Question 1

In which of the following numbers does the digit 5 stand for 50?

Accepted Answer

(3) 7590. The digit 5 in 7590 is in the tens place, which means its value is 5 x 10 = 50. In 5790, it stands for 5000. In 7905, it stands for 5. In 9750, it stands for 50.

Question 2

Which of the following numbers when rounded to the nearest ten becomes 81 500?

Accepted Answer

(2) 81 496. To round to the nearest ten, look at the digit in the ones place. If it is 5 or more, round up the tens digit. If it is less than 5, keep the tens digit as it is.
(1) 81 444 rounds to 81 440.
(2) 81 496: The ones digit is 6 (>=5), so round up the tens digit. 49 becomes 50. So 81 496 rounds to 81 500.
(3) 81 506 rounds to 81 510.
(4) 81 554 rounds to 81 550.

Question 3

Which of the following is a multiple of 9?

Accepted Answer

(1) 36. A multiple of 9 is a number that can be divided by 9 without a remainder. 
36 ÷ 9 = 4, so 36 is a multiple of 9.
28 ÷ 9 = 3 remainder 1.
3 is not a multiple of 9 (it is a factor).
19 ÷ 9 = 2 remainder 1.

Question 4

What fraction of the shapes in the box are ____?

Accepted Answer

(3) 7/10. Count the total number of shapes in the box: There are 10 shapes (3 stars and 7 pentagons).
Count the number of pentagon shapes: There are 7 pentagons.
The fraction of pentagon shapes is 7/10.

Question 5

Which of the following decimals is the smallest?

Accepted Answer

(3) 4.036. To compare decimals, start from the leftmost digit and compare digit by digit.
All numbers start with 4. Comparing the tenths digit: 4.06 (0), 4.16 (1), 4.036 (0), 4.306 (3). The smallest tenths digit is 0, so we compare 4.06 and 4.036.
For 4.06 and 4.036, compare the hundredths digit: 4.06 (6), 4.036 (3). The smallest hundredths digit is 3.
Therefore, 4.036 is the smallest decimal.

Question 6

In the figure, which angle is a right angle?

Accepted Answer

(2) ∠ b. A right angle measures 90 degrees and is typically indicated by a small square symbol in the corner of the angle. In the given figure, angle b has this symbol.

Question 7

Nelly sells 384 muffins every month. How many muffins will she sell in a year?

Accepted Answer

(1) 4608. There are 12 months in a year. 
Total muffins sold in a year = Muffins per month × 12 months = 384 × 12 = 4608 muffins.

Question 8

When a number is divided by 9, it has a remainder of 2. Which of the following could be the number?

Accepted Answer

(4) 5789. If a number divided by 9 has a remainder of 2, then (number - 2) must be a multiple of 9.
(1) 5786 - 2 = 5784. Sum of digits = 5+7+8+4 = 24 (not a multiple of 9).
(2) 5787 - 2 = 5785. Sum of digits = 5+7+8+5 = 25 (not a multiple of 9).
(3) 5788 - 2 = 5786. Sum of digits = 5+7+8+6 = 26 (not a multiple of 9).
(4) 5789 - 2 = 5787. Sum of digits = 5+7+8+7 = 27 (a multiple of 9). 
Thus, 5789 divided by 9 gives a remainder of 2.

Question 9

Joel runs 300 m every morning. His slowest record is 1 min 35 s. His fastest record is 55 s. What is the difference between his fastest record and his slowest record?

Accepted Answer

(4) 40 s. First, convert the slowest record to seconds: 1 minute = 60 seconds, so 1 min 35 s = 60 s + 35 s = 95 s.
Difference = Slowest record - Fastest record = 95 s - 55 s = 40 s.

Question 10

The table below shows the prices of tickets for a carnival.
On Sunday, Mr. Lee and Mrs Lee brought their 10-year-old son to the carnival. They bought three tickets in all. How much did they pay for their tickets altogether?

