. For instance, in the tessellation pictured,
at each vertex the polygons are arranged clockwise in the order square-octagon-octagon or (4-8-8).
There are only eight types of semi-regular tessellations.

4-8-8

Exercise

Use the table below to find the other seven semi-regular tessellations.

Angles of regular polygons

Polygon Sides Angle size

Triangle 3 60°
Square
Pentagon 4 90°
Hexagon
Heptagon 5 108°
Octagon
Nonagon 6 120°
Decagon
Undecagon 7 128 -4 °
Dodecagon
7

8 135°

9 140°

10 144°

11 147 --3-- °

11
12 150°

Answers can be found in the Interactive Student CD. 4 Copyright © Pearson Australia 2009
(a division of Pearson Australia Group Pty Ltd)
INTERNATIONAL MATHEMATICS 4 CHALLENGE WORKSHEETS This page may be photocopied for classroom use.

13:03 Challenge Worksheet

The Range of Values of the
Trig Ratios

Name: Class:

Exercise

In the diagram shown: E
• ∠ABE is a right angle
• X is any position on the ray BE X
• ∠XAB = θ. B

1 As X moves along the ray BE, away from B, what

happens to the:

a size of ∠BAX? θ

b length of BX? A

c length of AB? -BA---X-B-

d value of the ratio ?
e size of tan θ?

2 Considering the above:
a What is the smallest value of tan θ possible?
b What happens to tan θ as θ moves from 0° towards 90°?

3 a What happens to AX as θ moves from 0° towards 90°?

b What happens to -AA----XB-- as θ moves from 0° towards 90°?
c What are the smallest and largest possible values of cos θ?

4 a Do BX and AX get closer in value as θ moves from 0° towards 90°?
b Why is AX always bigger than BX?

c What happens to A-B---X-X-- as θ moves from 0° towards 90°?
d What are the smallest and largest possible values of sin θ?

Answers can be found in the Interactive Student CD. 5 Copyright © Pearson Australia 2009
(a division of Pearson Australia Group Pty Ltd)
INTERNATIONAL MATHEMATICS 4 CHALLENGE WORKSHEETS This page may be photocopied for classroom use.

Challenge Worksheet

13:06 Trigonometry and
the Limit of an Area

Name: Class:

We can find the area of a unit circle, using trigonometry.

O O OO

Square Pentagon Hexagon Dodecagon
n=4 n=5 n=6 n = 12

• These regular polygons are drawn inside a circle of radius 1 unit. As the number of
sides (n) of the polygon increases, the polygon area gets closer to the area of the circle.

• The vertices of each polygon are joined to the centre of the circle, forming congruent
isosceles triangles. If there are n sides, there will be n triangles.

Angle sum of a polygon = (n − 2) × 180°

Size of each angle = -(--n-----–----2----)-n--×-----1---8---0----°-

Exercise

Complete the following tables and area calculations.

1 2θ n 2θ θ OC AC AB

O1 B 4 2θ = (---n----–----2---)---×-----1---8---0---° θ = 2----θ- -O--1--C-- = sin θ A---1-C-- = cos θ AB = 2 × AC
1C n 2 OC = sin θ AC = cos θ = 2 cos …

θ = (---4----–----2---)-4---×----1---8---0---° =…
A
=… = sin … = cos …

Area of ᭝OAB = 21-- bh Area of square = 4 × area of ᭝OAB =
= cos … sin …

2 2θ n 2θ θ OC AC AB

1 B 5 2θ = (---n----–----2---)---×-----1---8---0---° θ = 2----θ- O---1--C-- = sin θ -A--1-C-- = cos θ AB = 2 × AC
n 2 OC = sin … AC = cos … = 2 cos …
O

C =… =…
1θ
A =…

Area of ᭝OAB = 21-- bh Area of pentagon = …
= cos … sin …

Answers can be found in the Interactive Student CD. 6 continued

INTERNATIONAL MATHEMATICS 4 CHALLENGE WORKSHEETS Copyright © Pearson Australia 2009
(a division of Pearson Australia Group Pty Ltd)
This page may be photocopied for classroom use.

13:06 Trigonometry and the Limit of an Area continued

From the tables on the previous page we see that:

Area of a square = 4 cos θ sin θ Area of a pentagon = 5 cos θ sin θ

where θ = -(--n-----–----2----)-n--×-----1---8---0----°- ÷ 2 = -(--n-----–----2---n-)---×-----9---0----°-

Call the area of the square A 4
∴ A 4 = 4 cos (---4-----–----2---4-)---×-----9---0----°- sin -(--4-----–----2---4-)---×-----9---0----°-

Call the area of the pentagon A 5
∴ A 5 = 5 cos -(--5-----–----2---5-)---×-----9---0----°- sin -(--5-----–----2---5-)---×-----9---0----°-

If A n is the area of a polygon with n sides,

A n = n cos (---n-----–----2---n-)---×-----9---0----°- sin (---n-----–----2---n-)---×-----9---0----°-

This formula applies to regular polygons drawn within a unit circle. We can use the
formula to find the area of polygons with n sides.

3 Use the formula to complete the table below. 20 100 1000 2000

n 4 5 6 12
An

4 How do the results in this table compare with the area of a circle of radius 1 unit using the
formula A = πr2?

5 How do the results compare with the value of π given by your calculator? Explain this.

Answers can be found in the Interactive Student CD. 7 Copyright © Pearson Australia 2009
(a division of Pearson Australia Group Pty Ltd)
INTERNATIONAL MATHEMATICS 4 CHALLENGE WORKSHEETS This page may be photocopied for classroom use.

Challenge Worksheet

13:08 Three-dimensional Problems

Name: Class:

Trigonometry can be used to solve three-dimensional problems. Look for right-
angled triangles, and try to work from what you know to what you wish to find.
Pythagoras’ theorem often proves useful.

Examples

1 For the rectangular prism drawn, find: D C
a ∠CEG 3
b the angle between the planes BCHE and EFGH. A B
H G
2
Solutions E 5 F
C
a ᭝CEG is right-angled at G. Using Pythagoras’ theorem 29 3
G
in ᭝EFG, EG = 29 units. 5 B
T 3
tan ∠CEG = ----3----- E Z F
29
6 cm
∴ ∠CEG = 29°7′ (to the nearest minute)
W
b The angle between planes BCHE and EFGH is the same as ∠BEF. 4 cm
tan ∠BEF = 5-3-
∴ ∠BEF = 30°58′ (to the nearest minute) A

2 The diagram shows a right square pyramid whose base edges
are 4 cm and slant edges are 6 cm. Find:

a ∠TWX
b ∠TWM.

Solutions TY M
6 cm X
a ᭝TWX is isosceles, so a perpendicular from
T will bisect WX at some point P, ie ᭝TWP X P W
is right-angled at P, and PW = 2 cm. 4 cm
cos ∠TWX = cos ∠TWP = 62--
∴ ∠TWX = 70°32′ (to the nearest minute)

b Because the figure is a ‘right’ square pramid, TM W
is perpendicular to the base, ie ∠TMW = 90°.
᭝WXY is right-angled at X. M 4 cm
Using Pythagoras’ theorem in ᭝WXY,

WY = 32 = 4 2 units. Y 4 cm X
T
Now MW = 1-2- WY, so MW = 2 2 cm.
Thus, in ᭝TMW, TW = 6 cm and MW = 2 2 cm. 6 cm

cos ∠TWM = -2---6----2-- M 2 2cm W
∴ ∠TWM = 61°52′ (to the nearest minute)

Answers can be found in the Interactive Student CD. 8 continued

INTERNATIONAL MATHEMATICS 4 CHALLENGE WORKSHEETS Copyright © Pearson Australia 2009
(a division of Pearson Australia Group Pty Ltd)

This page may be photocopied for classroom use.

13:08 Three-dimensional Problems continued

Exercise

1 The figure shown is a cube. D C In this exercise, give
B answers for angles to
Find the size of: A the nearest minute.
G
a ∠CFG

b ∠CEG. H

E 6 cm F G
H
2 The figure shown is a rectangular prism.

Calculate the size of: E F 2 cm
D
a ∠HAD b ∠CDB C
A 3 cm
c ∠HBA d ∠HBD. B

6 cm T

3 The figure shown is a right square pyramid. Calculate:

a the length of PR (to 3 significant figures) 12 cm
b the height OT (to 3 significant figures)

c the size of ∠TPQ S
d the size of ∠TPO R
e the size of ∠TMO, where M is the midpoint of QR.
P OM
8 cm Q

4V U The figure drawn is a rectangular prism. Given that

S T ∠VXZ = 21°43′, calculate the height of the prism, VZ,
Z Y to the nearest millimetre.

W 7 cm 5 cm
X

5 The figure is a rectangular prism where the ratio of D C

the sides EF:EH:EA = 3:2:5. Find: AB

a the angle between AF and EF

b the angle DF makes with the base EFGH

c the angle between the plane ABGH and EFGH HG

d the angle AG makes with the plane BCGF. EF

6 13 cm N The figure drawn is a right triangular prism where KL ⊥ LP

K and ∠KPL = 17°35′. Find:

5 cm M O a the length of KP (to the nearest millimetre)

b the size of ∠KPN.

LP

7 A flagpole stands at one corner P of a level square field PQRS,

each side of which is 120 m long. If the angle of elevation of QP
the top of the pole from Q is 13°19′, find:

a the height of the flagpole (to the nearest centimetre) RS

b the angle of elevation of the top of the pole from R.

8 A right regular hexagonal pyramid has base edges of 9 cm and a height
of 12 cm. Find:
a the angle one of the slant edges makes with the base
b the angle one of the triangular faces makes with the base.

Answers can be found in the Interactive Student CD. 9 Copyright © Pearson Australia 2009
(a division of Pearson Australia Group Pty Ltd)
INTERNATIONAL MATHEMATICS 4 CHALLENGE WORKSHEETS This page may be photocopied for classroom use.

"AOnTsXwFeSrTs'FPoVuOnEdBaUtJiPoOn 8WPoSrLkTsIhFeFeUtTs

2:01 Sides of Right-Angled Triangles

1 Check with your teacher.

2 a BC, AC b BC, AC c XY, AY d YZ, AZ
g HJ, AJ h CB, AB
e MJ, AJ f JK, AK
c ZY d LJ
3 a AB b CB g AB h JI

e PQ f GH

2:03 The Tangent Ratio b o 5, a 8 c o 4, a 7 d o 6, a 5
f o 7, a 13 g o 9, a 10 h o 11, a 20
1 a o 5, a 3 j o 8, a 5 k o 7, a 4 l o 5, a 6
e o 11, a 5 n o 13, a 7 o o 10, a 9 p o 20, a 11
i o 3, a 5
m o 5, a 11 b 1–150 c 5–671 d 0–577
f 1–004 g 1–893 h 0–081
2 a 0–306
e 0–291

2:04 Finding Unknown Sides Using Tangent

1a 5 b5 c 7–3 d 25

2 a 1–3 b 5–9 c 101–6 d 13–6 e 21–3 f 2–5
d 20–8
3 a 12–6 b 20–4 c 60–2 j 10–2 e 12–9 f 15–6
k 18–5 l 38–8
g 3–4 h 38–8 i 3–7

2:05 Finding Unknown Angles Using Tangent

1 R column spaces: 49o, 62o, 15o; tan R column spaces: 1–072, 0–325, 4–705

2 a 40o b 56o c 7o d 72o e 31o f 24o
f 16o
g 43o h 14o i 67o

3 a 31o b 17o c 19o d 61o e 49o

g 36o h 30o i 65o

2:07A Finding Unknown Sides Using Sine and Cosine

1 a sine b cosine c cosine d sine e cosine f cosine
k cosine l sine
g sine h sine i sine j cosine
e 12–6 f 8–8
m cosine n sine o sine p cosine k 27–7 l 5–6

2 a 5–2 b 11–7 c 4–1 d 18–2

g 20–4 h 3–0 i 58–7 j 21–1

m 11–7 n 2–4 o 5–8 p 95–1

2:07B Finding the Hypotenuse

1a -1- , 2 b -s--i--n---1-3---0---o- , 20 c --------1--------- , 8–19 d --------1-------- , 101–12
5 cos 27o sin 40o

e c---o---s--1--6---0---o-, 9 f s---i--n---1-7---2---o- , 37–85 g s---i--n---1-1---5---o- , 77–27 h -c--o---s--1-3----9---o-, 19–56

2 a 18(–9F3OFSBMJTFEb "1SJ2UINFUJD c 20–53 d 122–93 e 19–35 f 79–32
g 6–07 h -m1---3--2+-–--2--n-5- i 17–17 j 65–27 k 8–91 l 350–86
B a b C D 6pq E 17x 5y F 10c ÷ 11d G (m 10)2

H 4a 7 I x-x----+–----4-8- J 35a5 K a2 b2

B 75x cents C (y 25) years D (3n 10) CDs E $(100 x 2y) F -4---n---3-+-----3-- years

G (160 2x)° H vt km I $0.3D J x2 + y2 K 6x 2

INNTEEWRNSIAGTNIOPONSATLMMAATTHHEEMMAATTIICCSS 410F/O5.U1–N5D.2AFTOIOUNNDWAOTRIOKSNHWEEOTRSKASNHSEWETESRASNSWERS 1 Copyright © Pearson Australia 2009
(a division of Pearson Australia Group Pty Ltd)
5IJT QBHF NB©Z CPFe QaIrsPoUPnDEPdQuJFcEa tGiPoSn DAMBuTsTtSrPaPliNa 2 V0T0F5 .
This page may be photocopied for classroom use.

