MATHEMATICS PSLE - GoGurucdn.goguru.com.sg/media/mce_sample/9789814736596.pdf · PSLEMATHEMATICS Revision Guide 2nd Edition Michelle Choo The most complete handbook for PSLE!

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MATHEMATICS

PSLERevision Guide

2nd Edition

Michelle Choo

The most complete handbook for PSLE! Includes questions which require the use of calculators

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Mathematics PSLE Revision Guide © 2009 Marshall Cavendish International (Singapore) Private Limitediv

What Parents Need to Know About the PSLE Mathematics Examination

What is a Good Examination Paper?Parents and pupils must understand that the PSLE is an assessment that measures how much pupils have learnt in their six years in school and is also used as a gauge to measure their performance against the other pupils taking the same examination. A good examination paper is not determined by whether it is easy or difficult, but whether it truly measures what it sets out to do. If a paper is easy and everybody scores high marks, then it is not a good paper as it does not reflect how well a pupil has learnt compared to others.

Format of the PSLE Mathematics Examination PaperThe examination paper is divided into 2 papers: Paper One (non-calculator) and Paper Two (calculator).

Paper One is made up of Section A and Section B (Part 1). Section A comprises 15 Multiple Choice Questions (MCQs). These are questions that test pupils’ understanding and application of basic concepts. Pupils have to shade the correct answer in the Optical Answer Sheet (OAS) using a 2B pencil. The Optical Answer Sheet is machine marked.

Section B comprises two sections (Part 1 and Part 2) and is also used to test pupils’ understanding and application of basic concepts. In Section B (Part 1), pupils fill in the answers in the spaces provided (questions 16 to 25). Marks are awarded solely for correct answers and not for working. For questions 26 to 30, 1 mark is awarded for working and 1 mark for the answer. As such, pupils must show how they derived their answers. Questions in this section may be multi-stepped. Note that the use of calculators is not allowed in Paper One.

Paper Two is made up of Section B (Part 2) and Section C. In Section B (Part 2), pupils are also tested on their understanding and application of basic concepts. Pupils must also show their working steps in this section. In Section C (questions 36 to 48), the word problems test the application of concepts. Pupils are required to show how their answers are derived and most of the marks will be awarded for working. Questions in this section are multi-stepped and are usually more difficult than questions in Section B. Pupils will need to apply heuristic skills to solve questions in this section. Note that the use of calculators is allowed in Paper Two.

The questions in the PSLE Mathematics paper are generally designed such that the questions for each section are arranged from those employing basic concepts to those that are more challenging. The paper is designed such that a pupil who has

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Mathematics PSLE Revision Guide© 2009 Marshall Cavendish International (Singapore) Private Limited v

studied for the examination and understands the concepts will be able to obtain a pass mark easily.

To obtain an ‘A’ grade, pupils are required to know how and when to apply the basic concepts that have been taught. To apply these concepts correctly, pupils need to understand the questions and apply the different heuristic skills they have learnt. Pupils are also required to solve very challenging non-routine questions whereby they have to use more than one heuristic skill to solve these questions.

Tips for Tackling the ExaminationAlways start with Paper One as the questions are relatively easier than those in Paper Two. The first few questions for each section always test pupils’ understanding of basic concepts. Pupils who have studied for the examination should be able to solve these questions easily, thereby boosting their confidence when they are faced with the more challenging questions in Section C.

Never begin the paper by tackling the word problems in Section C. If pupils start off with the word problems and do not fare well, they are unlikely to do well in Sections A and B (Parts 1 and 2) when they attempt these at a later stage. In addition, pupils tend to spend too much time on the word problems so much so that it compromises the time needed for them to complete Sections A and B (Parts 1 and 2).

Pupils are also advised not to spend too much time attempting questions in Section A. They need to move on so as to score as many marks as possible. Thus the technique is to first attempt the questions they can answer and return to those questions they have problems with only after that.

Some Other AdvicePupils may use the Guess and Check method as the last resort to solve problems. When using Guess and Check, it is important to label the graphs, tables, etc. so that the examiners understand the steps in the working.

Pupils and parents must remember that for word problems in Section C, only 1 mark is awarded for the correct answer, while the rest of the marks are allocated for working. Hence, it is critical that pupils show how their answers are derived.

Most pupils tend to lose marks due to carelessness. Very often, this can be attributed to untidiness and/or when they rush through the paper. If they are untidy, pupils tend to transfer errors and calculation mistakes to their working and answers. This may also make it difficult for the examiners to understand the pupil’s working, and therefore cause pupils to lose marks they could have otherwise gained from showing the working.

