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PMR

PAPER 1

FORMULAE

CALCULATOR

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LAWS OF INDICESBrief Notes:

3 (am)n = am xn

4 a0 = 1

61

na = an5 a-n = 1

an

1 am x an = am+n

2 am an = am - n

Add up the indices.

Subtract the indices.

Multiply the indices.

A number raised to a power of zeroalways equal to 1.

Negative index written with a postive

index.

Fractional indices give us root terms.

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Fine the value of

17.4 + 12.6 0.6

A. 50

B. 38.4

C. 19.5

D. 5

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An integral part of mathematics learning.

Polyas modelThe four steps

Understand theproblem.

Devise a plan.

Carry out the plan.

Look back.

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14 x 20 22/7 x 7

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25.04

1

,....2.05

1

75.04

3

,.....1.0

10

1

5.02

1

Fractions to Decimals

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Pythagorean Triples

3,4,55,12,13

7,24,258,15,17

6,8,10

9,12,15

12,16,20

10,24,26

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Perfect Square

366

255

164

93

42

11

2

2

2

2

2

2

14412

12111

10010

819

648

497

2

2

2

2

2

2

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25616

22515

1961416913

2

2

2

2

40020

36119

3241828917

2

2

2

2

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Perfect Cube

1255

644

273

82

11

3

3

3

3

3

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PMR

PAPER 2

FORMULAE

GEOMETRICAL SET

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LOCI (LOCUS)

L - Designs

Parallel Designs

A Point

Two Points

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Loci9.2

example 1 B

CD

The locusofy it isequidistantfrom CBand CD.

y

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AB Equidistant CDparallelDesigns

A B

CD

The locus

ofy it isequidistantfrom AB

and CD. y

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2 cm

3 cm

3cm

Locus P

p

AD

CB

The locus of p

2 cm from B

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Locus yA

D

CB

The locus of y

YB = AB

y

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Locus P

p

A D

CB

The locus of p

Such that itsdistance from Band D are the

same

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CONSTRUCTION

Construct the angles

Construct the bisector

Construct the perpendicular

Construct the shapes

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A protractor is not used ingeometrical constructions.

While constructing geometrical, shapes, makesure that,a) all construction lines are clear and sufficiently

long to show how the construction is made,b) all construction lines are not erased after the

construction is completed.

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Constructing Angles of 60

P

60

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P

30

Example 1 : Construct 30

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P

45

Example 1 : Construct 90 and 45

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P

45

Example 1 : Construct 90 and 45

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P

45

Example 1 : Construct 90 and 45

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P Q

RS

4cm

45

P Q

45

S

4cm

R

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Example 2 : Construct a perpendicular to line AB that

passes through point P.

B

P

A

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k

R

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GRAPHS FUNCTIONS

SCALE

* X

axis* Y axis

PLOTING

DRAW

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Draw the graph of functionScale 2 cm to 1 unit on the X axis

2 cm to 2 unit on the Y - axis

-4 -3 -2 -1 0 1 2 3 4 X

Solution:

-4 -3 -2 -1 0 1 2x

y

3 4

-7 0 5 8 9 8 5 0 -7

x

2

4

6

8

10

Y

-2

-4

-6

x

x

xx

x

x

x

x

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Draw the graph of function

Scale 2 cm to 1 unit on the X

axis2 cm to 10 unit on the Y - axis

-3 -2 -1 0 1 2x

y

3

-32 -11 -2 1 4 13 34

2004

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TRANSFORMATIONS

REFLECTION

TRANSLATION

ROTATION

ENLARGEMENT

11 3h S l i P bl I l i R fl ti

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11.3h Solving Problems Involving Reflection

y

A

A

P

Q

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ab

Positive a , a unitsto the right.

Positive b, b unitsvertically upwards.

-ab

Negative a, a unitsto the left.

Positive b, b

vertically upwards.

-a-b

Negative a, a units to theleft.

Negative b, b unitsverticall downwards.

a-b

Positive a, a units tothe right.

Negative b, b units

vertically downwards.

Directions

(1)

(2)

(4)

(3)

I fi b l d th i f M d

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In figure below, draw the image of M under

a translation

M

M

4

6

4

-6

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Determine the image of the PQRS under a rotationabout point 0, through an angle of 90 anticlockwise.

0

P Q

RS

P

QR

S

Describing a centre of Rotation

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Describing a centre of Rotation

2

1

-1

4

-4

-3

-2

3

y

-1 x3-2-3-4 1 2 40

M

MCentre ofRotation

M is the image of M

under a rotation about

the point

(-2,-2) through an angle

of 90 anticlockwise.

The Centre Of Enlargement

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The Centre Of Enlargement

O

O is the centre of

enlargement

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STATISTICS

PICTOGRAMS

BAR CHARTS

LINE GRAPHS

PIE CHARTS

PICTOGRAMS

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PICTOGRAMS

Month Number of bicycles

April May June July Represents 20 bicycles

Month April May Jun July

Number of bicycle 60 80 140 120

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BAR CHARTS

FormNumber of

members

One 40Two 60

Three 120

Four 100

Five 80

F 1

NumberofS

tudents

0

20

40

60

80

100

FORM

120

140

F 2 F 3 F 4 F 5

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Line Graphs.

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1999

Num

berofStuden

ts

0

50

100

150

200

250

Year

300

350

2000 2001 2002 2003

Year 1999 2000 2001 2002 2003

Number of students 150 300 200 150 300

20

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1999

0

50

100

150

200

2000 2001 2002 200320

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1999

0

50

2000 2001 2002 200320

100

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1999

0

50

100

150200

2000 2001 2002 2003

300

350

400

h t

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charts

Factory A B C

Number of

Workers

5 9 10

5 X 360 = 7524

9 X 360 = 135

24

10 X 360 = 150

24

75

A

C

B

A