# PSLE Math Final Revision

Matrix Math has compiled a list of “Must-Mastered” PSLE Math concepts. This series of video lessons and notes will be an effective and efficient way to preparing for the coming PSLE Math exams. We strongly recommend all Primary 6 students watch the video lessons and attempt the sample questions provided.

We recommend viewing the lessons on a desktop browser.

The lessons are organised into Topics and Concepts. To fully derive the benefit of these lessons, students should learn in the sequence as presented. Avoid skipping from one section to another. Students should first read the accompanying notes. If there are sample questions, attempt to solve them. Watch the video lesson last.

We wish all our Primary 6 students the best, and we are confident you will do well. ## 1. PSLE Algebra  #### Practice questions

Peter bought 2 pens and 5 stickers. Each pen cost q cents. He gave the cashier \$5 and received \$1.20 change. How much, in terms of q, did 1 sticker cost?

## 2. Whole Numbers and FDRP

##### Fractions
• Conversion between decimals, fractions, and percentages.
• Fractions as measurements VS Fractions as units.
• Used  6/7 kg  VS  Used 6/7 of the sugar
• Units in the numerators and denominators – what do each of them refer to
• E.g.  2/5 of the original cookies are left  VS  The vanilla cookies left is 2/5 of the chocolate cookies left.
• Equivalent proportion
• Make numerator same
• When applying the ‘Before Change After’ concept, a change involving proportion (fraction or percentage) can be written as a BCA ratio.
• When there is more than 1 set of ratios recorded, look for the common base. If there is no common base, apply units and parts.
• Identify unchanged group, unchanged total, unchanged difference for the common base.
##### Percentage
• Percentage discount and percentage GST cannot be added or subtracted together.
• 100 units in the percentage discount refer to the original price
• 100 units in the percentage GST refers to the discounted price
• Percentage ‘more than’ or ‘less than’ – always treat the subject at the end of the phrase as 100%.
• E.g. Yenni has 40% fewer beads than John.
• Percentage increase or decrease – express the increase or decrease as a fraction of the original first, then multiply by 100 to convert the fraction to a percentage.
• Percentage discount – express the discount as a fraction of the original first, then multiply by 100 to convert the fraction to a percentage.
• “20% decrease from July to August and 5% increase from August to September” – The first month mentioned in each phrasing is treated as 100% (100 units).
• Statements containing a fraction or percentage which shows a comparison of units between two groups – use ratio to solve, then identify the common base.
• E.g. John has 20% as much money as Peter.
##### Divison statements
• Division statements that produce decimals (e.g. 7.033333… or 7.5) – three types of answers to give depending on what the answer should represent.
• Remainder (usually for grouping)
• Fraction (for long string of digits)
• Decimal (for terminating decimals)
• Do not round off the answer (for decimals especially) unless required by the question

#### Fractions in terms of units and measurements

Peter had 5⁄8 kg of oil. He used 1⁄3 of it on Monday, 3⁄10 kg on Tuesday and the rest on Wednesday. How much oil did he use on Wednesday?

#### Equivalent Proportion

John uses 40% of his savings while Yenni uses half of her savings to buy a present. As a result, both John and Yenni are left with equal amounts of money. If the difference between John and Yenni’s savings is \$20, how much is the present?

#### Overlapping shapes using ratio

The figure below is made up of 3 rectangles X, Y and Z placed such that they overlap at S and T. The ratio of the area of Rectangle X to the area of Rectangle Y to the area of Rectangle Z is 6 : 4 : 1. The ratio of the area of Rectangle S to the area of Rectangle T is 3 : 1. If the area of Rectangle Y is twice that of Rectangle S, what is the ratio of the total area of shaded parts to the total area of the unshaded parts? #### Age – difference unchanged

The ratio of Peter’s age to Yenni’s age is 3 : 7 now. In 9 years, Peter’s age will be 3⁄5 of Yenni’s. Find Yenni’s age now.

#### Percentage Discount

A 20% discount was given during a sale. There was a further 10% discount on the discounted price when one uses his membership card. Peter used his membership card and paid \$1800 for a television set at the sale. What was the original price of the television set?

#### Percentage Discount with GST

During a promotion, a car is selling at a discount of 20%. The usual price of the car was \$43875. The GST was 7% of the discounted price. How much is the GST?

#### Percentage of a percentage

Peter saves 30% of his monthly salary. When his salary increased by 10%, his savings increased by \$189. Find Peter’s salary before the increase.

#### Internal transfer with Proportion Change

Yenni and Amber had a total of 700 beads. Yenni gave 30% of her beads to Amber. Amber then gave 1⁄11 of her beads to Yenni. In the end, they each had the same number of beads. How many beads did Amber have at first?