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Mathematics PSLE Revision Guide © 2009 Marshall Cavendish International (Singapore) Private Limitedvi

How To Use this Book

Unit

6

Geo

met

ry •

Mathematics PSLE Revision Guide

© 2009 Marshall Cavendish International (Singapore) Private Limited

127

Unit 6

What you need to know

• Measuring angles using a protractor

• Perpendicular and parallel lines, and angles

• Symmetry

• Properties of a square, a rectangle, a triangle,

a parallelogram, a trapezium and a rhombus

• 8-point compass

• Nets

• Tessellation

To measure �XYZ, we need to place the base line of the

protractor on line YZ, and the centre of the protractor at the

vertex of �XYZ.

�XYZ = 40°

GEOMETRY

Measuring Angles Using A Protractor

vertex

X

Z

Y

X

Z

Y

010

2030

4050

6070

80100 110 120 130 140

150160

1701800

1020

30

4050

607080100

110

120

130

140

150

160

170

180

90

Mathematics PSLE Revision Guide © 2009 Marshall Cavendish International (Singapore) Private Limited

138

Worked Examples

1. In the figure below, not drawn to scale, ACE is an isosceles triangle.

AC = CE, �BED = 47° and �ACB = 106°. Find �ADE.

(1) 80° (2) 74°

(3) 27° (4) 17°

( )

Solution

Method 1�ECD = �ACB = 106° (vertically opposite angles)

�ADE = 180° − 106° − 47°

= 27°

Method 2�ACE = 180° − 106°

= 74°

�CAE = �CEA

= (180° − 74°) ÷ 2 (base angles of an isosceles triangle)

= 53°

�ADE = 180° − 53° − 47° − 53° (sum of angles in a triangle)

= 27°

Ans: Option (3)

106°

47°

A

B

D

C

E

Mark out important

information given in the

question on the diagram.

An isosceles triangle has two equal sides and the base angles

are equal. So mark out these sides and angles in the diagram.

Common Error

�ADE = 180° − 53° − 47°

= 80°

Pupils omit one of the 53° which is one of the base angles of the

isosceles triangle.

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Mathematics


5 h 18 min after 9.42 a.m. is 3 p.m.

James arrived at Bravo Town at 3 p.m.

E-Yang started working on his Science project at 2.45 p.m. and e

5.37 p.m. How long did he take to do the project?

Time taken → 2 h + 15 min + 37 min = 2 h 52 min

E-Yang took 2 h 52 min to do his Science project.

Duration Of Time Interval

At Your Fingertips

When we use a 12-hour clock, we write time using a.m. or p.m.

9.15 a.m. refers to 9.15 in the morning while 9.15 p.m. refers to 9.15 at night.

When we use a 24-hour clock, we write time as follows:

9.15 a.m. is written as 09 15.

We read it as “zero nine fifteen hours”.

1.00 p.m. is written as 13 00.

We add 12 hours to 1.00, and we read it as “thirteen hundred hours”.

9.15 p.m. is written as 21 15.

We read it as “twenty-one fifteen hours”.

A time line is useful

when it comes to

finding out duration

of time.

James drove 5 h 18 min from Amazing Town to Bravo Town. He left at

9.42 a.m. When did he arrive at Bravo Town?

9.42 a.m.

11.42 a.m.12 noon

3 p.m

2 h

18 min

3 h

2.45 p.m.

4.45 p.m. 5 p.m.5.37

37 min

15 min

2 h

Unit

6G

eom

etry

•

Mathematics PSLE Revision Guide© 2009 Marshall Cavendish International (Singapore) Private Limited 131

A rectangle has 2 pairs of parallel lines.EF // HG and EH // FG.A rectangle also has 2 pairs of equal sides.EF = HG and EH = FG.

�EFG = �FGH = �GHE = �HEF = 90°Triangles EFG, FGH, GHE and HEF are right-angled triangles.

A square has 2 pairs of parallel lines. AB // DC and AD // BC. Triangles ABC, BCD, CDA and DAB are right-angled isosceles triangles.

Good To Know

Do you know that a square is actually a special rectangle?

Properties Of A Square, A Rectangle, A Triangle, A Parallelogram, A Trapezium And A Rhombus

Square

A square has 4 equal sides.AB = BC = CD = DAAll the angles in a square are right angles.�ABC = �BCD = �CDA = �DAB = 90°

A B

D C

A B

D C

RectangleE F

H G

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Dear pupil and parent,The PSLE Mathematics Revision Guide (2nd Edition) is your answer to concise and precise revision for the PSLE. This revision guide strictly follows the latest primary school mathematics syllabus issued by the Ministry of Education, and is a structured, all-in-one guide that directs pupils in their revision with the following features:

• What you need to know is a summary of key points pupils must know as stipulated in the syllabus.

