**1. Difficulty Level: 7/10**

The 2022 PSLE Math paper was challenging in parts but overall a manageable paper with little surprises. Unlike previous years, the 2022 paper included more syllabus-based questions and fewer questions that were IQ-based and that which required thinking out of the box.

Let’s look at the trickier questions from 2022:

**2.** **2022 PSLE Mathematics Paper 1 Booklet A: Rearrange and Form**

In order to get Question 4 right, we need to remember that fractions mean EQUAL parts of the same whole. In option 2, although the circle was divided into 4 parts, they were not 4 EQUAL parts.

The correct answer is therefore option 3. Since there are 8 equal triangles, and 2 were shaded, it means that 2/8 of the figure was shaded. 2/8 is equivalent to 1/4.

Another way would be to **Rearrange and Form**. By shifting the triangle over, the figure is now divided into 4 smaller squares, and of the 4 smaller squares, 1 of them is shaded. The **Rearrange and Form technique** can be applied to more complex question types. Watch the video below to see how else it is applied!

**3. 2022 PSLE Mathematics Paper 1 Booklet A: Nets and Solids**

Although **Nets and Solids** is not a major topic in the syllabus, a question on nets and solids can be a stumbling block especially for those who are less spatially gifted. Fret not! With some tips and tricks, students can quickly identify which of the above is the net of a cube. If a net falls into a 1–4‑1, a 1–3‑2, a 2–2‑2, or a 3–3 net, then it can most certainly be folded along the lines to form a cube.

**4. 2022 PSLE Mathematics Paper 1 Booklet A: Gaps and Subjects**

In Question 14, a less commonly seen shape is featured—the hexagon. This question, however, draws inspiration from the **Gaps & Subjects** question type. To work your way around this question, first identify the dots on the fixed spots—the corners.

Since a hexagon has 6 corners, there will definitely be 6 dots in total for these 6 corners.

Bearing in mind that the remaining dots are split equally among the 6 sides, we have 18 – 6 = 12 dots to split among the 6 sides. 12 ÷ 6 = 2. We would then place 2 dots in between the corners.

This means that along one side of the hexagon, there will be the 2 dots in between, plus the 2 dots on the corners, and that will leave us with 4 dots along one side.

In a bigger hexagon with 96 dots, there will still be 6 corners.

96 – 6 = 90 dots. This leaves us with 90 dots to split among the 6 equal sides.

90 ÷ 6 = 15.

Along one side of the hexagon, we will have 15 dots in between, plus the 2 dots on the corners, and that will leave us with 17 dots along one side.

**5. 2022 PSLE Mathematics Paper 1 Booklet A: Equating Numerators**

Whenever a fraction of A is equal to a fraction of B, this is an **Equating Numerators** question type. In this question, 23 of A is equal to 78 of B. When you equate the numerators, you make them the same number. The lowest common multiple of 2 and 7 is 14. Therefore, 1421 of A is equal to 1416 of B.

A is 21 units long with 14 units of it above the ground, and 7 units of it in the ground.

B is 16 units long with 14 units of it above the ground, and 2 units of it in the ground.

Since the length of A in the ground is 30cm longer than the length of B in the ground, this means that 7u – 2u = 30cm

5u **→** 30cm

1u **→** 30cm ÷ 5 = 6cm

21u + 16u = 37u

37u **→** 6cm × 37 = 222cm

The total length of sticks A and B is 222cm.

**6. 2022 PSLE Mathematics Paper 1 Booklet B: Tricky and Challenging Questions**

Booklet B is relatively easy. The following would be the 3 trickiest / most challenging questions of all the questions in Booklet B.

Question 20 might cause careless students to lose marks since the units of measurement given in the question were not the same. As the final answer is in kilograms, it would be wiser to change 450g to kilograms, and work with that.

Question 29 is a **Sets** question type. This is a little tricky since it is asking for the GREATEST possible number of letters if there were 137 letter “A“s in the pattern. First, we’d identify the repeating pattern, then proceed to find out how many sets we would have.