4 3 2 1 0 1 2 1 0 1 2 3 01 2345 6

H I J
5 4 3 2 1 0 2 1 0 1 2 3 01 2345 6

KLM

3 2 1 0 1 2 2 1 0 1 2 3 01 2345 6

B x 4V2CTUJUVUJPCO m 8 D n
3 E y 5 F a 3 G a
4
HB t 9 2 C I48 c 5 D 12J f E1 23 KF 2q·5
9 G 2·8L x 4H9 193 MI c3 5 18
NJ y 6 6 K O2·2k 9
TB a6 4 P x 4 Q y
5 R f 2 S t 16
C U7 x 3 D 1 V x 9E 6 WF 0x 4.5 G 40X w H4 20 YI p10
0 7·5
2:0J9B36CompasKs B e4a·5rings L 2·5 M 7-1- kmF
1 Ba "35'4PJNSNQVMJGMBZCNFJOH1 8"MHFCSBJDD ' SB4D0bUJPOT FE 12 I 23
E N c N I 7-9-
ME 1--W2--1-
19 35° 36 G H 411--9-6-1-2°
1-3-47 H
JB 27-4-W8 KC 1--7-7-3- E LD 2-1--3-01- 0 W 50 -7- G E
5 9
B 11-52-15 400 km45CK°CS 162-1-34 D 9 1--7-3-0- 0 E 3651--44 S F 04-3- G 145--1 H 6-54- I 13-1-8
JB LD ME F G H 75 km I

154--·728 CKN 3-12-6 DL 62-3-1 e M 15-- N S

BJ fN
d
4 2 3 B((BHaRaJaB 0 ,"1#xxx41623--1-22,---5Wx---( –02---5 1nx) 9---445 33SPayJk2-nIB-Nkk-M1-m)Q F-W–mm0-2-Q I-J0-y84O-m-MJk-JVDHmGBZ C-CSKSMJT OJ.UUHJCICF6--3-51cU---35 --FSV--2"qa0--BUU0IMxxxMJ H °P&P FOEERC((3 12--aV 11--.Sy-Py-2B,,B-GJ 24FU D4JDLTbbb))UP aIP'OPM218S---211VT---432B---E–58---91y8---U00--D42--JkcDJD--PUkJkkOPmmmxxxW OT 6----p- 7----m--- -7---a- 1----3---b- I -2-3--3-0--x-
E 25 F 12 G 30 24 km 45°H 20

6pa-h-0--MU---- --k++c--f--m---- m--77--b1g6----6----02ndn--°S((33,, EE 1-xx-1--3-5 --x- pm-n--q O -5W---m---F x g f2--3--3-0--t E G x1-m---0 - p q
N 24 P Q p-----+7-----q-
K M
2) (2, L x f S gh ( 2, x
1) 3) 2)

E x -b-a--c ( 1F, 3)x -t---–-u---w--- (1,G 2x) y-----+2-----5-

5 BH3B –8xx-19-4--5- k1lm mn CC xI1-6---30- x8 a(c DD bx1) -21 ---14-J2 x 2EEy x3-3---h65- 3 FKF x2-1x---01- 6-5-3--y- GG x1 -26 ---35-L2 x y--H-H--–4----x5--32-- 54-- MII xx-21- 7---2--3–-----y-
6 BDNa1J 91xxx3704-3 k- mk7((mx1y 2x5)) 13O-40,-7--5-,xxx 2 4r(t a--M---b–----c-83-- QC xx 2 x6 y 3 ,zx 3
7 K Lb s)113-12-2P kmx E x 2(x 2) 1, x 3


3 2 1 : 0 HBJHFBHHBNcbaJaBd 3 25$3$AA1-a-xx19x-BC-0&b-U00 Y 5 sU(22.SiD6DxnB((023E gF 1,x, CCB1B Z)xoBCKC N8) n ) CIgFm--3815-- --Fr-OEy41x-uE2F,U,$$e,T,,xx51n CBx18 tAA3. 7T15. 75 ri52EFaDLDDng,,2m-2--l-e1-n--JDAAs E 5-6---dc- GF 42x-2€€-uxx-- t11 FF 405 46(33 ((33x)xx G 87,)-23x- --ab- 5F , x2£ 2825H 15-- I 1-4-
€€1122DD06,,M.90BB-2-y--4- CCKEKI 2) 8, x 2 G
E, $137.20
E, GGI
y$$$yGPS1-83---1-7846A-6Q- H553ST 26258, J.Ox2SJHTK0 ,,43QHJ5NRCKI–8 V CIOIC38MKUT3-1B-LUO€€y$y,,F691I RGP859 P 206V 061T L&UDbLJR,SV,6S1--3-BS-4G-USPDJDJPJ,P y O£€$yy T163J ,U4S545P 0, 4033 EMo4.1H2PQ06 32-M-W F K1,TSP,CIMR FEKEKcFN TLA6y$$yA43U 73S 43, .41h8 0 -3--2-c---2-FF y$7 048H.403-1- M €y4-19- 220
G L $676 c 26o $670.80
5–1
d RHS,

3 Ba xx 5 (By4SY1P BoVU,3JQPRJOHO HS 4ZNCPMT Cb 2mx y3– 1,1A2AS Dc xk y8– 3,4SAS Ed 2y( x 1 2 y3)o , S1A2S

I 464 2N 35 1 T: E0HHBBNBHBHBBBBNHBFFBFBHBRBHHaaNBaaaTBa N1A€$$$$€T$26sx$yx2$t$$7y$1182 155-13-21-9-23-1-2I6a------i11508421---O0%·483x12590--yc420-00615n --#- n1NP9145.494%·152Txny4 B 67AF439033 5rx539030J xLY 5 O To03002,5x00M B U °3Hb°y0yA,56 , U,T2# a2yJ5H51 6Pyb3VEy2 S·MO 2i5JZ· lAH 48 2i
Tt PI6C4ySOICCIOCIICICOCIbbbbbbICCCC4RCUIICCOPFPeON$$$$$Q1$c$3c$11$$$$Uv3-51-1-13-1--22------1 24x 7135oo51828----N13852682928Q----50i261F----20me21Dss01321108·37112·%JU45A+nOw48S57676675·7602T77%0ZptIH220222O 522 N°°Ux 22 -,,6P 6GCGGCW2J24n mOT'10·2RU72x3xxKJTOSxx
HE E JDDPJ$JDJDPDJDJccccccEDDDD831 T 4Iy3y,,SJAB€yyy€$$$$€t38$$8$$$2sE 52-1-2-N32--431-a------JVPDDDJOi19272313---73··9735321---003SF n---n455W153966H356%6933· 3%5E-344447794F7497 1326358R85F72220S2022qa6c00010°O°22mma747,,H g342U 263 qI ··c6 T86201n EH EEj2xyy$$$$x 231223 9082d04533925m8l3,xx2526yy 4 7119 F FFFL£$$$£562112I 53349572J(T5c2752a 02Q2IEEIacd265B65iHv 37Fix43xs iN1oxx nC0B Zooy2 pC f74,yFP r yyyeiQgaI4hr PstUo©P47nDGMMGS8PAPGGGMQueJasF$$$$$trE4 r rs17121 ao2G11lP40305nia S58 534A87DG uM3B378rsoTrt023TurSap7PliPPaNt2y0 LV0tTd9F)
L
KD
EH F
DK L
Q E$21064y0 24 R
E K $228y92 7y F L$184x225 12x G M $4700a5 30b
QKKEKEKEEEEEddd Q$$$$ts3461$$49-1-2-a---i252312--661844--56n n--9002·69%9%4141452·5.8k969405260°° 4,, 1l138··69 LRLFFLLFFFFFee R£$$££$1sc481-112---i5o26--12117·20--356n--93s95272%9·353557106·20%82q622.569°° 37,2, 4221605·9·2 MGMSGGMGGGGMfS $$$$¥c5$684t-1 a-7o1121-2%4··9-0-n234s30546.·5%8x23474780251738 °°320,, 7716x56··00

5 : 0B 1 75#G0FrgTaUp #hVicZa
l4MCIPeQt1hQ0o0JOdgHo -fJSTUoTl
u $tDiIoBn4O0H0Fg E 7t F 50 cm G 5m
4 (2,FL3)£5102g0 5 ( 2GM , 2$4)4·2.5k0g
1 BH(0,$5230).075g CI $522080(g1, 2) DJ $57030 g 3 (3, 2) EK $115905g

6 H( 1$,5 420) I $781(01, 4) J €33 8 (3, 1) K $89.60 9 ( 1L, 3$)136.92 10 (1,M 2¥)264
I 5 N1 :T 0EHBHBNHBRag 2NAA5277€$T¥xxI500%O617( TN%00970APh05. 1Lgg5PeM-540-AESTTHuE MBbAOsTIEtCiICICSOCI bht44uFFtO1151iS$$$xxUoW6020N023 nJD·0%0...D5834A8 FMT%gg510IT2ON e5WthBOYRoK dSHEJDJDDJPcETS
25% E 14% F 12·5% Copyright ©G Pea5rs%on Australia 2009
A345€$$xN00·115S4 W00210%E.242Rgg7S.050 LF 45$$x00583 I%58Jc(T.a6m 7QdB0iHvFis NionBZo Cf FP eQaIrPsUoPnDMGGMfPAQuJsF85$$xtEr·57 a3mG lP50i%aS 2DGMBroTTuSpPPPNty LVtTdF)
KE 6$42%700 FLe

2 Ba €x1 .2(0x 2) 1C0, x$2 .440 D £5.68 KEKQd 71£$x510t 05.6. g7530 L 50 g M 4·2 kg
Eb x$1 02.2x0 3, x 3F $550 G $520

Hc $x7( .7P(31PE Tx B)O E3 I4, FxS$ W2J25DF0T 5BY J ¥400 Kd x$5 42(x 2) 1L, x $ 1 132 M € 89

BNe ¥$217x7.5 00(x 1) CO14€$, 2x3.5 3.552 DP $15172.5.500 EQf x$21 73502(0. 6x5) 8, x F 2$88 G $70

NHgi €$35%67xx90J T5.5U22B0((O23Dx F x#8)F)IO UX 1F$$2, F03x, O..x 84 1011P J2OUT J €12.70 Kh 4$x0. 653(3x 7) L5, x$3 52.70 M $55
P $504
Qj 2£x15 .730(3x 2) 8, x 2 Copyright © Pearson Australia 2009
I 3NTEBaRNA€xTyI1O N.2A16L03MATHEMACTICCSxb4 FO$yU2N5 .D48A T0I6ONDWORxKS HEDc2ET0S£AyN5S .W6E 8RES1 x 233 Ed $y1 0. 210 Fe $y55 I5J(T04a QdBiHviFs iNonBZo Cf FP eQaIrPsUoPnDGfPAQuJs$FytEr5a G2lPiaS02 DGMBroTTuSpPPPNty LVtTdF)
HBg $4y7 .723 C I3h $y2 50 1 D 3 Ji ¥y4 004E 4 Kj $y5 4 4
L $112 M € 89

NB $57.50 C O10 € 35.52 D 1P7 $57.5E0 20 QF $13342.65 G 41 H 61 I 34

N $493 O $10 722 P €7572 Q $2040 R £17 263 S $104 307

#FTU #VZ
4IPQQJOH -JTUT
$IBOHF

B $3.75 C $28 D $73 E $195 F £120 G $4.50
K $89.60 L $136.92 M ¥264
H $540 I $810 J €33
E 14% F 12·5% G 5%
B 20% C 12·5% D 25% K 64% L 40% M 8·3%

H 7% I 16% J 3·4% E 7t F 50 cm G 5m
K 150 g L 50 g M 4·2 kg
B 750 g C 100 g D 400 g

H 500 g I 500 g J 500 g

(PPET BOE 4FSWJDFT 5BY

B ¥170 C $2.35 D $112.50 E $2700 F $88 G $70
H €695 I $3.81 J €12.70 K $0.65 L $35.70 M $55
N $70.50 O $0.40 P $504 Q £15.70

B €1.20 C $2.40 D £5.68 E $10.20 F $550 G $520

H $7.73 I $250 J ¥400 K $54 L $112 M € 89
N $7.50 O € 35.52 P $57.50 Q $132.65

B 6"%OJ'THUPMBFSONTD PVFGM C B#&FFM9FUXWBFUFJPOO 1 BPOJDOEU T%5 FQSFTTJPOE
5#FBSJOHT F 8 G 10 H4 I7 J 4
0B27x5°4 o01r° 3N27°EC 1x0 80°58 D x36 02° 0 30E07x14m 40°233 F 2520° G 33264m0° H 360° I 900° J 360°
1B1°7420° C 31260° D 3540° 68E k54m40° G 1243440m°
F 1080°

b(BBBBB eu xAt5117(t1B.34·1e3CSr21-··/-P52JiB,Eo CCP3rQMOD)FPa NnJOB=OgCVTUCCCle CC NDXoB521F J(1fD820U0S0IO··°JC,64D 3B.BB)CMD P1DCSS)FP DPUIDDGT1B 7O(1· 11021--7,O3F-21 -5)SJBEEOH(M2F2, 05) F 34 G 41 H 61 I 34
I (6, 5 -21- )
F a((c2noF,dBBBAr rB1e531)sE 3·0p4G·°o8BnEdG Gin(CCCBg4E,174C249·s3)D,°·8FA¹¹HEDDC() 72491,·°15)

(=Bi s o(6scA(1-2-eB,lFeC6Os)F trS iBaMnCBJTgDFl(eCE2) ," 7S)JUIBNDCFDUJD( 3, 5) E (8, 3) F ((c4o, r2r)espondG in(g3,6s), AB¹¹HCD(7) 2-1- , 5) I (7, 5)
=  FAB ECD ( EGB)
I N T E(=aa(JBBJBBHBBGBJBR ca nnNolAB Addt(( 2(4a(7 6 T-23r-AeC(32 I12O5ar96r CD,e36BN1-24xnS- s5AA0BEB,-21bVa-Lp c )E,BCB7t2MCe oeJ1DAnD2-1T 1-2nF-=- T28tUHdO))C sx J 0E2UsiU)MB n°V,T°A1CCCCKKAtCKCEgA UT8CJICC CP 0( ( (SBCI47258-A-O°¹3114Bs·8*-41-31B¹--B2(F,,,, DO BA 33A -x-mUxCH-- CE--))1GN*--C--+–*--D)2))+--H¹--A--(4--8¹Tv(--Csn-Iy-tOBtDrNkE aDDLDDLDDWm) i(2OgsR5h( 1((t1 12-K-r66 )tS31aH,1-21-2ayi2--EDJg ,n,EeTh3ag7 Str)lA)632esNa5p)12-Sn-Wqa)gE5RlEEMEEEEMeSDI)2 ((( 6225 43($-31-,,130 3,n.3)72 D)) 10)F FFKEFFCD1T2(2(021a3as8·h2-1-2l75NLZM,0tex M YeLnN r 4V MbNn La)b 2a n5 t y ge l111EJ1e888WGGGGG8s000s05uX,$°°°(14 213-m -W(V 0x·41 81 a20iX0ocab F5e,°0°+°f ¹ 4 aa¹(O ((0 3y11sYss ) t825ttL0 Zxr rrI0bbMca aa)J( T1iiai ÷ gNQgHHHg 8HHd2B hhh01icccHvygttFti1 (12s) i aNiadav209o2-3 -nnn3nBCe1a133Zgo,sgg8o86 Cplfll 000FeyeeP FKr 8b))Qe)iga)Ih rPst6U 4-o©P-c-xn-Dn-IIIGII-PA-P3 -Q+-ue-J -asF (-1(234---trE33-0rms-0 -53a-oG5,Pl0niyaS0 AeDG) Mua1BrsoTr0tTusrSa)pPl2iPPaNt2y 0LV0tTd9F)
(bJoupt3p6oBsiAteD soK fBpC a4Dr·a5llelograLm)2·5 and YVZ WVX (vertically opposite)
M 17-- but ZYV YVZ