• Revision notes are found at the beginning of each unit. These serve as a quick revision of concepts covered in the unit.

• At your fingertips are essential formulae and concepts that are highlighted for pupils to take note of.

• Worked examples are questions with step-by-step solutions. Pupils are guided to work out the questions by utilising important concepts and methods.

• Good to know provides additional information about a topic or concept, which aims to stimulate pupils’ interests in the topic. This complements key concepts covered in the revision notes.

• Common error highlights misconceptions that pupils often have, which in turn lead to careless mistakes. These point out the common mistakes they tend to make.

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Unit

4

Mon

ey A

nd M

ensu

ratio

n •


e Limited

69

ct at 2.45 p.m. and ended at

project?

= 2 h 52 min

ence project.

at night.

ours”.

ime line is useful

hen it comes to

nding out duration

of time.

Town. He left at

3 p.m.

3 h

.45 p.m. 5 p.m.5.37 p.m.

37 min

15 min

Unit

12



251

Rout

ine

Que

stio

ns •

NON-ROUTINE QUESTIONSUnit 12

Beverly was strolling along a path planted with trees. All the trees were

planted an equal distance apart. Beverly took 22 minutes to stroll fro

m

the 1st tree to the 12th tree. At which tree would she be after strolling for

120 minutes?

Solution

Strategy: Draw a diagram. It can help to visualise and understand the problem better.

Parental Tip

Non-routine questions are application questions. They can be solved by non-

conventional methods. Normally such questions are best worked out by careful

reading of the question and making inferences through logical deductions.

It takes 22 minutes to walk from the 1st to the 12th tree. There are

11 ‘spaces’ in between.

22 ÷ 11 = 2

It takes 2 minutes to walk from one tree to another tree.

Look at the above diagram. The total number of trees is always 1 more

than the total number of spaces in between the number of trees.

(120 ÷ 2) + 1 = 61

Hence after 120 minutes, Beverly would be at the 61st tree.

1st

12th

22 min

Beverly was strolling along a path planted w

planted an equal distance apart. Beverly too

the 1st tree to the 12th tree. At which tree wo

120 minutes?

Worked Examples

Exam Practice Paper 1© 2009 Marshall Cavendish International (Singapore) Private Limited

268

Section A – Calculators are NOT allowed in this section.Questions 1 to 10 carry 1 mark each. Questions 11 to 15 carry 2 marks each. For a question, four options are given. One of them is the correct answer. Make your choice (1, 2, 3 or 4). Shade the correct oval (1, 2, 3 or 4) on the Optical Answer Sheet.

(20 marks)1. Simplify 35 – 5 × 2 + 20 ÷ 4. (1) 10

(2) 20 (3) 30 (4) 50

2. When x = 8, find the value of 3x + 24x – 15.

(1) 1112

(2) 13 (3) 17 1

2 (4) 30

3. The figure shows part of a post which is used for measuring the height of water. What is the height of the water level indicated by the post? (1) 15.42 m

(2) 15.47 m (3) 15.53 m (4) 15.70 m

15.5 m

15.4 m

PSLEPRACTICE PAPER 1

Paper One 40Duration: 50 min

Uni

t 11

Heu

rist

ics-

Bas

ed Q

uest

ions

•



227

HEURISTICS-BASED QUESTIONS

Unit 1134 mm

Act It OutWorked Example 1 A net of a cube is shown below.

(a) Which of the following cubes can be formed?

(i) (ii)

(iii) (iv)

(v) (vi) (vii) (viii)Cut and then fold the given net from the Appendix to help you

find out which of these cubes can be formed by the given net.Solution

You would find that cubes (i), (ii), (iv), (v) and (vi) can be formed.

Mathematics PSLE Revision Guide © 2009 Marshall Cavendish International (Singapore) Private Limited130

line of symmetry

Symmetry

All the figures below are called symmetrical figures.These figures have been divided into equal halves by lines of symmetry.

The figure below has 2 lines of symmetry. The star has 5 lines of symmetry.

The figures below are non-symmetrical.

Maths At HomeUse coloured papers, fold them into halves or quarters.

Cut with a pair of scissors.

Then unfold.

What do you notice?

The figures below have 1 line of symmetry.

Parental Tip

Help your child to identifythe dotted lines whichform the lines of symmetry for these cut-outs.

Place a rectangular mirror on the line of symmetry to check if the figures are symmetrical.

• Heuristics-based questions are questions that involve reasoning and logical deduction. MOE has stressed the need for this category of questions. The PSLE Mathematics Revision Guide (2nd Edition) has an entire chapter dedicated to heuristics-based questions and provides 1 or 2 worked examples for each heuristic. Similar practice questions are given on that heuristic as reinforcement.