#### Internal transfer with Proportion Change

John had \$190 more than Peter at first. After he gave 20% of his money to Peter, Peter had \$234 more than him. How much money did John have at first?

#### External transfer with Proportion Change

Yenni had a total of 5070 yellow and red beads at first. Her mother gave her some more beads. As a result, the number of her yellow beads increased by 20% and the number of her red beads increased by 3⁄5. The ratio of her yellow to red beads then became 3 : 8. How many yellow beads did she have at first?

#### External transfer with Proportion Change

There were 1600 pupils in a primary school. When the number of boys increased by 76 and the number of girls decreased by 4%, the total enrolment in the school increased by 3%. How many boys were there in the school at first?

#### External transfer with Proportion Change

Amber had 19.8 kg more flour than Yenni at first. After Amber used 2⁄3 of her flour to bake some cakes and Yenni used 1⁄4 of her flour to bake some muffins, Yenni had 30.9 kg more flour than Amber. How much flour did Amber have at first?

#### Internal/External transfer with 2 scenarios

There are some mangoes and pears at a fruit stall. If 16 mangoes are sold, the ratio of the number of mangoes to the number of pears would be 1 : 4. If 16 pears are sold instead, the number of mangoes would be 1⁄3 the number of pears. How many fruits are there altogether?

#### Internal/External transfer with 2 scenarios

A farmer had some apples and pears. If he buys another 40 pears, the ratio of the number of pears to the number of apples will become 5 : 6. If he buys another 60 apples instead, then the ratio of the number of pears to the number of apples would become 2 : 3. How many more apples than pears did the farmer have?

#### Quantity and Value – involving extra quantity

Box A contains only 50-cent coins while Box B contains only 10-cent coins. There are 23 more coins in Box B than in Box A. If the total amount of money in Box A and Box B is \$13.10, how many coins are there altogether?

#### Quantity and Value – involving difference in quantity and difference in total value

Yenni bought some cups and plates. She bought 2 more plates than cups. However, she paid \$25.20 less for the plates than for the cups. Each cup cost \$2 more than each plate. Each plate cost \$2.40.
(a) How many cups did Yenni buy?
(b) What was the total cost of the cups?

#### Quantity and Value – involving difference in quantity and difference in total value

Mrs Tan bought some guavas at \$1.20 each and some mangoes at \$2 each. She spent \$2.40 less on the mangoes than on the guavas. However, she bought 8 more guavas than mangoes.
(a) How many mangoes did she buy?
(b) How much did she spend on guavas?

#### Quantity and Value – proportion of quantity and difference in total value

Peter sold 4 times as many tablets as laptops and collected a total of \$8400. Each laptop costs \$325 more than a tablet. The amount collected for all the tablets sold was \$3480 more than the amount collected for all the laptops sold. How many laptops did Peter sell?

#### Quantity and Value – involving Lowest Common Multiple (LCM)

John bought some pens at the prices shown below.
(a) He bought an equal number of blue and red pens. He paid \$99.20 more for the blue pens than the red pens. How many pens did he buy altogether?
(b) Yenni spent an equal amount of money on the blue and red pens. What fraction of the pens she bought were red pens? Express your answer in the simplest form.

#### Quantity and Value – given quantity ratio and value of each group

At a birthday party, the ratio of the number of adults to the number of children was 1 : 4. Each boy was given 3 chocolates, each girl was given 2 chocolates while each accompanying adult received 1 chocolate. 403 chocolates were distributed and the ratio of the number of boys to the number of girls was 1 : 2. How many children were there at the party?

## 3. Average

There is a “rule” in Average that we teach our Primary 5 and Primary 6 students. That is – whenever a question provides the average value, always compute the total. However, sometimes this “rule” cannot be applied. This happens when the number of related items is not provided.

For example, we can find the total mass of 5 tables, given their average mass is 5 kg. However, we will not be able to find the total mass of some tables, given their average mass is 5 kg.

In Matrix Math, we developed a method we coined as the Circles’ Method to solve such questions.

#### Average – Two-layered circles method

On Monday, the average number of books donated by each pupil during a donation drive was 23. On Tuesday, 30 pupils donated an average of 14 books each. In the end, the average number of books donated by each pupil on both days was 20. How many books were donated on Monday?

#### Average – involving wrong value recorded

The average mass of a group of boys was 45 kg. When the nurse measured and recorded the mass of one of the boys, she wrongly recorded his mass as 42 kg when it should have been 24 kg. As a result, she calculated their average mass as 47 kg. How many boys were there in the group?