=B 1"8-74-04° J= N QMBBJGAAZGGCJOH -1-7- -3-"18MHH0CF°CD S BJDHD 'CS1-2D--B-01-DUJPOT E 5-3- (base s of isosceles triangle)

F ==-79- OWWVXXV i sG isoW-1-2-s-1-cVeXles H -1-9--1- I 79--
F =4-3- L WKXM WVGLM-54-K *
B H52--JC C 1-2- D 1--7--0- E 1-5- H -4- I -1-
  EMC 5 3

(J co5-4r-respondinKg 1-2-s, JH¹¹ MEL) 3-2- M -15- (base s of isosceles triangle)

(BbEa3-sC-5-e-x-M s of EisMoCsCce-3c-les trianglDe) 2--3--y- E -62---5p- F =b-71-u--m2- -t- tJhKeMse =arGe aL7-3l-M-t-0a-eKrn(a te *a)nHgle-1s-2--3-C0--b-opyright ©IPea-2r-3s--3o-0-n-x-Australia 2009
IN T E= ==RJRN A HOT2-1-2I--xO--J--51nHH--N $AJJLCCPHMOAiC TsHH SiEsMVoEASKFTsCIOcCMSeU6-5-1-- 4l5--5--2eqaF--OsSUJBNDOAHTIMOFNTWTLORK--11--42S----91H--00----Ekc--ETS N =1--1--3- 5-J-x-K¹¹ LM O 5-2---m4--- 5IJ(Ta QPdBiHvFis 2--N3i-o-3-0nB--Zto CfFP QeaIrPsUoPnDQPAQuJsF1-tEm-r- a-0G-PliaS DGMBrToTuSpPPPNty LVtTdF)
ANSWERMS -71---2d-
U 7--6--n-

B #AA4SJNQMJGZCJOHR H"SMHFCSBJDD 'SSSBSDUJPOT E SAS F AAS G SAS H AAS I SAS J SSS
F 12----10- G 1 -62---53- H 3-2- I -21-
B n-1-4-o-5- C n6-1--o-03- D n1o1-2---41- E 33----65-
B C D

J 3 -43- K -4-7--5- L 1 12-- M 8-3-

B -1a---0b- C 3-8---yx- D -m2---1-n-- E 5-6---dc- F 2--u--t G -23---ab- (a Hdivis1-5-ionCoopf yPreigahrsto©nIAPueastrrs4-1-aolniaAGursoturapliPat2y0L0td9)

INTERJ NAT3IONAL MATHEMAKTICS-m5-4-FOUNDATION WLOR2KSHEETS ANSWERMS -2-y--4- F6 5IJT QBHF NBZ CF QIPUPDPQJFE GPS DMBTTSPPN VTF

B 8-- C 3 -1- D --3--- E6 G -3--2-c---2- H 1-- I -1-
3 3 14 3 4

J --1--- K8 L6 M -2-

15 63 24 36 21 63 3 2

J 3 -34- K 4--7--5- L 1 12-- M -38-

B -1a---0b- C 3-8---yx- D m-2---1-n-- E -56---dc- F -2-u--t G -23---ab- H -1- I -1-
5 4

J 3 1ZUIBHPK SB-mT5--± 5IFPSFNL 2 M -2-y--4- G -3--2-c-2--2-24

B -83- 11 C 3 31--29 D 21--3--46- E 641 F 6 98 H -13- I 41--

JB x1--1--6- 8, y K 288 LC 6x 8
y M 20-23-8 D x 5, y 10 E a 7, b 17

F a 34, b 480 G a 3, b 97 H m 39, n 1921 I x 30, y 14
J p (5SP, qVQ JO11H 4ZNCPMT

B 12y C 24p D 30a E 20m F 3c2 G 15
HBB 581 541IxZFU I*OBEHFPCYS B-8TBIC1±X 547TI FPSFND 125
J 10m2 j 4l2 L 35a M 18
D 5Ea 64 F E323 d
521826pnax24c0y1111 1212xn68 18 357 2 ,,4 3056yq,25b yy 1KKCC12841y1c8IUOC 406320023942x1 8 2m014+n82t 5 x 6 6CGLDD2nm12x4xxa29706 9836
, ybVPJD F5 G4
BB 2Eq2 24 14 q01 F E59910864y9 24G 5823224F 2cH 7 17076 IG 1r020 0 30r0
HJB 36EM6c1292m407aq g881 3 2 c6 201n HNFD QK 2mwx21 2 0 0y4532k,9 y , 7 nly1 GO0 38x52qIEHP axrg 12562 0x370, ,by 1QI17SM 4dm4 304ax2 3 70xb
NBF 8119021 L
TJJ p2 R

B 6h7 C 40a4 D 9x8 E 5c3 F 12k3 G 16y13 H 80x7 I 64p6
J 1255IdF1 2*OEFKY -3BcXT L 343m15 M 21t10
B 8 C 81 D 125 E 64 N 4j6 O 1000y9 P 20x12 Q 3n9
F 32
B 21/6FHBUJWFC *O1E0J2D4FT D 4096
E 2401 F 59 049 G 5832 H 7776 I 100 000
I 6--1--4-
JB 214--187 CK 1-81-6 384 D -91- E 1--1--0- F 2--1--5- G 16-- H -6-1--4- Im

JB 6--1--1-1 CK c---4-1---- LD x--1-9-- ME a--1-1--2 NF 2----21--0-- OG 8--1--1-0 PH r---5-1---- Q d3
J n4192 K y10300 L x173 M q881 N w14140 O p821 P g5612 II 56 44p6
BB 64 h17 CC 42 03a4 DD 93 x28 EE 52 c13 FF 41 23k3 GG 31 66y13 HH 1800 x27
JJ 71 265d12 KK 31c1 4 LL 2340 31m15 MM 92 13t10 NN 419j6 OO 51 01000y9 PP 2120 x612 Q 3n9
B 2 3 C 11 2 D 5 2 E 3 3 F 4 3 G 7 2 H 10 3 I 2 4
J 9 /2 FHBUJWFK *O3E J5DFT

B -14- 'SBDUJPOBCM *-18O- EJDFT D 91-- E 1--1--0- F 2--1--5- G 1-6- H -6-1--4- I -6-1--4-
LD 1-1-1--13- ME 2-8-1--81-
JB 6-4-1--9- CK 81----10---0- NF 61----41---4- OG 58--1--1- PH 25----11---2-
GO 31 26 I1
NF 14 3 OG 52 10
BJ 34 1 KC 72 3 DL 31 62 ME 12 01 GO 71 22 (a HPdivis81io0nC oo2pf yPreigahrsto©nIAPueas5trrs aol4niaAGursoturapliPat2y0L0td9)
I NTERJBNAT67IO N6AL MATHEMACKTICS1841FO 4UNDATION WDLOR12KS10H EE1TS ANSWERMES 99 3 NF 219 5IJT QPHBHF31 N2B Z6 CF QIPUPDIPQJF1E1 GPS DMBTTSPPN VTF
BJ 1392 532 CK 2314 115 2 LD 532 02 EM 312 53 FN 14 83 HP 410 3 QI 22 4
R S T U
J K

HBB 604'SDBJFDOUJUPJGOJDB M/ *COPEUBJ6DU0JFP0TO D 6000 E 0·06 F 0·4 G 0·0004
860000 C I8 0·008 D 11 J 250 E 28 KF 6250000 G 5 L 0·025H 2 MI 136
0·81M 10 S 304
NJ 39300 K 7O 0·093 L 16 P QN 17000000 O 12 R 3040P 8 I 11
BT 06·054 C U8 832000D 11 E9 F2 G 2 H3 GQ 23 t 104
M 5 t 103
JB 41·53 t 102 K C21 4·3 t 10L3 30 D 4·3 tM 10145 NE 198t 102 O 12 F 8·2 tP1043 S 2 t 10 2
36 t 10 1 S 4 6 t 10 3T 2 J 2·7 U 102 1 G 0·0004
R I t K 4 t 10 2 L 8 t 10 4 M 36
H Q 3·2 t 10 4 R 2 t 104 S 304
I 30
N 6·48DtJF1O0UJGJD /OPUB3UJtPO1 0 P 7·5 t 10 2
GI 63 t2104
TB 160·75 t 103 CU 16·0203 t 105 D 6000 E 0·06 F 0·4 MQ 55 t5103
S 2 t 10 2
HN 8930400V00S0ET I 0·008 J 250 33 K 250000 L 0·025 26
BT 0·03504 O 0·093 P 0·81 Q 7000000 R 3040 I5 2
C U 21832000D 35 E F 110 G 30 H

BB 43·32t 102 C C6 24·3 t 10D3 3 D5 4·3 tE1034 3 FE 29 t15102 G 4 3F 8·2 tH1093 2

HJ 62 t1140 1 K I3 66 t 10 3L 6 J3 2·7 tM 106 1 17 NK 140t 310 2 O 2 5L 8 t 1P0 42 11
610·8 t210 31t0 10 7·5 10 12 0 Q 3·2 t 10 4 R 2 t 104
NR 1·75 t 103 S O32 1·23 t 1T0520 P2 tU
T U
B 7 C6 D26 E2 3 F 10 G 35 H4

J 3 4V2SET K 4 3 L 10 M6

B 30 C 21 D 35 E 33 F 110 G 30 H 26 I 30
G 43
B 3 2 C6 2 D35 E3 3 F 2 15 O2 5 (aHdivi9sionC2oopf yPreigahrsto©nIAPueas6trrsaolnia2AGursoturapliPat2y0L0td9)
5IJT QPBHF2 NBZ1 C1F QIPUPDQPQJF5E GP5S DMBTTSPPN VTF
INTEJRNAT2IONA1L4MATHEMAKTICS34 FO6UNDATION WLOR6KSHE3ETS ANSWERMS 6 17 N 10 3

R 10 2 S 32 10 T 20 2 U 10

B 7 C6 D26 E2 3 F 10 G 35 H4 I5 2

B 60 C 600 D 6000 E 0·06 F 0·4 G 0·0004

H 80000 I 0·008 J 250 K 250000 L 0·025 M 36

N 9300 O 0·093 P 0·81 Q 7000000 R 3040 S 304

T 0·054 U 832000

B 4·"3EtE1JU0JP2 O BOCE 44V·3CUtSB1D0U3JPO PDG 44V·S3EtT 104 E 9 t 102 F 8·2 t 103 G 3 t 104
M 5 t 103
BH 46 t510 1 I 6 t 10 3C 7J 2·7 t 10 1 DK 24 t610 2 L 8 t 1E0 64 3 S 2 t 10 2
561··7815t0t10103 3 t 10 P117·5 10 2 3·2 10 4 2 104
N O 1·23 t 1G 0513 t Q 15 2t R t I 0
F U H
T

J 15 K 11 6 L 12 13 M 3 2
B 6 43VS ET 2
FB 2302 4 C3 21 C 6 5 3 3 D 9 6 3 3 E 4 5 3 6
GD 4 355 4 2E 33 HF 11100 G 30 IH 3 276 3 I 30

JB 33 52 C6 2 KD 3 35 5 2 E 3 3 LF 42 215 7 6G 4 3 MH 291 22 I6 2

NJ 42 1114 K 36 OL 56 130 4 M 156 17 PN 210 73 2 6O 2 5 QP 2 211 2 5Q 5 5

RR 610 72 2 1S1 32 10 ST 620 62 6 3U 10
BB 47 2
C6 CD 32 66 E2 3 DF 103 G 35 EH 74 5 I5 2
K 43 GL 710 3 M6 H2 I 2 10
FJ 73 2

2

J 6 "3EEJUJPO BOE 4VCUSBDKUJP4O P5G 4VSET L3 3 M 3 C2opyright © Pearson Australia 2009

I N T EBR NA4TIO.N5AVL MMUAJTQHEMJMDABTIUCJSP4OFO UBNODEAT IO%NJCWWOJTRKJSPH7OEE TPS AG N4SWVESRES T D 2 6 (aEdivi6sion3of Pearson Australia Group Pty Ltd)
5IJT QBHF NBZ CF QIPUPDPQJFE GPS DMBTTSPPN VTF

F 5 10 G 13 11 H 15 2 I0
B 35 C6 6 D 66 E 18 15 F6 G 30 H 28
J 15 K 11 6 L 12 13 M 3 2
I 8 30 J4 K 25 L 40 M6 N5 2 O 6 42
63 2 6 356 3 3 9 6 3 3 E4 5 3 6
B 30 Q 48 21 C R S 12 D 3 7 U 65
P 3 T
F 2 2 4 3 G 4 5 4 2 H 10 I 3 7 3
B 2 C5 D 23 E2 F 13 G5 H8 5
J 35 L 4 2 7 6 M 21 2
I2 5 K 3 5 2
J3 K6 L5 M33 N 10 O4
N 4 11 O 5 10 4 15 P 2 7 2 6 Q 2 2 5
P4 3 Q3 5
R 6 7 2 11 S 6 6 6 3