• Non-routine questions are challenging questions that require thinking out of the box. Worked examples and practice questions are provided to give pupils more practice.

• Maths at home provides pupils with hands-on activities that reinforce concepts that are difficult to visualise.

• Parental tips provide suggestions to parents on how they can facilitate their child’s thinking process.

• Exam practice papers are provided to simulate the PSLE examination. These papers follow the latest PSLE examination format.

• Detachable coloured concept maps are useful for pupils when doing a quick revision prior to their examinations. These are summaries of key concepts for each chapter.

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Mathematics PSLE Revision Guide © 2009 Marshall Cavendish International (Singapore) Private Limitedviii

Contents

Unit 1 Whole Numbers 1

Unit 2 Fractions 27

Unit 3 Decimals 49

Unit 4 Money and Mensuration 68

Unit 5 Statistics 109

Unit 6 Geometry 127

Unit 7 Average, Comparison of Quantities and Speed 158

Unit 8 Ratio 175

Unit 9 Percentages 197

Unit 10 Algebra 217

Unit 11 Heuristics-Based Questions 227

Unit 12 Non-Routine Questions 251

Appendix 256

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Mathematics PSLE Revision Guide© 2009 Marshall Cavendish International (Singapore) Private Limited ix

Concept Maps

Whole Numbers 359

Fractions 361

Decimals 363

Money and Mensuration 365

Geometry 367

Statistics 371

Average, Comparison of Quantities and Speed 371

Ratio 371

Percentages 373

Examination Tips for the Pupil 263

PSLE Exam Practice Paper 1 267

PSLE Exam Practice Paper 2 291

Solutions 315

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Unit

1W

hole

Num

bers

•


100 000

200 000

300 000

400 000

500 000

600 000

700 000

800 000

900 000

1000 000

WHOLE NUMBERS

Unit 1

What you need to know• Counting in hundred thousands up to 1 million• Number notation and place values• Odd and even numbers• Comparing and ordering numbers up to 10 million• Approximation and estimation• Factors and multiples• Multiplication and division• Order of operations

Counting In Hundred Thousands Up To 1 Million

One hundred thousand, two hundred thousands, three hundred thousands, four hundred thousands

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Let’s find out what each digit stands for.

There are 100 000 tens in 1 million.

How many hundred thousands are there in 1 million?

There are 10 one hundred thousands in 1 million.

How many tens are there in 1 million?

1 Million

10 Hundred Thousands

100 Ten Thousands 1000 Thousands

10 000 Hundreds

100 000 Tens

Number Notation And Place ValuesReading Numbers

Number In Words

1 234 567 One million, two hundred and thirty-four thousand, five hundred and sixty-seven

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Unit

1W

hole

Num

bers

•


Odd And Even NumbersOdd Numbers

Odd numbers are numbers that cannot be divided exactly by 2. For example, 1, 3, 5, 7, 9, 11 and 13.

103, 245, 287, 999, 1117 are some other examples of odd numbers.

Odd numbers always end with 1, 3, 5, 7 or 9.

Even numbers always end with 0, 2, 4, 6 or 8.

Place Value

1 2 3 4 5 6 7

7 Ones 7

6 Tens 60

5 Hundreds 500

4 Thousands 4000

3 Ten thousands 30 000

2 Hundred thousands 200 000

1 Million 1 000 000

Even Numbers

132, 258, 554, 996, 1000 are some other examples of even numbers.

Even numbers are numbers that can be divided exactly by 2. For example, 2, 4, 6, 8, 10 and 12.

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Comparing And Ordering Numbers Up To 10 MillionComparing Numbers

Let us find out which number is greater: 456 789 or 457 698.

Hundred Ten Thousands Hundreds Tens Ones Thousands Thousands

4 5 6 7 8 9

4 5 7 6 9 8

7 Thousands is greater than 6 Thousands

So, 457 698 is greater than 456 789.

Rounding Off NumbersRounding Off to the Nearest Ten

Therefore, 33 becomes 30 when rounded off to the nearest ten.38 becomes 40 when rounded off to the nearest ten.

3530 40

3833

Both 33 and 38 are between 30 and 40.

Since the digits in the hundred thousands and ten thousands are the same, we move on to compare the thousands.

33 is nearer to 30 than to 40.38 is nearer to 40 than to 30.

When we do comparison, it is important to study the place values of each digit carefully.

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MATHEMATICS PSLE - GoGurucdn.goguru.com.sg/media/mce_sample/9789814736596.pdf · PSLEMATHEMATICS Revision Guide 2nd Edition Michelle Choo The most complete handbook for PSLE!