There are 3 letter “A”s in a set. 45 sets would contain only 45 × 3 = 135 letter “A”s. Therefore, if we count forward 2 more “A”s, that would be our 137^{th} “A”. Since the question wants to know the maximum number of letters possible without including the 138^{th} “A”, we will need to include the letter “C” that appears after the 137^{th} “A”.

If 1 set has 5 letters, 45 sets will have 45 × 5 = 225 letters.

Since we’re including up till the letter “C” in the 46^{th} set, that would be an additional 4 letters.

Hence, the greatest possible number would be 225 + 4 = 229 letters.

Question 30 is what we would recognise as a **Before-Change-After** question type.

A **Before-Change-After** question type can be identified by proportion-change-proportion In the question. This particular question involves 2 changes. Hence, the Before-Change-After table is lengthened to reflect 2 changes (B‑C-A-C‑A).

We start off by writing 9 under the number of red beads and leaving the number of blue beads blank. After adding a certain number (?) of red beads, the number of blue beads became 25 of the beads. Hence, 2u for blue beads, and 3u for red beads. We can now fill in the “Before” stage for the blue beads as 2u since there was no change to the number of blue beads.

Then, we add a column for the yellow beads. The change that occurred was an addition of 56 yellow beads. Remember, the number of blue beads remained the same throughout. Therefore, 2u are blue, 3u are red, and the remaining 9u – 2u – 3u = 4u must be yellow beads.

If the red beads started off at 9, and ended up at 42, this would mean that 33 red beads were added.

**7. 2022 PSLE Mathematics Paper 2: Model Drawing**

Moving on to paper 2, it was manageable with no overly complicated diagrams for the geometry, circles, area and perimeter, and pie chart question types. The bar graph and line graph in the data question types were not difficult to read, and the questions tested were straightforward.

Most of our students would have been conditioned to drawing the **Fraction-of-Fraction** Model (aka Drop-down Model) once they see the phrase “fraction of the remaining” (highlighted in question).

By using this model technique, our steps are kept short and simple, leaving less room for careless calculation mistakes and the loss of precious marks.

**8. 2022 PSLE Mathematics Paper 2: Simultaneous and Substitution**

Question 13 might seem tricky at first, but it is a **Simultaneous & Substitution** question type that is simply presented in a more visual way.

I would think that person who set this paper was very kind to have included Figure 3. Looking at Figure 3, one can clearly see that 2h and 1 side of the square = 58cm, and 3h + 2 sides of a square = 94cm. Based on these 2 equations, we will then apply the **Equate-Multiply-Subtract technique **to solve this **Simultaneous** question type. For a deeper understanding of this, watch the video on the Simultaneous and Substitution question type below.

**9. 2022 PSLE Mathematics Paper 2: Fractions**

Question 15 does seem a little out of the ordinary. Have you noticed it yet? Yes, there are no whole numbers in this question at all! You simply work with **fractions** without ever knowing the cost of a file or how much Muthu had exactly.

To start off, you would write down:

6 pens **→** 4/7

1 pen **→** 4/7 ÷ 6 = 2/21

4 pens **→** 2/21 × 4 = 8/21

His remaining money was used on 4 pens and 3 files. If his remaining money was 37 of his money, and buying 4 pens took up 821 of his money, this means that 3 files would cost him:

3/7 — 8/21 = 1/21

Muthu spent 1/21 of his money on the 3 files.

1/21 of his money **→** 3 files

Therefore, if he were to spend all of his money on files only, he would be able to get:

21/21 **→** 63 files

Since an additional file was given free for every 5 files he bought, this means that he would be able to get (63 ÷ 5 = 12 r 3) an additional file 12 times!

63 + 12 = 75

With the good deal in place, Muthu would go home with 75 files.

**10. 2022 PSLE Mathematics Paper 2: Rearrange and Form **

This question makes use of the **Rearrange, and Form** technique.

Lines highlighted in blue are 12m each, lines in yellow are 27m each, and the lines in purple are the same length.

Since these lines add up to 177m, and we know the lengths of the blue and yellow lines, it is not difficult to find the length of each purple line (line AB).