B 4 #2JOPNJBM 1SPEVDUT­4C V3SET6 D3 E7 5
F 3 I 22110
BF 75 22 5 C 10 G 7153 D 3 10 2 5H E2 3 7 7 G 5 2 2

HJ 62 3 6 I 6 K4 43 5 J 7 21 L 3 3 M 32

B x2. V5MxUJQ M6JDBUJPOC B1O1E %5JWJT5JPO PG 4DVSE2T E 17 8 2 F 1 3 G 19

HB 103 5 4 6 C 6I 63 D 66 J 1 2E 718 15 K 9F 65 5 LG 1 30 H M2840 11 10

NI 814 30 J 4O 21 7 1K 1 2 5 P 19 L4 420 M6 N5 2 O 6 42
G 5 2 6
PB x320 4x 4 Q 4C8 721 4 3R 36 D 18 S8 122 3 E 2T1 3 87 5 FU 86 52 15

H 16 6 7 C I 36 10 11 J 10 4 6 K 16 2 39 L 355 10 10 H M 27 10 2
B 2 5 D2 3 E 2 F 13 G 8 5

I2 5 J3 K6 L5 M33 N 10 O4

P4 3 Q3 5

#JOPNJBM 1SPEVDUT­4VSET

B 5 "2SFB5 C 10 15 D 3 10 2 5 E 3 7 7 F 3 21 G 5 2 2
31J 4·27 m 2 21 E 353·4 cm2 F 127·2 m2 G 1963·5 cm2
HB 219·36 c m62 C I 3·56m 2 4 3 D E 17 8 2
426 cm2
BH x220 1·51xm m62 I C 98111·7 m5 2 5 D2 2K829m 25 5 F 1 3 G 19
B 78 mm2 C 96103 cm2 D 285 m2 E F 257 m2 G 313 cm2
HH 12037 54m26 I I m2 J 23J 6 c1m 22 7 K E 21 8 5 L L5501cm2 MM 245000 c1m1 2 10

N 14 O 21 7 11 P 19 4 2
D 18 8 2
B x2 4x 4 C 7 4 3 F 8 2 15 G 5 2 6
M 27 10 2
H 16 6 7 I 36 10 11 J 10 4 6 K 16 2 39 L 35 10 10

INTERNATIONAL MATHEMATICS 4 FOUNDATION WORKSHEETS ANSWERS Copyright © Pearson Australia 2009
(a division of Pearson Australia Group Pty Ltd)
E 353·4 cm2 5IJT QBHF NBZ CF QIPUPDPQJFE GPS DMBTTSPPN VTF

"SFB

B 19·6 cm2 C 3·5 m2 D 314·2 m2 F 127·2 m2 G 1963·5 cm2

H 201·1 mm2 I 981·7 m2

BBB 11J 44II44I477ccVPPmmSMMVVG33BNNJDJ FFF3 "84CCSFuBn22 Pi55tGs22 21mmSJ33TNT C DDJ II333300 ccJmmJ 33528 units2 EE 1177D6622J 55I mmmm33JJ 53FF2 u33n33it77s552 mm33 GG 44990000 ccmm33
E GG F1111 991122 ccmm33
BB 33F11a44cemm33 A CC B 225511 Cmm33 D DD 11E44113377Fccmm33 EEC 11F00a11c88e mm33 A BFF 3355C0022 mmmmD33

A&&reRRaVVJJWW1BB2MMFF8OOUU &&12RR8VVBBUUJJ9PP6OOTT 96 48 48 Area 225 375 375 375 375 225

HBBDH kmkmF a c e11117744 A CC B nn 1133C009900 D DD qmqmE 22220044F EE ff 2244 FF xx 2200 GG yy 99
NN aaA re11a66 200 II cc JJ KK tt 88 LL pp 1155 MM xx 2299
OO40yy 6680 80 PP 2xx00 775540 QQ zz 2266 FF cc 44 GG mm 22
LL nn 22 MM yy 1155
BB akk7a6 83366m2 CC xx 11 C 262JDJD0 ctnntm 2 22 EE 1yyxx1 20 66m44 m2
BHH II hh 11 44 KDK
NN qq 66 OO xx 11 PP aa 55··55 QQ uu 88

&&RRVVBBUUJJPPOOTT XXJJUUII ((SSPPVVQQJJOOHH 44ZZNNCCPPMMTT

BB 55xx 1155 CC 77aa 2288 DD 1188yy 2277 EE 2244mm 88 FF 44kk 2288 GG 33qq 2244
HH 1122yy 66 II 2200xx 1155 JJ 4400nn 5500 KK 1166xx 88 LL 77tt 3355 MM 1122cc 1122

HBBNNBH ada1rdr 4 47111111c0033PmMV3NF CC mm 33 DD nn 11 EE xx 55 FF yy 44 GG kk 33
II xxx2x5 26611m993 JJ mc3cm3 01111cm22 3 KK 1bbaa7 6774425 mm3 LL t3tcc 3 700115 m3 MM py4yp9 0 44 0··2255cm3
OCO PPD EQQ FRR GSS
B 31&&4RRmVV3BBUUJJPPOOTT CXXJJUU2II5 ''1SSmBBDD3UUJJPPOOTT D 14137 cm3
E 1018 m3 F 3502 mm3 G 11 912 cm3

BB xx &R66VJWBMFOUCC &RaaVB U J P11O00T DD mm 99 EE yy 88 FF tt 2211 GG xx 2211

BHH ppm 122788 CII ana 113009 DJJ wmw 11200400 EKK fhh 2664 LFL xx 55200 GMM ytt 11922

BHB aka 22 14 ICC xcx 110880 DDJ 2q2mm 2011 KEE tcc 81166 FFL 4p4yy 1151 MGG 3x300 2yy9
HHN 7a7xx 1886 IOI 22ykk 655 JJP 44xmm 751122 QKK z1166 2556aa
LL 44cc 66 MM 33mm 77
BBB xax 33 CCC cxc 11 DDD nmm 21155··55 EEE ydd 22677 FFF cee 11 44 GGG mm 255
NHHH qhkh 6556 IIOI htxt 111100 PJJJ mtma 5664·5 K x 4 L n 2 M y 15

Q u 8

BHBHB 655561222yxyxxaa&&&y RRR 1VVV919156BBBUUUJJJPPPOOOTTT CCCCCIIIXXXJJJUUU78x8x211IIImam000 ''(pxp SS 11S BBP222DD1228VUU555JJQPPJOOOTTH 4DDJJDDJD ZN6cc111462082ttC ynnnP33M T 25227000 EE 21525323cxx64ctt xm 1177 2288 FF 4371361655axtakxkk 344112500989 GG x137hhx7qn2n c 1111 00255142
HBB EKK LLF GMM
HBH 7a7xx 1 JJD 22nhh 11199 KEE FFL MGG
IIC 3m3qq 311 EKK x22xx 5 LFL 2y211 4 MMG k55cc 3
NHN 1r133 pp10 IOO x88mm 1988 PPJ 11c 44 xx1 1100 K a 4 L t 0 M y 4·5

N d 13 O x 6 P m 12 Q b 7 R c 1 S p 2
4PMWJOH 1SPCMFNT 6TJOH &RVBUJPOT
BB &R5V B8UJPOT XJUI 'SBDUCJPO7Tx
a C a 10 42 9 D -7ky- 9 E y 7 19
x 6 D m E 8 F t 21 G x 21
FH p5q 828 47 I a 10 G 5c J 2w0 100 KH 3hn 67 20 x4y ((5aa 01ddiivvEIiissiioow2nnCCoonoopp ffyy PPrreeii8ggaa3hhrr sstt oo©©nn2MG2AA6PP1uueeaass,3tttrrrrssn0 aaoollnnii aa 1AAGG21uuyrrss2oottuurraapplliiPPaatt22yy00LL00ttdd99))
-3nc- 166 13, n L
B 3an 29 27, nC 1x2 18 C 7(nD 42)m= 631, n 5 ED 71n6 1 53a 90, 2F1
IINNTTEEFHRRNNAA57TTIIOOnxNN AALL 88MMAA TTHHEE7MM3AA,TTIInCCSSI 44 FFOO12UU3NNkDD AATTII5OONN GWWOORR4KKSS(HHnEEJ EE TTSS6AA4NN)mSSWW EE RR5SS61,2n 20 KH n L11455cII JJTT QQ6BBHHIFF NNnBBZZ CCFF 2QQ2IIPPUU PP DDM PPQQ8JJFF,3EEnm GGPP SS DD1MMBB74TTTTSSPPPPNN VVTTFF

B xh-n--- -+3----35-8- C c 1 D m 15·5 E d 27 F e 14 3--5--n- G m 5
JH 10, n I 2t2 10 K 6n J 24m 465, n 3·5 L n 8 94, n 86 M 15, n 25

N 4----n-&---+-8R---V-1---B-2-UJ PO4T, nX JUI5 'SBDUJPOT
B 2a 1
C 8m 2 D c 3 E 3t 12 F 3x 4 G h 1
12n 20 K 2c 7
H 6y4 PM9WJOH *OFIRV1B0UJpPO T2 5 J E 5x L 15k 9 M x 10
6tC 0 K 12x 2 3
BB 5x C x 1 D 2h 19 2 1 F D6a 10 G 7n 5
0 12 3
H 7x 1 0 1I 23q 3 1 4 5 J L 21 3 2 1 0M 51c 2 3

EN 13p O 8m 8 P 14Fx 10 G
01 2345 6
4 3 2 1 0 1 2 1

H I J
5 4 3 2 1 0 2 1 0 1 2 3 01 2345 6

KL 0 1 2 3 M Copyright © Pearson Australia 2009
5IJ(Ta QdB0iHvFis Nio1nBZo Cf FP eQ2aIrPsUoPn3DPAQuJsF4tEr aGlPiaS D5GMBroTTuSpP6PPNty LVtTdF)
INTERNATIONAL M3ATH E2MAT IC1S 4 FO0UNDA1TION W2ORKSHEETS ANSWERS 2 1 E y 5
K q
9
B x 2 C m 8 D n
3 Q y
5 F a 3 G a
4

H t 2 I c 5 J f 1 L x 49 M c 18

N y 6 O k 9 P x 4 R f 2 S t 16

1 0 1 2 3 4 5 2 1 0 1 2 3 3 2 1 0 1 2 3

E F G
4 3 2 1 0 1 2 1 0 1 2 3 01 2345 6

HI J

4P M5WJO H4 1 SP3 CM F2N T1 6T0JOH &RVBUJPOT 2 1 012 3 01 2345 6

KB a 5 8 C 7x 42 L D 13-7k-n 9 M E y 7 19
0H 2 7 0I 1w 28 236 4 5 6
F 5q 83 427 1 0 1 G2 5c 20 2 1 320

HBB xt3n 4 P 2M92WJ O2H7 1, SnPCI CM1Fcm2N T 685TCJOH7 (&nDJR V4Bnf)U J
P=O 6 T133, n 5 ED 3-nqy- 6 59 13, n 2F1 a 3E 2n 3 GM21,can
14182
K
L x 49

BFN ya55an---nq- -+3-- --5-8- 688 4 8147073,, nnUO 21kx23 9 G 74x(n P 462x) 5 64, n 20 DQH 3n7-7kyx-nn
8 9715 34 . 5290940, ,nn RX1816wf 42IEIM -3wny-5--n- 7 282 1 512, SY9 6n8 ,pt n 2
5 711·456
FTJ 3 C 65cn V 224x0 495, n 3·5 LHW
GK

BBN 334---5n-n-'-- -+-8P---S9-1-N---2 -V2 MB7C4,F,nn1 8 152 C 7(n 4) = 63, n 5 D 3-3n-6 6 13, n 1221 E 2n 3 21, n 12
D 40 E 19 F G H 4 I 23
12115-n4-----·518n--n7--+43---- --2-+-8P--8 --8-M8-11-W-- -2J -O170H 03 ,*CCKK4,On,n1Fn 316 R 6347 V2122B53UJP3OT 4GDKLLD 4 (3n0 6) 5M 6,1n47 20 H 7n 13 90, n 11
JBFJB I n 22 8, n 14
6 n30 24 C 4E5, 6n4 3·5
J 95 M 3 42 1 FL n0 8 94G, n1 1 86D H M 6 3--5--n- 15,In 1825 3
61
BN 01 2 3 3 2 1 0 1 2
F
E G
01 2345 6
44PP MM4WWJJOO HH3 *-OJ UF2FRSVB MB1 &UJRP0VOBTU J1POT 2 1 0 12 3

HBB x a y C x 31-2a- D x IC p mn E x pq F JDx g f G x p q
13 5
15 04 22 40 2 1 01 2 3 30 12 21 03 14 25 36
I x 1--y--2- 2
EKH x y 8 J x FL a-----+c-----b- K x m-n-- L MGx f gh 2 M x p-----+7-----q-
2
B x n- 2---34-–-2----m- -23 12 01 01 12 D x h-----+-----g- 2 1 00 11 2-b-5a--c 3 F x t----–0----w--- 1 3 4 5y-----+-----65-
HB x D n I
3f E F Ja 3u G
42
C x 3y a E x G x
C m 8 y a

HH tx l 52 m n4 3II cx2 a1 (5c 0 b) JJ fx 2 y1 h2 1 0 KK 1qx

2-5- 53--y-9 3 LL Mxfxw y-4--4-2-900–4----5-- 1 3MM xc4 7-51---8-–-----y-6
Q y R 1 S t 136
KTNN y 6 O k 9 P x L a- 9----4b–----c- 2
ax 7 y34 52 1OU 0x 1r (t3 2 s) VP x 1 0 QW 1x 2 64y.35 z X 3Y p4
57·5 6

