Question 1

73 thousands and 8 tens is the same as

Accepted Answer

4) 73 080. 73 thousands = 73 × 1000 = 73000.
8 tens = 8 × 10 = 80.
Combining these gives 73000 + 80 = 73080.

Question 2

13 845 rounded to the nearest hundred is

Accepted Answer

1) 13 800. To round 13 845 to the nearest hundred, look at the tens digit, which is 4. Since 4 is less than 5, we round down. The hundreds digit (8) remains the same, and the tens and units digits become 0.
So, 13 845 rounded to the nearest hundred is 13 800.

Question 3

What is the missing number in the box?

Accepted Answer

4) 39. The image shows a blank box over 5, followed by an equals sign, then the number 4. Mathematically, this reads as '? / 5 = 4', which implies the missing number is 4 × 5 = 20.
However, 20 is not among the given options, and the provided answer key indicates option (4) 39. This suggests a potential misrepresentation in the visual or a different intended question.
Given the constraint to follow the answer key, the correct option is (4) 39, despite the visual ambiguity.

Question 4

What fraction of the shapes in the box are ✶?

Accepted Answer

3) 6/10. Count the total number of shapes in the box. There are 4 diamond shapes and 6 star shapes, making a total of 4 + 6 = 10 shapes.
Count the number of star shapes (✶), which is 6.
The fraction of star shapes is (Number of star shapes) / (Total number of shapes) = 6/10.

Question 5

In the number 45.67, the digit ____ is in the tenths place.

Accepted Answer

2) 6. In a decimal number, the first digit immediately to the right of the decimal point is in the tenths place.
In 45.67, the decimal point is between 5 and 6. The digit immediately after the decimal point is 6. Therefore, 6 is in the tenths place.

Question 6

Write 4 and 3/20 as a decimal.

Accepted Answer

3) 4.15. To convert the mixed number 4 and 3/20 to a decimal:
First, convert the fraction 3/20 to a decimal. To do this, make the denominator 100:
3/20 = (3 × 5) / (20 × 5) = 15/100.
As a decimal, 15/100 is 0.15.
Now, add this decimal to the whole number part:
4 + 0.15 = 4.15.

Question 7

Arrange these numbers from the smallest to the greatest.
5709, 5079, 5790

Accepted Answer

3) 5079, 5709, 5790. To arrange numbers from smallest to greatest, compare their values:
1. Compare the thousands digit: All numbers start with 5 (thousands). 
2. Compare the hundreds digit: 
   - 5079 has 0 hundreds.
   - 5709 has 7 hundreds.
   - 5790 has 7 hundreds.
So, 5079 is the smallest.
3. Now compare 5709 and 5790:
   - Both have 7 hundreds.
   - Compare the tens digit: 5709 has 0 tens, 5790 has 9 tens.
   - So, 5709 is smaller than 5790.
Therefore, the order from smallest to greatest is 5079, 5709, 5790.

Question 8

Which of the following is a multiple of both 3 and 4?

Accepted Answer

4) 24. A number is a multiple of both 3 and 4 if it is divisible by both 3 and 4. This is equivalent to finding a multiple of their least common multiple (LCM). The LCM of 3 and 4 is 12.
Check the given options:
1) 7: Not divisible by 3 or 4.
2) 9: Divisible by 3 (9 = 3 × 3), but not by 4.
3) 16: Divisible by 4 (16 = 4 × 4), but not by 3.
4) 24: Divisible by 3 (24 = 3 × 8) AND divisible by 4 (24 = 4 × 6).

Question 9

Beads are used to form a pattern as shown. How many beads will there be in Figure 6?

Accepted Answer

3) 21. The pattern shows triangular numbers:
Figure 1: 1 bead
Figure 2: 1 + 2 = 3 beads
Figure 3: 1 + 2 + 3 = 6 beads
Figure 4: 1 + 2 + 3 + 4 = 10 beads
Following this pattern:
Figure 5: 1 + 2 + 3 + 4 + 5 = 15 beads
Figure 6: 1 + 2 + 3 + 4 + 5 + 6 = 21 beads

Question 10

Which of the numbers when rounded to the nearest tenth becomes 82.3?

Accepted Answer

2) 82.34. To round to the nearest tenth, look at the hundredths digit:
1) 82.24: The hundredths digit is 4. Round down. 82.24 rounds to 82.2.
2) 82.34: The hundredths digit is 4. Round down. 82.34 rounds to 82.3.
3) 82.235: The hundredths digit is 3. Round down. 82.235 rounds to 82.2.
4) 82.354: The hundredths digit is 5. Round up. 82.354 rounds to 82.4.
Only 82.34 rounds to 82.3.

Question 11

Which of the following decimals is closest in value to 0.5?

Accepted Answer

3) 0.46. To find the closest value, calculate the absolute difference between each option and 0.5:
1) |0.5 - 0.4| = 0.1
2) |0.5 - 0.6| = 0.1
3) |0.5 - 0.46| = 0.04
4) |0.5 - 0.56| = 0.06
The smallest difference is 0.04, which corresponds to 0.46.

Question 12

Mrs Lee bought 9 similar packets of milk.
After she used 6 packets of milk to make some cakes, she had 3.42 L of milk left.
How many litres of milk did she have at first?

Accepted Answer

2) 10.26 l. Mrs Lee used 6 packets out of 9, so she had 9 - 6 = 3 packets left.
These 3 packets contained 3.42 L of milk.
So, 1 packet of milk = 3.42 L ÷ 3 = 1.14 L.
At first, she had 9 packets of milk.
Total milk at first = 9 packets × 1.14 L/packet = 10.26 L.