## 4. Area and Perimeter

#### Area & Perimeter – maximum number of shapes to get from figure

John has a rectangular piece of cardboard measuring 28cm by 13cm. He needs to cut out some right-angled triangles shown below from the cardboard. What is the maximum number of such triangles he can cut? #### Area & Perimeter – Rectangle involving units for length and breadth

The area of a rectangle is 490 cm². The breadth is 2⁄5 of its length. What is the length of the rectangle?

#### Area & Perimeter – Folded figures

A rectangular piece of paper is folded to form the figure below. The area of the shaded triangle is 18 cm². What is the area of the rectangular piece of paper before it was folded? #### Area & Perimeter – Percentage increase/decrease

If the side of a square is increased by 50%, find the percentage increase in area.

## 5. Area of Triangles

##### Ratio in Terms of Base/Height = Ratio in Terms of Area

(a) Triangles with the same height, their bases can be summed to form a single triangle of the same height. (b) Triangles with the same base, their heights can be summed to form a single triangle of the same base. #### Ratio in Terms of Base/Height = Ratio in Terms of Area

ABCD is a rectangle. AB is 4 times of AF. AE is 3⁄5 of AD. What fraction of the rectangle is unshaded? #### Combined area of triangles using common height/common base

Find the total area of the three shaded triangles. ## 6. Circles

Notes:

• Circumference = π x d
• Area = π x r x r
• Area of half petal = Quadrant – Triangle
• Area of full petal = Half petal x 2
• Area of boomerang = Square – Quadrant
• Finding the difference between overlapped shapes
• Observe which two shapes that overlap.
• Take the difference between the two shapes will remove the overlapped area, as well as get the difference between the un-overlapped parts of the two shapes. #### Circles – Sum of diameters

The figure below is made up of two semicircles and two rectangles. Find the perimeter of the figure, giving your answer in terms of π. #### Circles – involving squares

The figure shows a square inside a circle, not drawn to scale. The area of the square is 98 m². Find the area of the circle, using π = 22⁄7. #### Circles – involving squares

The figure is made up of 4 identical circles in a square. The area of the square is 144 cm². Find the area of the shaded part, using π = 3.14. #### Circles – Revolutions

A wheel with a radius of 7 cm was rolled from one wall in a room to the opposite wall. The distance between the two walls was 4.54 m. How many revolutions did it make before coming to a stop? (π = 22⁄7) #### Circles – Finding the difference between odd areas

The figure below is made up of 3 identical quarter circles and a square of sides 8 cm. Find the difference in the shaded area of A and the sum of the shaded areas of B and C. (π = 3.14) ## 7. Geometry #### Geometry – overlapping angles

The figure below is not drawn to scale. It shows two identical right-angled triangles ABC, ECI and a square GHFC. ∠GCI = 42° and ∠FCB = 35°. Find ∠ACE. #### Geometry – involving circles

In the figure below, not drawn to scale, O is the centre of the semi-circle, PR = RS, QT is parallel to RS and ∠PRS = 86°. Find ∠OPT. ## 8. Rates

#### Rates – involving work done

20 boys take 2 days to paint a room. How many rooms can 15 boys paint in 8 days?

#### Rates – involving work done

Amber can fold 30 paper planes in 1 hour. John can fold the same number of paper planes in 3⁄4 of the time. At these rates, how many paper planes can they fold altogether in 6 hours?

#### Rate – involving water in the tank

A tank with a square base of side 50 cm was half-filled with water at first. At 10.00 am, Tap X with water flowing in at a rate of 2 litres per minute and Tap Y with water draining water out of the tank at a rate of 0.6 litres per minute were turned on simultaneously. At 10.45 am, the tank was filled to the brim. Find the height of the tank.

## 9. Patterns

Tips to solve pattern questions:

• Square numbers (1, 4, 9, 16, 25 …)
• Patterns with common difference (+2, +2, +2 ..)
• Apply intervals concept
• Patterns question with alternating common difference (+2, +1, +2, +1 ..)
• Apply intervals with grouping
• If diagrams are given, use the diagrams to help you identify the pattern or the relationship between figure number and the quantity

#### Practice questions

Yenni used sticks to form figures that follow a pattern. The first four figures are shown below. How many sticks would he use for Figure 40? How many squares are formed in Figure 50? The figure below are made up of identical circles.

1682 circles are needed to form a certain pattern. Which pattern is it? ## 10. Others

#### Practice questions

Peter needs 220 pieces of string, each of length 30 cm, to tie some presents. The strings are sold in rolls of 20 m each. What is the least number of rolls of string that Peter needs to buy?

At a mini fun fair held in Matrix School, there are 4 game booths. There can only be 4 children playing at each game booth at any one time. If there are 40 children and they are given a total of 4 hours to play, how much time does each child get to play such that everyone can play for the same amount of time? Express your answer in hours.