B x $ &'PYP2UNSSNBN 1VPMBBOZF N'CBFDOUUPmTS T 8 D n
3 E y 5 F a 3 G a
4

BHBB $3ta95 0 2 C CI1C8 c$61 83 .575D 40JDD f€c1 20 E1 19 EFKE 3€q661,
434 9 G 12FLF £x32 854H9 4 GMIG 2c$331 371.820
JHNH $2y118 056.60 K OI I7 k$45h 1.795 L 30PJJ x€ 1 26 M.940147 KQ €y1
065 R f 2 S t 16
EWFD 06x$(3 x7 3 .184)0.5 G
TBBB $a1575( 3x8 43) C U1C3 €x9 90 3 DC a3(0aDV €x36) 539E.2064 KH 4$(4c3 4 4) 11 FX w$7 08H4.E406q(q 10) YGI €1p89
20 7·5
HJF $1418('51P5 SN3kV)MBKF 6I4 $682 LG 93x J(x £344)3M 34 FLP 3br6((ra 87)) G
BBNNJ 321$223·854pyt74(5((2tP3828 pyM.W2 3 J0O) 51H)) -CKC JUO 31F86S7B€M 1&5R6V0BUDLDJKOSPO6 215T143x2(400((Px3 3$ 32h1))y5)0ME4 T 8(2 f) L $676I 4(4c 1) M $670.80
JR 19 FED 0 xc (cp q 3) G 12 HQM 425((57xm 8 1)0nI) 23
147
H 2t(2 9t) U 3(2c 1)
BBB 1x1 1538 ((a22mk y 15))CK 16C34 x -a- DC 9 3x20(xD3( xxx ) 2p)EM 36m44n 11 F x gHE f6 13(a 2)GI 1x8 p q
2 LG KL x2 (hm-n-- 2) L x5 IJ(Tfa Q dIMBiHvgFis hiNo1(nCB42Zoo cp(Cf yFmP r eiQg aI7 hrPst)Uo©2PnD)MPAPQueJasFxtrErs ao GlPniaS Ap-DG--uM-Br-+7s-oT-t-Tur--Saqp-PliPPaNt2y0 LV0tTd9F)
JF
I NTEHBRJNATx1 IO·4 7Ny2AyL(82M AyT8H EM3AC)TICSI346FOxUN DAT-1-yI-O-2-N DWK OR6K S14HE(JE5TSpAx NS W1E2-aR--)S--+c-----b-

B xxxxxx((((((nygxmx( &4 YSP aly7nn-- P --U --324yM3 4--S --W5V––--22B)))))-- --J)m(((Q(--( y8O--mm(--13xg3m--J5naHOxB HZ- 47 a N J 25JU))6)O)CICICOF)F) SO1BUBxxxxxxMT J& S TRr33a -2-1aV--(y-(yy-2Bt-c U JCGGCKO PaasbO))((((((Ttxykyy DDJPJD 813335))))))xxxxxx((((((t24xyk p2 a-hh-------3 ---- y----71b4b ----b)+–++c----ff----))))) --------mc----bgg---hn E (xxx p-b3-a-q-c)(x 2) F x -t---–----w--- 5)(q Gx py--- --+2---q--5-
BB ED F x gE u f(q G 3)x
(((xxx3um c -5m-n 5--3-- 26-y1-))y()(t( 73 z 1 n)d)) fy--- IE--–4---g-5-((-h52 p7----------+37–----------yq--
HF KH L x a)(a M 3)x y-----+2-----5-
KD L x y)(4x M 1)x
HB x
QH ((xyb -bc2-a--c))((ay -t--MIQ-–-u---w--(((-jcp 311))0(()52(cp G m 41)x)0)
NF
EL 1) F
BJ P d)
N EKT (€xm1 4 45- -3-8-y-)(m 8) FL £x2 85y---U--–4----5-(-q 7)(q GM 1)$x1 377---.--23–---0--y-

HBR x$(9c 0 l 6 )m(cn 1)IC $x1 8a3(.7c5 S b)(3 JD h)x€(13 2 20 y5 h)h

NBHB $x$117' a30Bn758Ddy.U6P4 0SJ5TJOHCIO 5SJ€$xO59P 19Nr.07(Jt5B MCT s ) 4DPJ an€x€d16 12563a---..--92b–---00-c- K €106
EQD $x 38 7a 3n.68dy0 2z
F $708.E4011 and 2 G € 920
$676E (p 4)(p M 5)$670.80
HB $$$((948xm&550 Y 25U1. S12B0)0 )(1(mxBZ N 48OCIF))OU€$$T611 885236.075CG (n J 1)£(3n4 3 2) KD ($m4 3 4 10)(m 1) L £285I (b 3)(b G 2)$137.20
NBF (b PD 2)$€(11b25 0041)
HJ $(1y0 5.36)0(y 4)I $51.75 K (d J 4)€(1d2 6.89)0 EH (€a1 443)(a 1) F M (q 3)(q 3)
KL (€c1 0 69)(c 2) $$7607(68a d.YQU4iv0is(((iotafnC oopf652yPr))e)ig((a(htrfast o © nGM25AP3)ue))as€$trrs69aol72nia00AGu.r8sot0urapliPat2y0L0td9)
BRN $$(((78xdy53 58996)))(((xdy 65))C O (k DJ 516))0£€(()36xk(45n 33 .452)1)0) ETP ((($$wxy34 37 43166.5)8)()0(y(wx 142)))
HV 4)I €990 S (n F 5IJT QBHF NBZ CF QIPUPDPQJFE GPS DMBTTSPPN VTF
$682 W (x KX L
FO€UN1D5A6TI0ON
INTENRNAT$IO4N5A2L .M2A0THEMATICSO4 WORKSHEPETS A$N1SW5E0RS4

"EEJUJPO BOE 4VCUSBDUJPO PG "MHFCSBJD 'SBDUJPOT

B 7-x- C -x--2- --xx----+-+----13----
D -x--5- --xx----–-–----13----
E x---1- --02----xx----––----71----
F ©- --x--P--e+-1-a--r1-3s--o-x-
-n- -+-Ax--u--8-s–--t-r-2a--l-i-
a 2009

Copyright

5BYBUJPO

B $2190 C $2352 D $1692 E $289 F $1425 G $705

H $854B0YBUJPO I $527 J $2940 K $3055 L $2556 M $153

B $1251390 C $8213752 D $316792 E $298292 F £$124220557 G $17305872

H €$$a$$0418945P330N0NPO 'BOICCDUP$$6$S8185T0112 6777222 J $323948007 K $132058564 L $62957526 M $21453783
NBB PDD €$c73567722
HH €$15$304(#x.97F3 5TU3 )#VZ
4COIIIPQ$4$$2Qh18810JO67H2 2-CJTUaT
( a$DPJJ IB€$$3 O773)H353F78207 QEE $6$22, 0394202 RFF £3£1272 206537 SGG $$311034837027
BN K $12 864 L $6972 M $24 783

EQD 6$$(12x90 5401) FR ££112702E63q(q 10) GS $$41.0540307

HF $45(#14F0 TU3 #k)VZ
4IIPQ$8Q1JO0H -GJTU3Tx
($J xI B€O43H)3F KH 4$(8c9 .640) L $136I.924(4c 1) M ¥264
272$$23%0typ35(((%4.t7830 5yp 3 ) 51)) 512x2(4((JDx3 3€ 32$ 32h·537)4)y%33%) 8rb61$$(((44r18a2%%99 5. 6 8 7f0))) £41$2011%·23506%UQM.92352(((275mxc 18 1))0nGM)
BJ 572 7 05%03800%((22ggmk 15)) C 1$2·85% K EL F 5$%4.50
HRN I 1$68%10 O KTP L ¥8·236%4
BHFB S
C 1020·5g% 2x(xDJ3( x5423x 005·)400%2%)gg EKDH 17612c544(tt0%%c(2 g 3)9t) F 5514002%·gc5m%EI 1123((am 22))MG 5%m
I 51060%g C L 48·23%kg
G
JB
BH 75¥(1054(700ySP0(Pgg2PVyEQ TJO B3HO) EJOCIC 4 1FBS$15JW200SJT.00D3 F5ggT 5K BY 4(DDJ5p 4 0102g) EL 72t(h 2) F 50 cmM (4c 7) G 5 m
$510102g.50
K $125700g0 L $5808g M $47·20kg
E F G

HB €(x6(9 P5 2P)E(3T BO aE)I 4FS$W3J.D8F1T 5CBY( x J 1)€(122 .7 b0) KD ($x0 .6 35)(x 2) L $35.7E0 (q 5)(q M3)$55
NBF $(¥n7107 .0 540)(m 5)OC $$02..4305 G (y PD 3)$$(51y01 42 .15)0 QHE (£$u12 57 .0570)0(t 1) F $88 I (5 a)(a G 3)$70
BHB €(m16.92 50 5)(a 2)CI EKD ($310c0.6 .25 10)(3 d) FL $5350.7E0 (2 y)(4x GM 1)$5250
HNF $(x7.0 7. 3530)(x 4)IO $23.4801 C (y DJ 3)£€(514.26 .87 b0) KQH (£$m5145 . 720)(7 n) L $112I (j 3)(5 Mm)€ 89
$205.400 G (t JP 8)¥($t45 0 043) QEL ($$y11 30 2.22.)60(5y 1) F $550M (c 1)(2c G 4)$520
NBJ €$(g71.. 52 004)(g 7)OC €$325.4.502 K (k PD 5)£$(55k7.6 .58 40)

NHRN ($$(%yc77.. J 57T 036U3B))O((c3Dx F 1# )6FIO)UXF€$F32O55 .015P2JOSOUT(( y3 J 3)¥(4x0 0 7) KP ($b5 4 c)(a d) L $112Q (p 10)(p M 1€08)9
P h)$(537 .5 50h)
QT ($m13 2 8.6)(5m 8) U (q 7)(q 1)

BBBJFBBBBB 5x4(1x%m' aBJn T11DdU 33U1BP4)OS(DJmTFJ O CCCC#H 8F 3x1xU)5X0 SJFOFP55ON88 1JPBMJDDDCCDTO UT3xx ( n 14 722a 1n00)d(n1 Ex 233 D 8 and 2 E 11 and 2
BN E4 20 233 FD (m3 4 10)(mG 1)41 HE (p6 1 4)(p I5) 34
BRBV E E2)x
(4.x JE1Q0P)J(OxU C 43) DG (3b 2)(b E1)4
H (a 3)(a 1) I (b 3)(b 2)

J (( (((22((5(((( ((3-2-23–-- -1-7--6 x1--------(.(6323 y yxd6233 -----"a222-----014 -----,3,33-----2-121-12-2-12121--2Sm -----S ---E---3ac+-----J55---B B,,,,,,2-111-2E2---x--E---9)693)---aEE,,74–---3263326Q---J+)---)))JUJ---))
))m–P21-----2121--21((((1FF---J---- ---1Pxdyy---JOO)))
)---a4O---+---O
--U 9U--–Um--TT --2CCKCCCKC CCKKCCCCC--B6--454 --79--O+)--)))--
-(( ((( 1(( ((( -8-5E58----41031212301-0-41-13-4-131- -----,,,,,,,,,,-
4 3733 3733V))))))))11C))MCHCMHUSB2-- --y D-xx-xx------2------223-U----4-2x 2DDLDDDLD2DDLDDDDOSDLKW------x-J------xyxcy-----x-P+–-----++-------+------+–-----+O+ (1(((((((((1(( (–-+12------12-1-4-------33-93166 nkxd6163------33 4-----31232-----x1Px7,,,,-----c2-12-121-211-2-21---- -- ---
---7

G 5 5-,,,,,,-– -5)-4)6133"3-7373 -1-)))0))-cM))2212--2-1(((-H--)-xdk-–-12-21())-F----n- ) C) 2---EEEMEEE EEEEEMEES-M
M485B))1)J (((2((((( ( (2D)2528 2582 44-131-3-IDDIN-2',,,,,,,,110S 353 353,,B))))))7272-6-- 16 -x-xD----------))5))2x-----9 xx2xU---------xxxJ----2+----+P–--------–----–++O---- 2----x5-------12FFFFF3FFTFXFPFFLT---1
5------ -x
--
x--x---- (((222(2(((((--–--+4342432cxyw--+---1221-----34,,,,,,x-- 4-- --34 2 2---- –--9-
1-)6)1414-6-)1-5)))))-)-((-)
(cy(wx GGGGG GGGGGG21JEJEO)42)((1(1((()3-1)-13--34 34 5-- 4- -1x-x-----4-----,,,,x11x1-----17 xx2-----1----26226,,02----–----–+–----x)))) –----xx--------12133----33----––4---
)+--)----x--- 71----x5----
--x+HHHHHHHHUYHQHHM-----2--(( (( (((((--
7 qa7 tf22-23-32--64343 -21-12 --1,,,,,,6532 5 555))))))88)()(KKFFP(())tfqa 2-- - -x - x----------3yx2x----2-IIIIIxIIIIII25-----3----3-h)-----)+++-----––1–)8-----)----------6( (((( (+143------34-y2359-6------9670670-----h-----53x5-3-----x-3

1,,,-,,,+---2--- ---4+505
505---x---y–5--- ))---))-12-12----8-40---–+---5---))---h---h2---7------–---
-
----1----


B

B
JB

J

BG
J
BL
BB
B
BG

B

L

INTERNATIONAL MATHEMATICS 4 FOUNDATION WORKSHEETS ANSWERS Copyright © Pearson Australia 2009
INTERNATIONAL MATHEMATICS 4 FOUNDATION WORKSHEETS ANSWERS (a division of Pearson Australia Group Pty Ltd)
5IJT QBHF NBZ CF QIPUPDPQJFE GPS DMBTTSPPN VTF

Copyright © Pearson Australia 2009
(a division of Pearson Australia Group Pty Ltd)
5IJT QBHF NBZ CF QIPUPDPQJFE GPS DMBTTSPPN VTF

Copyright © Pearson Australia 2009

(SBQIJOH -JOFT Cx 0 1 2 Dx 0 2 Ex 2 4 6
B x 0 1 2 y234 y20 y024

y012

F (xSBQI0JOH -3JOFT Gx 0 1 2 Hx 012 Ix 1 3 5
y 3 0
B x01 2 y258 y 0 1 2 y420
Cx 0 1 2 Dx 02 Ex 2 4 6

J xy 00 11 22 K xy 02 33 4 L xy 42 50 6 M xy 00 12·5 4

y 0 5 10 y60 y0 y30
Fx 0 3 Gx 0 1 2 Hx 0 1 2 Ix 1 3 5
B x-iynterc e3pt 01, y-intercept 4y
25 8 C 4y, 10 1 D 2 0, 0 y 420
4, 1 H 2, 2 2-1- 0 1·5
E 3, 3 F 2, 2 G 0 3 Lx 4 I 1 , 3
6 M
Jx012 Kx 5 x