Question 13

Similar balloons are tied on a pole and placed at an equal distance.
Both ends of the pole are tied with balloons.
The distance between two balloons is 1.65 m.
What is the total distance between 8 balloons?

Accepted Answer

2) 11.55 m. If there are 8 balloons, the number of intervals between them is 8 - 1 = 7 intervals.
Each interval has a distance of 1.65 m.
Total distance = Number of intervals × Distance per interval
Total distance = 7 × 1.65 m = 11.55 m.

Question 14

ABCD is a rectangle. Find ∠X.

Accepted Answer

1) 10°. The diagram shows a rectangle ABCD. The angle ∠DAC is marked 20° and ∠BCA is marked 60°. The angle ∠X is marked as ∠ACD.
In a rectangle, adjacent angles sum to 90°. Therefore, ∠ADC = 90° and ∠BCD = 90°.
If ∠DAC = 20°, then in triangle ADC, ∠ACD should be 90° - 20° = 70°.
If ∠BCA = 60°, then in triangle ABC, ∠BAC should be 90° - 60° = 30°.
Also, in a rectangle, alternate interior angles are equal, so ∠ACD = ∠BAC. This would imply X = 30°.
However, the angles ∠DAC=20° and ∠BCA=60° are inconsistent for a single rectangle (since ∠DAC should equal ∠BCA if AD || BC, and 20° ≠ 60°).
Given the answer key indicates 10°, and there are inconsistencies, the most likely intended calculation (though not directly obvious from a consistent diagram) involves a subtraction from a right angle. One way to get 10° using 20° and 60° would be `90° - 20° - 60° = 10°`, assuming these angles are parts of a larger 90° angle, or other non-standard interpretation. For example, if X was the result of `∠ADC - ∠DAC - ∠DCE` for some point E. Since the question is flawed, we state the answer as per the key.

Question 15

Study the piece of folded paper. Which symmetrical figure was cut out from it?

Accepted Answer

1) A multi-pointed star/flower shape.. When paper is folded multiple times and a cut is made, unfolding it creates a symmetrical pattern. The folded paper shown has complex folds. Option (1) represents a figure that, when folded and cut in a specific way (e.g., a pointed cut at the edge), would result in a symmetrical shape with multiple 'petals' or points upon unfolding. This is a common paper-cutting activity where such shapes are generated.

Question 16

Jan has 3/4 m of cloth. She has 1/2 m more cloth than Helen.
How much cloth do they have altogether?

Accepted Answer

2) 1 m. Let J be the amount of cloth Jan has and H be the amount of cloth Helen has.
Jan has 3/4 m of cloth, so J = 3/4 m.
Jan has 1/2 m more cloth than Helen: J = H + 1/2 m.
Substitute J = 3/4 m into the equation: 3/4 = H + 1/2.
To find Helen's cloth (H): H = 3/4 - 1/2 = 3/4 - 2/4 = 1/4 m.
Total cloth they have altogether = J + H = 3/4 m + 1/4 m = 4/4 m = 1 m.

Question 17

How many minutes does it take for a minute hand of a clock to make 1 1/4 turn round the clock?

Accepted Answer

3) 75 min. A minute hand completes one full turn around the clock in 60 minutes.
1 full turn = 60 minutes.
1/4 turn = 1/4 × 60 minutes = 15 minutes.
So, 1 1/4 turns = 1 full turn + 1/4 turn = 60 minutes + 15 minutes = 75 minutes.

Question 18

Jenny was working from 11 10 to 13 05.
How much time did she take to complete her work?

Accepted Answer

3) 1 h 55 min. Start time: 11 10 (11:10 AM)
End time: 13 05 (1:05 PM)
First, calculate time from 11:10 AM to 12:00 PM:
12:00 - 11:10 = 50 minutes.
Next, calculate time from 12:00 PM to 1:05 PM:
1 hour and 5 minutes.
Total time = 50 minutes + 1 hour 5 minutes = 1 hour 55 minutes.

Question 19

The area of a square is 36 cm². What is the perimeter of the square?

Accepted Answer

2) 24 cm. The area of a square is given by the formula side × side (s²).
Given Area = 36 cm², so s² = 36 cm².
To find the side length (s), take the square root of 36: s = √36 = 6 cm.
The perimeter of a square is given by the formula 4 × side (4s).
Perimeter = 4 × 6 cm = 24 cm.

Question 20

The graph below shows the hourly sales at a departmental store on Saturday.
During which one-hour interval had the greatest decrease in sales?

Accepted Answer

3) 8 p.m. to 9 p.m.. Read the sales values from the graph for each hour:
5 p.m.: $1500
6 p.m.: $2500
7 p.m.: $4500
8 p.m.: $3500
9 p.m.: $1500
10 p.m.: $500
Calculate the change in sales for each interval:
1) 6 p.m. to 7 p.m.: $4500 - $2500 = $2000 (increase)
2) 7 p.m. to 8 p.m.: $4500 - $3500 = $1000 (decrease)
3) 8 p.m. to 9 p.m.: $3500 - $1500 = $2000 (decrease)
4) 9 p.m. to 10 p.m.: $1500 - $500 = $1000 (decrease)
The greatest decrease in sales is $2000, which occurred from 8 p.m. to 9 p.m.

P4 Mathematics SA2 2023 — Pei Hwa

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