Every year, there will be some challenging and unique math PSLE (Primary School Leaving Examination) questions that will raise some discussion.
These questions are usually out of the box and will help to differentiate students of different standards.
To ensure primary 6 students have a higher chance of scoring well for their upcoming national test it is routine to do past year papers.
In this post, let’s go through three thought-provoking Math PSLE questions from the year 2022.
2022 PSLE Paper 1 Q30
There were 9 red beads and some blue beads in a box. After some red beads were added, the fraction of the blue beads was ⅖. After 56 yellow beads were added, the fraction of the blue beads was 2/9. How many red beads were added?
Solution
This is a Quantity Unchanged question.
Red beads: 5u – 2u = 3u
Before
R:B
3:2
Blue + red + yellow = 9u, and we know blue is 2u, red + yellow = 9u – 2u = 7u
After
B:R+Y
2:7
In this question, the number of blue beads didn’t change. Coincidentally, the units of blue beads are the same, this means that 1u of before and after ratio has the same value.
Do note that, if the units of the ratio are different, we need to make the units for blue beads the same.
In the after ratio, the number of red beads also didn’t change.
And since red beads = 3u, yellow beads = 7u – 3u = 4u
B : R : Y
2 : 3 : 4
4u = 56
1u = 14
3u = 42
Number of red beads added → 42 – 9 = 33
If you want more practice for Ratio before and after concept, buy this resource for more practice.
2022 PSLE Paper 2 Q15
Muthu spent 4/7 of his money to buy 6 identical pens. He spent the rest of his money to buy another 4 such pens and 3 identical files.
(a) What fraction of Muthu’s money was spent to buy the 3 files? Give your answer in the simplest form.
(b) For every 5 files bought, 1 additional file was given free. How many files would Muthu get in total if he were to spend all his money to buy files only?
Solution
(a)
Method 1: Fractions
Cost of 6 pens → 4/7 of his money
Cost of 1 pen → 4/7 ÷ 6 = 2/21 of his money
Cost of 4 pens → 2/21 x 4 = 8/21 of his money
Cost of 3 files → 1 – 4/7 – 8/21 = 1/21 of his money
Certain students have become accustomed to familiar questions where they tend to offer convenient responses like whole numbers.
In this scenario, it’s important for students to acknowledge that 1 pen signifies a fraction of Muthu’s money, rather than representing a whole number.
Method 2: Whole numbers
Cost of 6 pens → 24u of his money
Cost of 1 pen → 24u ÷ 6 = 4u of his money
Cost of 4 pens → 4u x 4 = 16u of his money
Cost of 3 files → 42u – 24u – 16u = 2u
Fraction → 2u/42u = 1/21
(b)
1/21 of his money → 3 files
21/21 of his money → 3 x 21 = 63 files
Number of additional file → 63 ÷ 5 = 12 r 3
Total number of files → 63 + 12 = 75
If you want more practice for multiplication and division of fraction, consider this discounted bundle that is available in TPT.
2022 PSLE Paper 2 Q16
A plot of land of area 876 m2 is divided into three rectangular fields of equal width. The fields are fenced using 177 m of fencing, indicated by ……. In the figure below.
(a) Find the length of AB.
(b) Find the perimeter of the plot of land.
Solution
(a)
Length of AB + Length of AB + 27 m + 27 m + 36 m + 36 m = 177 m
2 x Length of AB + 126 m = 177 m
2 x Length of AB = 177 m – 126 m = 51 m
Length of AB = 51 m ÷ 2 = 25.5 m
(b)
Perimeter → 25.5 m + 36 m + 36 m + 27 m = 124.5 m
Final Thoughts
Numerous challenging questions often appear difficult because students struggle to identify the right approach to solve them. Familiarizing themselves with various question types can provide valuable insights into how to tackle these problems effectively.
In the worst-case scenario, if a question seems insurmountable, it might be better for them to move on and concentrate on problems where they have a better chance of success.
Checking their work to catch careless mistakes and transference errors can help them secure the marks they’re sure about.
Ultimately, it’s not always necessary to achieve a perfect score; at times, employing a strategic approach to an exam paper holds greater significance.
Related read: 5 Strategies In Math Problem Solving Your Students Need To Know Today
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