(ySBEJF0OU¬*5OUFS1D0FQU 'PSN y 6 0 y0 y30

B J 1 JJ 1 CJ 6 JJ 3-2- D J 44, JJ 2 E J2 JJ -12-
B x-intercept 1, y-intercept 4 C 1 D 0, 0
B yy3, 43-21-xx 35 C y G 3-34-x4x, 1110 D y 2,x2 2 E3 y 7x 2
E F 2, 2 G y H I 1 21-- , I y 6x 1-2-
F H y 5x

B y( S2BxEJ FO2U¬*OUFSDFQU 'PCSNy 4x 3 D y 1-3- x 1 E y 54--6xx JJ61 2-1-
FB yJ 1 5x J4J 1 C GJ y6 x JJ 2 23-- JH y4 8x JJ 2 IJ y 2
D E

B y 4x 3 C y 3x 1 D y x 2 E y 7x 2

F yy1 PJ2-12O-xxU¬ (15S0BEJFOU 'PSN G y 2-34-xx 110 H y 5x I y 3 64-5-y3xxx 1-216-38
B C y D y 5 3-1-x3xx 714 E y
FB yy 62xx 122 GC yy 44xx 232 HD yy xy
IE 0

JF 5yx 45yx 148 0 KG 3yx 5xy 223 0 H y 8x I y 6x 1

B y 4x 21 C y 3x D 5x 2y 0 E x 10y 5 0
F y1 P JOxU¬ (1SBEJFOU 'PSN G 4x 3y 35 0
B y 2x 10 C y 2x 1 D y 5x 7 E y 3x 8
F y1 BS6BxMM FM1 B2OE 1FSQFOEJDGVMByS -4JOxF T 22 H y 3x 4 I x 3y 13 0

CJ ol5uxm n4Ay: 1B8 10 CK 43x 5y 2D3 10 E 55x4-5- F 2 G 23- -
KD 0L 3 ME 5x
B y 4x 21H 4-1- IC 3y 3x J -72- 0 2y 10y 5 0
F y x 1 G 4x 3y 35
Column B: B 1 C4 D1 E 4-5- F 1-2- G -32-

BCC ooall(1uu, bmmBS,BSnnBlQMBAIMF:J:OM BHHOHBB *EO4 F111R-41-FVSQBMFJUOJFETJD ICICC VMc344B13--,Sd -,JeO,FgT, i,JJDDk 172-- K 55-4- L -1- M5
E F G 32--
7-2- 3 2 M5

1 K5 L 3

B x 1 C y x 1-3C- D x 2y 22-7- E 54-y- 2 F 2-1- F x G 23-3- G 3x 2y 6
B y H4 I yJ E L 13-y- y
K 5 D M5 E y

B a, b, l C c, d, e, g, i, k

2

(SBQIJOH *OFRVBMJUJFT D x 2y 2 2 1 F x y 3
y 3 xE
B x 1 C y x x x E y 2 G 3x 2y 4 6x
D
B y C y 2 y 3

F y2 Gy H yI y

4x 2 x 1 4x
2 1 3
3x
2 x 2x x
1
4x
y
Fy Gy H y 4 I

4

4x 2 x 1
2 x Copyright © Pearson Australia x2009
INTERNATIONAL MATHEMATICS 4 FOUNDATION WORKSHEETS ANSWERS
(a division of Pearson Australia Gro u1p Pty Ltd)

4 5IJT QBHF NBZ CF QIPUPDPQJFE GPS DMBTTSPPN VTF

Copyright © Pearson Australia 2009

(SBQIJOH *OFRVBMJUJFT

B x 1 C y x D x 2y 2 E y 2 F x y 3 G 3x 2y 6
D yE
B y Cy y

$PNN2PO 'BDUPST

B a C6 Dc 2 x E 6, 3 1F3 G3 4x
H1 I 4hx J 2
C a (a 3) D 6(x 1) 3x 3
B 5(x 3) H 4(c 4)
L b(aH 7) E q(q 10)
P r(r 8)
F 4(1 3k) G 3x (x 4) T 8(2 f) I 4(4c 1)
FJ 3y(3y y 1) K 2G (4 3h) y x D c(c 3) y M 2(7Im 10n) y
N 2t(t 34) H 2t(2 9t)
R 2p(8p 5) O 5x(x 3) L 2(h 2) Q 5(5x 8)

S 12(3 2y) U 3(2c 1) 1

B 3(2m 5) x C x2(x3( x2x ) 2) 2 Ex 13(a 2) 1 x
F 8(2k 1) 4 G I 12(m 2)
J 4y(2y 3) 4 M (4c 7)
K 4(5p 12)

(SPVQJOH JO 1BJST
B (x( S B2Q)(I3JD B Ma .) FUIPE PG C4P(MVxU JP 1O) (2 b)
D (x 3)(x 2) E (qC o p5yr)ig(hqt © 3Pe)arson Australia 2009
I N TERB((FN 0A,1T((I2,nmO)N A L2 4M)5)A)(T(HmaEM AT 25IC)S)4 FOU NDA((T11IO,,N42WCG))OR((KyySH EE T33S ))AN((4ySW ER S1b)) (3, 2) (u 5)(t 1) (2, 3) 5IJ(Ta QEIdBiHvFis(( Ni25onB Zo C fayFP ))eQ((aIr4aP((sUxo1 P nD,2 PA3 ,Q1u)J22sF)tE))r aGlPiaS DGMBroTTuSpPPPNty LVtTdF)
(3, 1) H (3c 1)(3 d() 1, 3)
D

RNFBJB "x(((x(cxgy 5 (1 I634x3F)))) ( (((4c xg32Vx )C C 147T )))6U1Jx)0UV , Ux8JP O 4 .FGKDOSUI(((x(P3tykE 2 835h))))((((txk3 3 E 745)))hx) 3 H (m 2)(7 n) I (j 3)(5 m)
D x (1 x) 3, x 2
FLP (xx((ybm 26 c2 x8))() (a(y m3 , Gxd1 ))8 x) 32 MHQ x((pc 11-45-)0()2(cp I 41)x0) 2
TC U (q 7)(q 1)
E x 2(x 2) 1, x 3

F 2'xB D(UPxS JT 1JO) H 51S4J,OxP N5JBMT G x 5( x) 8, x 2

BH 15xan d2(43 x) 1, x 1 C 4 and 1 ID 4 x8 an3(d3 x2 7) 5, x 2 E 11 and 2

BJ 3(mx 21()2(xm 8 8)) 2, x 2C (n 1)(n 2) KD (2mx 31(03)x(m 2 )1 ) 8, x 2E (p 4)(p 5)

FB (yx 610)(x 4C) y 6 G (b D 2)y(b 1) HE (ya 31)(a 1) F y 4I (b 3)(b G2)y 2

HJ y(y 23)(y 4)I y 1 K (d J 4)y(d 48) LK (yc 94)(c 2) M (q 3)(q 3)

N (y 6)(y 5) O (k 6)(k 5) P (x 15)(x 2) Q (t 6)(t 2)
R (x6 TJ9O)H(x 4 JN6)VMUBOFPVT &S RV(nBU JP1O0T) (UnP 4P1)MWF 1SPCMFTNT(y 6)(y 1)
VB x(d y9 )(3d 4) U (a 2)(a 3)
WC (2xx y5) (x12 4) XD (xw y 6 )(4w 4) YE (2f(x 5 )y()f 152)

F y x 2 G x 3y 14 H y 3x I x y 4
B 6"x E E5JyUJP O2 8BOE 4VCUSBDUCJPO3x P G "y M HF5CSBJD 'SBDUJPODT 2x 3y 19 E 3x 4y 78

BF xy7-x- 5x 3 C x---2- GC--xx----+-+x2---x- 13--- -
8 3, yy 4 D x---5- --xx----–-–----13HD----
y 3x 7 E x---1- --02----xx----––----71----
I 4x 7yF -4--x----+-1---1-3---x-
-- -+-x----8-–----2----

B 5, y 2 4 x 5, y 1 E x 2, y


FG x- --2- --m--- 1---24–---,-m-1-y--
--+- --m- -2- --9-6+-----4----
H ---2-G--c----–-x--9--3 --c-
--1-– --,3--1-y-c----– --- -2-3---
I ---2---x-----+- ---2-1--x-
--- -–-4---4x-----–----1----
J 4-1---7x- K ---y----+-8----y5----
+-- ---y5---0-+-----7----

BBGBBBBBBBBB L 75266715st- 1--6---6ai ---29·424a---0n n1---3---000·0T2---//a+---6''4-- 3°°°°J2--x--OPP0--aPP37--3--+°--HSS°OO--
–--,NN,-- -- 1--516--OOa4--VV--
2S·-9VV-5–J-·MM-HCCCCCC4-BBNN--7P-FF--
FFO911191CCCCSS2002PJJ8686DDNc3c1BB0000oo39FMM°°°° ss·7U11HCM4S66·SS0Z02PP 2--y -°°xUx---PP---,,3P---4x 22DDDDDD----GG--24-y y--xTT-–--++-'--0·--- ---7+355553–-+--J1---33-O---4664--22--x7--E0000---
DDDD°°°° 4J88stEai·9Fnn5· 35-4EEEEEE5F7°O°,,515515H344444UIDN26I4004··°°00T86°°6--16 -x------x---9xx2x-------2+--+–------+--2--x5---EEFEFFFFEF-
5-- -x-x--112882-3s4t-+-+0505a-i66-n-n28824-·6-3-10000-41-·-
9°°°°94°°,,
O 111331004224 - -----xx4444--1--FFF--2--0000–--+--x–--°°°°----12--c183--4--
+o--·7--x-9- -s9-x5--1·--8x+HHHH-2---°-2-,-4343--
266600·°°9 P 2- -x----3--GGGxIIII2----h----––------69797+6t4--9--9a--00h·9--n21-00·2--8
-2°°-–- -5-4--5°--h,-hJJJJ--1-–---53344--1-·66-0--
00°°
GG 5----x-F---–-----s3-in 32°, 415·2 F ---x-G----–---c-6--o---s 71°, 66·0
1138GGGG··6JE9 x2 – 1 K x2 + 2x

((bb((LiieeuussxxAAoott–-1tt-BBss-ee-14-ccCC-rr-3cee-iiBBooll CCeerrssDDaattnnrrBB==iiggCCaallnneeDDggooBBll ffeeDD))OOCCBBBBCCDDDDMCC)) --2---x----+-----4--- aa((((==ccccnnooooFF ddAArrrrrrrrBBFFeeeessssAAEE ppppBBGGooooBBnnnn EEdddd GGiiiinnnnEEBBggggCCEEDDCCssssDD((,,,, AAFF 5AABBI¹¹J¹¹(T¹¹EEa¹¹ QEEdGGCCBiHCCvDDBBFis ))))Ni))onCBZoo pCfFyPr eQigaIhrPstUo©PnDPAPQueJasFtrErs aoGlPniaS ADGMuBrsoTtTurSapPliPPaNt2y0 LV0tTd9F)
x2 + 4x

INTE==RNA TIOAANABBLCCMA T H E22MAttBBTIDDCSCC4BBF ODDUCCNDBBATDDIOCCN WORKSHEETS ANSWERS
(==(((aaccaannoollAA ddttrreeCCrrrrCCeeBBnnssAAEEaapp BBBBttooeeDDnn==ddCC ssiiBB nn,,AAEEggAACCCCCC BBAA¹¹ss**BB¹¹((,, BBAA EE**CC**))))¹¹¹¹ BBEE)) LLMMNN 118800°° ccbbaa°°°°°° ((ssttrraaiigghhtt aannggllee))
 MMNNLL 118800°° ((ssttrraaiigghhtt aannggllee))
 NNLLMM 118800°° ((ssttrraaiigghhtt aannggllee))

TThheenn aannggllee ssuumm ooff OOLLMMNN ggiivveess
118800 bb 1188005544 00 aaii 55ee 44aaaa 0011 88 00bbbb 11 88 00cccccc Caa111133o888866p 00y0000 rbbigh t ©cc Pearson Australia 2009
IN TEaaRNnnABBddTIAAONDDABBL MCCA11DDT88HE 00M°°A11T 88IC 00S4°°FBB OAAU NGGDHHA((TCCssIOttNDDrraaWii((OggssRhhttKrrSttaaHaaiiEggEnnThhSggttAlleeNaaS))nnWggERllSee)) aa((bb((bbaannuullZZaaddttttssYYeeeerrVVnnZZYYaa YYVVsstt eeVVZZooff WW iiss ssXX,,ooWWVVssYYWWccVVXXeeVVZZll¹¹eeXX¹¹ssYY((5ttZZvvrrIiiJ))(eeTaaa rrQnndttBiiiggHvcciFllsaaee iNoll))llnByyZo Coof FPpp eQppaIrPoosUossPniiDttPAeeQu))JsFtEra GlPiaS DGMBroTuTSpPPPNty LVtTdF)
bbuutt BBAADD BBCCDD
((ooppppoossiittee ss ooff ppaarraalllleellooggrraamm))
==118800°° BBAAGG 118800°° HHCCDD

B 540° C 1080° D 360° E 1440° F 2520° G 3240°

B 72"0E°EJUJPO CBO1E2 460V°CUSBDUDJP5O4 P0G° 4VSETE 540° F 1080° G 1440° H 360° I 900° J 360°

B 4 /5 PO OVNFSJDBM 1SPPCGT 7 D26 E6 3

F(exA5tBeCr1io0 r BCD  BDC G 13 11 H 1(5coFAr2rBes ponEdGinBg s, FA¹¹IEC0)
angle of OBCD) L 1a2nd 13EGB ECD M 3 2
Jbut 15BCD =  BDC K 11 6

B(is6osc3ele s tr2iangle) C 6 5 3 3 D 9(co6rre sp3on3ding s, AB¹¹ECD4) 5 3 6
= ABC BDC BDC =  FAB ECD ( EGB)
F 2 2 4 2 t3BDC G 4 5 4 2 H 10 I 3 7 3

JA3CB5 CBE * K 3 5 2 L 4L2M N7 1680° b° (straiMgh2t 1ang2le)

N(al4tern1a1te s, AC¹¹ BE) O 5 10 4 15 P 2M7N L2 1680° a° (straiQgh t an2gl e)2 5
R(acno6drre7sEpB oDn2d i n1g1CAsB, * NLM 180° c° (straight angle)
AC¹¹ BES ) 6 6 6 3
Then angle sum of OLMN gives

