Primary 5 Math :
Top Schools Exam Problems Explained
Welcome to your go-to guide for navigating Singapore Primary 5 Math! The jump to Primary 5 introduces new concepts and longer word problems, which can feel like a big adjustment for both you and your child. Take a deep breath. You are exactly in the right place.
On this page, we carefully break down actual past-year exam questions from top primary schools in Singapore. For every problem, you will see the exact working steps required to score full marks (just look for the neat blue handwriting). Below that, we provide a crystal-clear, step-by-step explanation so your child can truly grasp the underlying concepts without the tears. Let's build their confidence and conquer math together!
Ryan baked 750 cookies. He sold 50% of the cookies and gave 23 of the remaining cookies to his neighbour. He then ate some cookies and had 80 cookies left. What percentage of the cookies baked did Ryan eat?
1 - 2/3 = 1/3
375 ÷ 3 = 125
125 - 80 = 45
45 ÷ 750 × 100% = 6%
Ans: 6%
💡 Detailed Explanation for Understanding
As the total number of cookies was given, we can work through the story step by step to find out exactly how many cookies Ryan ate.
Ryan baked 750 cookies and sold 50% of them. Since 50% is exactly half, we just divide by 2.
750 ÷ 2 = 375 cookies remaining.
Ryan gave away 2 units out of 3 from the remainder. This means he was left with 1 unit out of 3 (or 1/3) of the remaining cookies.
We can find this by dividing the remainder by 3.
375 ÷ 3 = 125 cookies.
Before he ate any, he had 125 cookies. After eating some, he had 80 left. We subtract to find out how many disappeared into his tummy!
125 - 80 = 45 cookies eaten.
The question asks for the percentage of the total cookies baked that he ate. We take the cookies eaten (45) divided by the total baked (750), and multiply by 100%.
45 ÷ 750 × 100% = 6%.
Charlene had $102 less than Bernice. After Charlene gave Bernice $90, Bernice had 5 times as much as what Charlene had left. How much money did Charlene have at first?
5 - 1 = 4
$282 ÷ 4 = $70.50
$70.50 + $90 = $160.50
Ans: $160.50
💡 Detailed Explanation for Understanding
This is a Changed Difference Concept question. When one person gives money to another, the gap (difference) between their money changes drastically. Let's see how the gap widens!
At first, Bernice has $102 more than Charlene.
When Charlene gives Bernice $90, two things happen. First, Charlene's money drops by $90. Second, Bernice's money goes up by $90.
This means the gap between them widens by $90 twice!
To find the new difference between their money, we add the changes to the original gap.
New difference: $102 + $90 + $90 = $282.
In the end, Bernice has 5 units and Charlene has 1 unit. The difference between them is 5 - 1 = 4 units.
We know this 4-unit difference is equal to $282.
To find 1 unit (which is what Charlene has left): $282 ÷ 4 = $70.50.
In the end, Charlene has $70.50 left. Since we know she gave away $90 to Bernice earlier, we just need to add it back to find her starting amount.
$70.50 + $90 = $160.50.
There were some fruits in a crate. 49 of them were strawberries and 23 of the remainder were mangoes. The rest of them were pineapples. There were 105 more strawberries than pineapples.
(a) How many mangoes were there?
Mangoes : 23 × 59 = 1027
Pineapples : 59 - 1027 = 527
Difference : 49 - 527 = 727
1 unit : 105 ÷ 7 = 15
Mangoes : 10 × 15 = 150
Ans: 150
(b) How many fruits were there in the crate?
Ans: 405
💡 Detailed Explanation for Understanding
Let's solve this using the Fraction of a Remainder concept. By multiplying the fractions, we can find out exactly what fraction of the total fruits each type represents!
The whole crate is 1. Since 49 are strawberries, we subtract this from 1 to find the remainder.
1 - 49 = 59 of the total fruits.
Mangoes are 23 of the remainder. We multiply these two fractions together.
23 × 59 = 1027 of the total fruits.
Pineapples make up the rest of the remainder. We take the remainder fraction and subtract the mangoes.
59 - 1027 = 527 of the total fruits.
The question tells us there were 105 more strawberries than pineapples. Let's find the difference between their fractions.
Strawberries ( 49) - Pineapples ( 527) = 727.
This means 7 units out of the total 27 units represent 105 fruits.
To find 1 unit, we divide: 105 ÷ 7 = 15.
We already found that Mangoes represent 1027 of the total, which means they are 10 units.
10 × 15 = 150.
The denominator in our fractions (27) tells us there are 27 units in total.
Since 1 unit is 15, we multiply: 27 × 15 = 405.
Peter has some 20-cent coins and 50-cent coins. The number of 20-cent coins is four times as many as the number of 50-cent coins. The value of the 20-cent coins is $11.40 more than the value of the 50-cent coins.
(a) How many fewer 50-cent coins than 20-cent coins does Peter have?
$11.40 ÷ $0.30 = 38
4 - 1 = 3
38 × 3 = 114
Ans: 114
(b) How much money does Peter have?
38 × $1.30 = $49.40
Ans: $49.40
💡 Detailed Explanation for Understanding
Let's solve this easily using the Grouping Concept. Because the question tells us there is a "four times" relationship, we can organize these coins into identical groups to make the math simple to understand.
Since Peter has 4 times as many 20-cent coins as 50-cent coins, we will put exactly four 20-cent coins and one 50-cent coin into every group.
In each group, the 20-cent coins are worth more than the 50-cent coin. Value of 20-cent coins (4 × $0.20 = $0.80) minus value of the 50-cent coin ($0.50) is $0.30.
The question tells us that in total, the 20-cent coins are worth $11.40 more than the 50-cent coins. Since every group gives us a difference of $0.30, we can figure out how many groups there are by dividing.
Total number of groups: $11.40 ÷ $0.30 = 38 groups
The question asks how many fewer 50-cent coins than 20-cent coins Peter has.
In just one group, there are 4 (20-cent coins) minus 1 (50-cent coin) = 3 fewer coins.
Since there are 38 groups altogether: 38 × 3 = 114.
Let's look inside one group again.
Value of the 20-cent coins ($0.80) plus the value of the 50-cent coins ($0.50) gives a total value of $1.30 for one whole group.
Since there are 38 groups altogether, we multiply the value of one group by 38.
38 × $1.30 = $49.40.