177m – (6 × 12m) – (2 × 27m) = 51m

51m ÷ 2 = 25.5m

The length of AB is 25.5m.

Part (b) is indeed more challenging with a higher weightage of 3 marks. As with most questions, information in the question is rarely given for the fun of it. Let’s make use of the area of 876m^{2 }to solve for the perimeter.

Since the figure is made up of rectangles whose lengths and breadths we know, it is not difficult to figure out the area of the rectangle in the middle.

The rectangle on top has a length of 25.5m and a breadth of 12m, giving it an area of 306m^{2}.

The rectangle at the bottom has a length of 27m and a breadth of 12m, giving it an area of 324m^{2}.

Therefore, the rectangle in the middle would have an area of

876m^{2 }- 306m^{2} -^{ }324m^{2 }= 246 m^{2 } and

a length of 246 m^{2 }÷ 12m = 20.5m.

The fencing took up 177m. To find the perimeter of the plot of land, we’ll be excluding the lines within the figure. We now know that those lines are 20.5m each.

Hence, we can find the perimeter by simply taking 177m – 20.5m – 20.5m = 136m

**11. 2022 PSLE Mathematics Paper 2: Number x Value**

By picking out the type of information given in the question, students will be able to identify this as a **Number × Value** question type. Most students will have no problem with solving for part (a).

To solve part (b), we’ll make use of the **Number × Value** table. Since we only know the proportion of cherries (and not the exact numbers) used for a large cake and a small cake is in the ratio of 3 : 2, we will use the units 3u and 2u to represent the number of cherries on each large and each small cake.

Therefore, 7 large cakes will have a total of 21u of cherries, and 15 small cakes will have a total of 30u of cherries. We can then easily solve for the total number of cherries used for all 15 small cakes, which is 30u.

Each large cake requires 3u of cherries. Since 1u = 4, then 3u = 12.

Mrs Li has decorated 7 large cakes. There are 25 large cakes so this means that she has 25 – 7 = 18 more large cakes to decorate.

If each large cake requires 12 cherries, 18 large cakes will require 18 × 12 = 216 cherries.

**12. Concluding Remarks**

We are pleased that the trickier questions in the PSLE 2022 Mathematics paper involve heuristics concepts covered in our curriculum. Our 2022 batch of graduates were all well-equipped to tackle the 2022 Math paper! Of course, Math is less about a stroke of good luck and more about being analytical in spotting exam trends or a shift in question types.

Over the years, we see shifts in trends and the evolution of question types, and our curriculum is updated annually to reflect the changes in the MOE syllabus. We want to place our eggs in the right baskets, and have our students reap as much fruit from their labour. Our role as teachers is to help students connect the dots in the question and teach them how to make sense of information in the question and solve it in the most time-efficient manner.

At Think Teach, Math lessons are structured so that learning is a breeze and not a torture. Your child will be challenged by tricky questions and trained to solve commonly tested ones with ease. Consistency is the key here to success. With a structured approach to problem-solving, every Math question would seem familiar. Your child will no longer perceive every Math question as a daunting mountain that he/she has not conquered. As I like to say, “Practice makes perfect”. If something at first seems unfamiliar to you, keep on working at it until you know it like the back of your hand!

After 3 years of being ravaged by COVID, 2023 heralds a change back to pre-COVID normal. With students no longer considered to be disrupted by the pandemic, we are expecting PSLE to return to its full force – something not seen since 2019.

What does full force mean? First, there will be no reduction of topics tested. Second, we expect PSLE papers will revert to their usual difficulty level from 2017 to 2019. Our teachers have found that the PSLE papers (not just Mathematics but English, Science, and Chinese) from 2020–2022 to be significantly easier than their predecessors.

With 2023 being a year that gets us back to what life was like before COVID, can we expect PSLE to be more challenging than 2022? We’ll find out together really soon!

This article was proudly written for you by TTA’s Math Team. Our strategy in helping students achieve exam excellence is simply to expose them to every type of question that could come out for PSLE and arm them with our easy-to-apply techniques and would help them approach these questions systematically