B= 4C2AB = ACB ( *) C 3 6 D 1830 b 180 a 180 E c7 1580

F72 G 73 H2 540 a b I c2 11800
L3 3 i5e4a0 b 1 M80c3 a326 0 b c
J 63 K 45

 BA.DV MU1JQ8M0JD°B U JPOB ABGOE( s%trJaWiJgThJPt Oan PgGl e4)VSET ZYV WXV

Bbanudt 35BBACDD 1C8B0C6°D 6 HCD (sDtraig6h6t angle) E 18 15 a(anldterFnYa6VteZ s,WWXV¹X¹ GY(Zv)ert3i0cally opposHite2)8

I(op8po3s0ite s oJf p4arallelogramK) 2 5 L 40 but M Z6YV YVZ N 5 2 O 6 42

P=13800°  BBAAGGQ 4 818H02C°1D  HCRD 36 S 12 3 =(basWeT X3sVo 7f isoWscVeXlesU tri6ang5le)
= E2 =OWF VX1i3s isoscelesG 5
B 2
C5 D 23 H8 5

I2 5 J3 K6 L 5 = WMX 3 W3V N 10 O4

P(coH4rJrCe3s p onEdMinCQg 3s, J5H¹¹ ME) LKM LMK *
(base s of isosceles triangle)

B ((= 0bE ,a5s2C(#e )HMJS2OJBC sPQ No 5If JJEDiBsBMMEo M1 CsC.cSMePFlCEeUsVI tDPrUEi(T1a 1­0nP,gG2 4l4e)V)PSM1EV5TUJ PO D 3 10(3 , 22) 5 = JKM = LMK ( *)

but these are alternate angles
=E JK3¹¹ L7M 7 (2, 3) F 3 21 ( 2,G 2)5 2 2
H(= 12O, H 3J2C) i6s isoscelIes (61, 44) 3 J 7 (231, 1) ( 1, 3) (1, 2)

B= "xH2 J 5 I5HFxC 4V6CTUJUVCUJP1O1 . 5FUI5PE D 2 E 17 8 2 F 1 3 G 19

HB 1x0 $1P4OH6SVCFOxU 5I S8JB3OHMFTD x 2 J E1 x2 73 F x K 69 5 G5 x 2 L 1H x -54- IM x4 0 2 11 10
NB 1xA4A S(x 2) C 1R0HO, xS 21 4 7D 1S1SS P E19S A4S 2 I SAS J SSS
CF xAA S2x 3, Gx S A3S H AAS
D 18 8 2 G 5 2 6
BHDHFB x152xn26xxo 1(4Z16(2xUx(I 3 B7x H4)1 P)xC S) B3 nT1,o±CIx41 5,, Ixx732F 6 P 15S4F1ND03 no J 10 4 6 E x 2(x 2) 1, x 3 M 27 10 2
11 G x E 52(1 x )8 85, x 2F 8 2 15

I 4xK 136(3 x2 73)9 5, xL 325 10 10

JB 3x1 1 2 (2x C 8) 229, x 2D 26 E 41 KF 2x9 8 3(3x G 2) 282,4x 2

BB yx 86, y 28C y 6 C x D8
yy 1208 ED xy 5 ,1y 10 F y 4E a Co7p,yrbigh t ©1G7Peayrso n2Australia 2009
INTEHFRNAyaTIO NA23L 4M,ATbHE MATIC4SI84 0FOyUN D A TI1ON GWORaKS HEJE3T,S AbyN S WE4RS97 KH my 394, n (a division of Pearson Australia Group Pty Ltd)
1921
5IJT QIBHFx N BZ3 C0F ,QIyPU PD1PQ4JFE GPS DMBTTSPPN VTF

J p6 T5JO, qH 4J1N1 VMUBOFPVT &RVBUJPOT UP 4PMWF 1SPCMFNT

FB xy 5 "IyxSFF *BO23 EFY -BXT C 2x y 12 D x y 4 E 2(x y) 12
G x 3y 14
BB 618x9 · 6 5cmy 2 2C8 C81 3·5 m2 CD 31x25 D y 3 154·2E m624 H y 3x I x y 4
DEF 233x25 3·34yc m12 9 F 127·2E m32x 4y 7G8 1963·5 cm2
FHB y201 165·1xm m3 2C I1029481·7 mGD2 24x09 6 3y 4E 2401 HF y59 034x9 7 G 5832 IH 47x77 6 7y I 100 000
BBJ x7281 8m57,my2 K2 C16 36814cm2 C x D8, y28 54m2
FHB x2631 17 52m, y2 C 6Ic4 90 m2 GD x9 J1, y23 6 3cEma212 DE x4 265,cmy 2 1 F 257 mE 2x 2, y 4G 313 cm2
KF 222802 m2 G 810L 550 cHm2r5 MI m2500 cm2

J n612TJOH 5SJHK POyP30NFUSZ UPL 'xJO7 E 4JEF -MFOqH8UIT N w10 O p2 P g6 Q d3
EF 1326k63·9 GI 664·2p6
BB 26·h17 C 4C0a143·4 D 9x8 D 89·3E 5c3 EN 44j66·1 G 16yF13 179·8H 80x7 GQ 34n99·8
BJ 1192·56d12 K 3Cc 397·0 L 343Dm185 ·5 M 21t10 O 100F0y89·9 P 20x12

B ta/n 3F3H°B,U6JW·5F *OCEJDcFoTs 62°, 4·7 D sin 55°, 32·8 E sin 49°, 13·6 F cos 12°, 26·9 G tan 25°, 15·0

BB s41--in 40°, 12·C4 -81C- cos 60°,D201-9- D tan 4E7°,-1-14--0-6·6 EF 2-t-1--a5-n 14°, 18G·9 61-- F sin 32H°, 6-4-1--4-15·2 GI c-6-1-o-4-s 71°, 66·0
5IJ(Ta QPdBiHvFis 5-Ni--o-11--nBC-2-Zoo Cpf FyPr QeigaIhrPstUo©PnDPAPQueJasFtrErs aoGPlniaS ADGMuBrsoTtTurSapPliPPaNt2y0 LV0tTd9F)
INTERJNAT-4I-1O--9-NAL MATHEMAKTICS1--4--01-F--0O- UNDATION WLORK-1-1S--3H- EETS M -8-1--1- N -1---14---4- O -8-1--1-

ANSWERS

B 4 1 C 2 3 D 3 2 E 2 1 F 4 3 G 3 6 H 10 2 I 5 4

J 7 6 K 11 4 L 20 1 M 9 3 N 19 O 5 10 P 12C o6pyright © Pearson Australia 2009
G 7 2 5IJ(Ta QHdBiHvFi1s Ni0onB Z3o Cf FP eQaIrPsUoPnDIPAQuJsF2tEr aG4lPiaS DGMBroTTuSpPPPNty LVtTdF)
I NTEBRNA2TIO N3AL MATHEMACTICS141F O2UNDATION DWOR5KS H2EETS ANSWERES 3 3 F 4 3

J 9 2 K 3 5

'SBDUJPOBM *OEJDFT

B0 2 7J "°IIOoI4rHVMNFSGT2B 7JPDJ°FGE3 &"8M4SFFWuBBn UPiJtPGs 2O1 SBJTONE T% CFQJ SIF ITTJ3P0OJ0J
7#52mF8BSuJOnHitTs2 DJI JJ 3563m2 units2
Face A 23B4 m C
B11°Face A B C D E 68 Fkm C D E F
225
1ArSePaCMFN12T8 XJ1UI28 .P9SF6 UIB9O6 0OF4 85SJBO4H8MF Area 225 375 375 375 375
F
B 7·34VSGBDFC "1S2F·B4 PG 1SJTNT B 13·8 C 7·3 D 21·1

BD J1F4IaI·cI2e JAJ C38540uB°nits2C DC J IIE JJF528 units2 BD J5I·4 JJ C53124u·8nits2

B 1AF1ar·ec5ae 2A0C0 284B·06 8C0D 187D0·1 2E00 4F0 B 30° C 49° D 79°
B C Face A B C D E

B 7A6r8eam2 128 128 96 C 926620 c4m8 2 48 D 11A2re0amm2225 375 375 375 375 225

D Face A B C D E F
Area 200 40 80 80 200 40

B 768 m2 C 2620 cm2 D 1120 mm2

7PMVNF

B 144 cm3 C 252 m3 D 330 cm3 E 17 625 mm3 F 3375 m3 G 4900 cm3
251 m3 D 14137 cm3 E 1018 m3 F 3502 mm3 G 11 912 cm3
B 314 m3 C

&RVJWBMFOU &RVBUJPOT

B m 71P7MVNF C n 39 D m 24 E f 24 F x 20 G y 9
LF 3p3 7155m3 GM x49 0 02c9m3
BH k14 4 c1m43 IC 2c 5 21m003 JD 3q3 02c0m3 KE t17 6825 mm3
PD 1x4 17357 cm3 F 3502 mm3 G 11 912 cm3
NB a31 41m63 OC 2y5 16m3 D n 2 QE z10 1 82m63 F c 4 G m 2
B a 3 C x 1 E y 6 L n 2 M y 15
H k &R6VJWBMFOUI &RhVB U J1POT J t 4
K x 4 F x 20 G y 9
L p 15 M x 29
NB mq 167 OC nx 319 PD am 52·54 QE uf 2 48

HN k &R1 V614BUJPOT IOXJUcyI (16S0P0VQJOH 4JPZNqx C P72MT50 K t 8
a
ka152x y 36 156 h7x2a0 x 11 2185 14tn80 yn 2 4 27 Q z 26 47nc tk 234258
BB CC DD 50 EE xy1246 mx 6 488 FF GG my132q c 2211452
HH II JJ KK LL MM
BN aq 16 CO mx 31 DP an 51·5 EQ xu 5 8 F y 4 G k 3

H r 10 I x 19 J c 1 K a 4 L t 0 M y 4·5
N d &R1V3BUJPOT OXJUxI (6SPVQJOH 4PZNmC PM1T2
Q b 7 R c 1 S p 2

BH 152x&y R 1V56BUJPOT ICXJU72Ia0 'x S B2D18U5JPOT DJ 18y 27 E 24m 8 F 4k 28 G 3q 24
BB ax 61 CC am 310 DD 40n 50
HH pr 1 028 II ax 1190 JJ mncw 111900 K 16x 8 L 7t 35 M 12c 12
BN da 213 OC xx 618 m2m 121 EE yx 58 FF yt 421 GG kx 231
PD 4m 12 KK ah 46 LL xt 050 MM yt 142·5
EQ bc 176 RF 4c y 11 GS p30 y2
H 7x 8 I 2k 5 J m 15·5 K 16 5a L 4c 6 M 3m 7
B x &R3VBUJPOT CXJUcI 'S1BDUJPOT D mm 96
BH xh 65 IC at 1100 JD w 100 E d 27 F e 14 G m 5
E y 8 F t 21 G x 21
2m 1
H p 28 I a 10 J 4c m 3 12 K h 6 L x 50 M t 12
1m2 n 152·50
B a &R2VBUJPOT CXJUxI 'S1B8DUJPOT D 6mt 6 E c 16 F 4y 1 G 30 y
BH 72xa 81 2h 19 EK 316t 152a FL 34cx 64 GM 3hm 1 7
IC 82mk 52 DJ EK 2dc 277 FL 1e 5 k1 49 MG mx 1 05
E 5x F 6a 10 G 7n 5
BH 6xy 39 CI c10 p1 25 DJ
BH h5x 5 IC xt 110 DJ K 2x L 21 M 5c
I 3q 1 J
H 7x

N 13&pRVBUJPOT OXJU8Im 'S B8DUJPOT P 14x 10

B 2a 1 C 8m 2 D c 3 E 3t 12 F 3x 4 G h 1
K 2c 7
H 6y 9 I 10p 25 J 12n 20 E 5x L 15k 9 M x 10
K 2x
B 5x C x 1 D 6t F 6a 10 G 7n 5

H 7x I 3q 1 J 2h 19 L 21 M 5c

N 13p O 8m 8 P 14x 10 Copyright © Pearson Australia 2009
(a divisionCoopf yPreigahrsto©n APuesatrrsaolinaAGursoturapliPat2y0L0td9)
INTERNATIONAL MATHEMATICS 4 FOUNDATION WORKSHEETS ANSWERS 5IJ(Ta QdBiHvFis NionBZo Cf FP QeaIrPsUoPnDPAQuJsFtEr aGPliaS DGMBroTTuSpPPPNty LVtTdF)
INTERNATIONAL MATHEMATICS 4 FOUNDATION WORKSHEETS ANSWERS 5IJT QBHF NBZ CF QIPUPDPQJFE GPS DMBTTSPPN VTF

Copyright © Pearson Australia 2009

3–4–6–4 3–3–3–4–4

$IBMMFOHF 8PSLTIFFUT

$I""BMMFOOOHTTF XX8PFFSLSSTITTFFUT

'SBDUJPOT BOE (SPVQJOH 4ZNCPMT
227-7-313----1--117-7---------------------------33mamaxx----------------'--------1166mm344-------- --------S11--------22––--------FB--------22--------11––22----------HD33------3------311------U--44V–--–J----111PM--3B2O–S–T4 11 –B2P3OM–ZE4H (POSPT VBQOCCCCCCCCCCJEO H5--3–3–--1-a-1x-xa------------- ----------55----------00Fmmmm4---------- ––55--------------------Txx66--------Z11--------11--------55T––N--------6622––------------Fyy------77------------M22C----M––--------B33P----------88U--MJTP$OITB MMFOHF 48DDDDDDDD–36P1414--1---1-– --–--------------S--------33003--mm1------22--L----------------–aa222--------mm112–2–------T--------33--––3--------2200------––--I------22--–--------––77--------------55--113F----------------66--33–xx--------F--6UT
B
B
B
B
B
B
B
B
B
B

"OTXFST T h e sev"eM3nHFFoHCtVhSBeMBrJDSs 1e&mPYQMiZ-SrHFePTgOTuJTlPa BrOOTteE sB sO5eEFllT a*TtOiFoEMnMJBDsUFaJTPreO:T
T hBeB se2--e ---- x---vxx---m2--- -'--e1--- 4-x--x--n-S1---–---B--- 2 2----o-D3----
1-t1U-3-hJ

Pe2-12-1--Or Tse BmOiE-ICrCI e(gSue-x-P -lx-x -aV1-- x2r- -Q--2 t CJe2Os11Hs–-

-e -512--–m4--l-21--l-ZaNtioCnPJDsDJMTar--eex---xe:21-2---1x-x - --x --o-2- r2 2-x- --1x---–21-- -- -1-(-- x- - 1--- G
– 1-2-
e 3x 32x 2) 2 G ex x 2
HH 1
–1 EE FF
B
e 2-x- D 4----m---2---–----7--
CHCIALLENx Gx Ex2W CCOR11KS-a1-

--H---21--–0-E--–5--12-E---x--T1--1--S--2–-A--N--2-S--W3--EDJ RS e12-- x or 1 D -1---3---a-E2---0-–----x1---–3--1-2- -12-
I N TEBBRBHNAT1-3-7-- xI-O-x2- -N-1-xx A--2L-- 33 -M1--––-A1-11-T66H

––E2-12-1--M33A––T66ICS x2 x
–1 D ----2----m-3-----–----6-- F (x 2) 2 G x 2 –




4 Copyright © Pearson Australia 2009
(a division of Pearson Australia Group Pty Ltd)
5IJT QBHF NBZ CF QIPUPDPQJFE GPS DMBTTSPPN VTF
BB DB r-71-ia----n--3a--4-- k--6m-- --P1----3 --2M--–2--W,---$-Jb-4-O2--1 -,Hi 5c5,eI-ccS FreF a m42JN V$3MUCC,BClOo3-x-Fml----l--Pm--y ----V 6---- --5–--T6--1--y-- $7--,--&-1–--nR-.--58-V 0B U3JP,OpT 433––44––66D––D441-x---0-- --1–--- 2--2-2--5-,--x--y 5, z 0 3–3–3–4–4
3–3–3–4–4

53IFFH V3MBBOS H1FP PMZGH 7PBOMTV FBTO EP G5 UFITFT 5FMSMJBHU J3PBOUTJP T
T h e B s eIvt4eanPpMpoWrtJhoOaeHcr h5seeIsmS9Fi-0Frp e4gJuNlaVrMUtBeCsOsFIetPlliVantTcio r&enRassVaeBrseU. J:POT D It stays constant. E It increases.

BF aIt in3c,reba se5s,fcro m 02 to infiCnitmy. 1, n 3, p 4 D x 2, y 5, z 0
DB ri0nk $2, ice-cream $3,CloIlltyin c$re1a.5se0s from 0 to infinity.
B It continuously increases in length. C It goes from 1 to 0. D 0 and 1
B Ye5sIF3 3–B1O2–H1F2 PG 7BMVFT CPG BUIecFa 5usSJeHi t3iBsUtJhPeT hypoten4u–s6e–o1f2the right-angled triangle ABX
DB IItt agpopes3ro–far1oc2mh–e1s029to0p1. CE 0It ainncdre1ases. 4D–6I–t1s2tays constant. E It increases.

F It increases from 0 to infinity.

B 0 5SJHPOPNFUSZ BOE UIFC -IJtNinJUc PreGa BseOs "frSoFmB 0 to infinity.

B It cno3n–t6in–u3o–u62slRy increasesR in lengthO. C AC C ItAgBoes from 1 to 0. D 0 and 1

B YIte4gsoes from900pto 1. 45CEp B0eacnadussi1ne 4it5pis thechosy3p4–o54pt–e6n–u42secoosf 4t5hpe right-angled triangle ABX
D 3–3–3–4–4

A r ea5oSfJHOPOOAPBN FUcSoZs B4O5Ep UsIinF 4-5JpNJU PG BAOr "eaSFoBf s quare 4 cos 45p sin 45p
n 2R R OC AC AB
n 3–3–41–20R38p–4 R OC AC 23c–oA3sB–534–p3–6
5 54p sin 54p cos 54p
BHBHAAAN srrroeee--ee --t----taaa----exxxxh----""----A:----54nn11----oooe ----MMnR----11HH----fff----v----e2222----FFOOO--as3----

CC3--lu--–33OOOu--SS–l1BBetAAA3s2JJ–oBBBDD–f4f o119&& –20nr2420YYR38cccApiQQp–ooonnCICI4SSssscFFar455rTTee544aTTee----pppsJJ--gxx--xxPP--e11--i2sss-- sv--OOiii54 --·--,nnn3e--22R545TTt7n22pp h4558BBe544cOOoppprEErer s**euOOcssl2EEtiitnnO·sJJt56DDDJJDoC54f9FFAAAo4583TTrpprr----eee--dA----aaaxxee--e--n11xx--c--ooo ----gi --fff--mcce--22--sppoo22tqaAss1eec3luC2nn54lpoa45ttaarlsppaeggecoor4 enna–s422n.63 dcc3––coo55·A1o320cssEE2s0B–9lcc54o30oo445s–33--ss5--pp11e--3--pxx--r55–44st6oippn3ssth41ii·nn105e40p55a044reppFFa
3------11--2----1--x000 G 20--e011----x--0
323x·142 G 3·1e4x2
of a circle
with a radius of 1 unit.

The rnaessunltins carreeags4eestt,itnhgecalroesa5eroaf nthdecploosle6yrgoton t(hAen)va1gl2eutes oclfoQs.erT2hto0isthisebaerceaa1uo0sf0etthheecairrec1al0eo0. 0f the cir2c0le00is Q square units
and,
Copyright © Pearson Australia 2009
I N TE R N ATIOA5NnAILSMFAFTH EEMJANTICF2S O4 CTHJAPLLOENBGM2E 1·W3OS7PR8KCSHMFEENTS ATN2 S·W5E9R8S
3 3·090 3·140 5I3JT((·aa 1Qdd4BiiH2vvFiiss NiiooBnnCZooo CpffFyPP r3Qeeig·aaI1hrrPsst4UooP©2nnDPAAPQuueJFassEttrrrs aaGoPllniiSaa ADGGMuBrrsTootTuurSappPliPPPaNtt2yy 0VLL0ttTdd9F))

I N TERABTBNNhsoAT34ettIeOh53r:NeppeRA40sLveuM1ba slAblut TusHletEasMroAfeTfoICgnrSCCeA4itnCtnHicn23AarLg65reLeEappcNs31glGeo64iEsvsWbb, eeOtnrRhKaecSnHorEdreErTDscSeulAcolNtt3SsstWe1oEfrpoR3S0trobdA tenhcegimevtaacllulpoelsaeocrfeEaQsn.. dT1h6clipos3si6esbr bteocathueseatrheae 5IJT QBHF NBZ CF QIPUPDPQJFE GPS DMBTTSPPN VTF

of a circle with a radius of 1 unit.
area of the circle is Q square units
aBnd1,1a—3s ncmincreasCes, t1h0e—6arcema of theD po7ly0gpo3n2b (A ) gets cloEser6t1op5th2eb area of thFe c6ir9cple1.8b

B -7---a---6- -----2-- C 3----m---6---–----7-- D 1----0----1–---2--2---5---x--

B 1----3---m------–-----4---1- C -x---- -----5---y----–-----8- e -2x- E x–1-2-
B 12
21-- 1 -1- 6 e12-- x 4–6–12 G x 2
–1-2-
2 x 1 C x2
2 D or F (x 2) 2 G x 2
–12--
T h BH e se xv2 exx3n FoH113tVh–

2-112-eM1--Br2S–s 1e1mP2MiZ-CIrHePgOux Txl a x2Br OteE11s s

5e-21–-Fl-21-lTaTtiFoMnMBDJsUaJPrexeO12-2-:Tx xo r E x–12-- F (x 2) 2
1-
x-–1
e2

H x x 1
12-- I x x 1
–-21- J x2 x 1
–1

4PMWJOH 5ISFF 4JNVMUBOFPVT &RVBUJPOT
B a 33, –b6 –35–,6c 2
C m 1, n 3, p 4 D x 2, y 5, z 0

Drink $32–, 3ic–e4-–c3re–a4m $3, lolly $1.50 3–4–6–43–3–3–3–6 3–3–3–4–4
4PMWJOH 5ISFF 4JNVMUBOFPVT &RVBUJPOT
B a " 5IM3HF,F bC3S BBO5JDH, Fc& Y PQG S72FBTMTVJFPTO CTP GB mUOIE F *15O,SEJnHJD F3T B3UJ,PpT 4 D x 2, y 5, z 0
DBDFBBBFBBBH riIIIIY00II-e -n--tttttte--xx--5k--aaiicgs--1--nn --Ippoo--1 --cc--nppeF--22--rr-s$rrt -ee-
3ioo-2aa-fn3-aarB,ssuocceeOiomhhcssHueeffF-ssrrs0coo l99Pyrtmmeo00Gia ICppn71m00c.BrttM ooeVe--a-x-$iixF-s1-nn- 3eT- -fifi-s ,-2CCCECCPnn2lioGnii ttB0IIIIlUyylttttlIe..yeaiiiicFnnnnnn a gccccd5u$trrrrshSeeee11Jeaaaa.H.5JDssssi teeee30ssssiB..s--ff-U-rrt-xeJ-ooh-P1x--mm -eT- -- -h2-002ypttoootiiennnfifiDDCunnsiiettIIIyyttt..ogssfEttoaatehyys3-sse-1--xf-ccrriooognnmhssttt1-aaanntnottg.. l0eF.d
---1---- E It incGreas-e1--ex-s.
32x

DE 0It ainncdre1ases.
triangle ABX

B It continuously increases in length. C It goes from 1 to 0. D 0 and 1
tria(andgivliesioAnCBoopXf yPreigahrst o©n Pearson Australia 2009
B Ye5sSJHP3O–1P2N–1F2USZ BOE UIFC -BJNecJaU uPsGe BitOi s"tShFeB h ypoten4u–s6e–o1f2the right-angled Australia Group Pty Ltd)

I NTEDRNAITtIOgnNoALeMsAfTrHoEMmATI20CRSt4oCH1A.LLENGE WREORK0SHEaEnTSdAN1OSWCERS AC AB 5IJT QBHF NBZ CF QIPUPDPQJFE GPS DMBTTSPPN VTF

54SJHPOPN9F0UpSZ BOE UI45Fp -JNJU sPinG B4O5p "SFBc o s 45p 2 cos 45p

Area nof OOAB 2Rcos 45p sinR 45p OCArea of sqAuCare 4 cAosB 45p sin 45p

4n 920Rp 4R5p sinOC45p coAs C45p 2 coAsB45p

Area 5of OOAB1 08cpos 45p si5n4p45p sin 5A4prea ofcsoqsu5a4rpe 42 ccooss5445pp sin 45p

Area nof OOAB 2Rcos 54p sinR 54p OCArea of pAeCntagon 5ABcos 54p sin 54p

5n 3–3–140–483p–4 554p sin654p cos1254p 23c–o23s0–534–p3–6 100 1000 2000

A reaA"onMfHOFCOSABJBD &2YcoQsSF5T4TpJP2siO·n3T75 8B4OpE *O2E·5JD9AF8rTea of pe3ntagon 35·09c0os 54p 3si·n14504p 3·142 3·142

aTANNHBnhsoodett-et ---ee,h--xx--Ar::--na--ee1-- nRR --s--s1--v--eeu--n22--ass-l--l
uuti-u-n3s-llettcassrroeffefooagnsrr42eeAAistnt,nniICctnaarhgrreeeace-sa-gg-lxe-xro-ii21-sevv- s-· ,-a3ee-5e-2t7nnr2oh8afeccnootrhdrreerrsceeuplccol2ottts·sltt5e6yooJDf9rgo833otron--ddA--t-xeee(-nh-1ccx-A- -egii- n-mme--)v2-t2aaa1gc3lll2eulppotesllsaaeocccrlfeeoaQsssn...ed3rT·2ht0co0E9lios0tshi3-es-1e-r-x-baterocea3tah1u·1o0es4f0ea0ttrhheeFaecoai3-rfr--e1c-32a-1-al-·x0e1co0.4ir0f2ctlheewciitGr3h2c·0l1ae0-e41--0rx-i2sadQiusqs uoafr1e unit.
units


TA hs ethr5eeIsvuSaFlltFus eEaroJNef gnFeOitntTicJnPrgeOacBsleMo s1s,eStrPhaCenMrFdeNsculTol tssefrotroAtnhegevtacluloeseorf and closer to the area of a circle with a radius of 1 unit.
Q. This is because the area of the circle is Q square units
aBnd4,5aps0nb increasCes, t3h5epa1r6eba of the polygon (An) gets closer to the area of the circle.
Copyright © Pearson Australia 2009
I N T EB3BB RN— 4A314TIc351O5mNpp—3IA40LSb1cM FmbA FTH EEMJNATICFCCCSO4 TCHJ312PA560LOL—ppE6BN13GM46c E1mbbW SOPRKCSMHFEENDDTSTAN 37SW01EppR03S 2b b E 16p36b
(a division of Pearson Australia Group Pty Ltd)
E 61p52b
F 659IpJT1 Q8BbH F NBZ CF QIPUPDPQJFE GPS DMBTTSPPN VTF

BB 3539pp24b1 b CC 5246pp3124bb DD 3618pp102b b EE 2196pp376b b
BBBB3BB—4115512c618963m—pp———4366820bbccc mmmm CC 1308p—64bc m D 70p32b E 61p52b F 69p18b
D 68p12b E 29p7b
C 5593p4783ppp 01402bbb b
C
C
C

B 28—40 m C 9p30b

B 53p8b C 57p0b

INTERNATIONAL MATHEMATICS 4 CHALLENGE WORKSHEETS ANSWERS Copyright © Pearson Australia 2009
INTERNATIONAL MATHEMATICS 4 CHALLENGE WORKSHEETS ANSWERS (a division of Pearson Australia Group Pty Ltd)
5IJT QBHF NBZ CF QIPUPDPQJFE GPS DMBTTSPPN VTF

Copyright © Pearson Australia 2009
(a division of Pearson Australia Group Pty Ltd)
5IJT QBHF NBZ CF QIPUPDPQJFE GPS DMBTTSPPN VTF