Accepted Answer

(1) $75.85. The family went on Sunday, so use the 'Sat and Sun' prices.
Mr. Lee (Adult) ticket: $29.95
Mrs Lee (Adult) ticket: $29.95
Their 10-year-old son (Child below 12 years) ticket: $15.95
Total cost = $29.95 + $29.95 + $15.95 = $75.85.

Question 11

The table below shows how Tiana spent her money.
Which of the following bar graphs best represents Tiana's spending shown in the table above?

Accepted Answer

(3). Match the spending amounts from the table to the heights of the bars in the graphs:
Magazine: $6
Storybook: $15
Bag: $20
Pencil Case: $15
Graph (3) accurately depicts these amounts with its bar heights, where Magazine is at 6, Storybook at 15, Bag at 20, and Pencil Case at 15.

Question 12

The areas of Square P and Rectangle Q are the same. The length of Square P is 8 cm. The breadth of Rectangle Q is 4 cm. What is the length of Rectangle Q?

Accepted Answer

(4) 16 cm. 1. Area of Square P = side × side = 8 cm × 8 cm = 64 cm².
2. Since the areas are the same, Area of Rectangle Q = 64 cm².
3. Area of Rectangle Q = length × breadth.
4. We know the breadth of Rectangle Q is 4 cm. So, 64 cm² = length × 4 cm.
5. Length of Rectangle Q = 64 cm² / 4 cm = 16 cm.

Question 13

Study the number pattern below.
What is the sum of the two missing numbers?

Accepted Answer

(4) 790. Analyze the pattern in the bottom row:
250 (+50) 300 (-30) 270 (+90) 360 (-70) 290 (+130) 420
The sequence of differences is: +50, -30, +90, -70, +130.
This sequence can be split into two alternating patterns:
Positive differences: +50, +90, +130 (increasing by 40 each time). The next would be +170.
Negative differences: -30, -70 (decreasing by 40 each time). The next would be -110.
So, after +130, the next difference is -110.
First missing number = 420 - 110 = 310.
After -110, the next difference is +170.
Second missing number = 310 + 170 = 480.
Sum of the two missing numbers = 310 + 480 = 790.

Question 14

Jeraldine baked a total of 749 cupcakes to sell at a carnival.
Figure 1 shows the number of cupcakes that were sold.
Figure 2 shows the number of cupcakes that were left unsold at the end of the carnival. The number of Red Velvet cupcakes that were left unsold is not shown in Figure 2.
Which table below shows the correct number of cupcakes which were left unsold?

Accepted Answer

(3). From Figure 1 (Cupcakes Sold):
Red velvet (R_sold) = 60
Caramel (C_sold) = 80
Chocolate (Ch_sold) = 100
Total sold = 60 + 80 + 100 = 240

From Figure 2 (Cupcakes Left Unsold - for Caramel and Chocolate):
Caramel (C_unsold) = 50
Chocolate (Ch_unsold) = 100

Total baked = 749

Total Caramel baked (C_baked) = C_sold + C_unsold = 80 + 50 = 130
Total Chocolate baked (Ch_baked) = Ch_sold + Ch_unsold = 100 + 100 = 200

Total Red Velvet baked (R_baked) = Total baked - C_baked - Ch_baked = 749 - 130 - 200 = 749 - 330 = 419

Red Velvet left unsold (R_unsold) = R_baked - R_sold = 419 - 60 = 359

Therefore, the correct numbers for cupcakes left unsold should be: Red velvet: 359, Caramel: 50, Chocolate: 100. This combination (359, 50, 100) is not available in the options. This indicates an inconsistency in the problem's data or the provided options. However, as per the given solution key, option (3) is selected. If we assume option (3) is the intended answer, it provides R_unsold=195, C_unsold=230, Ch_unsold=100. This implies inconsistencies with Figure 2's Caramel bar (50 vs 230) and the total baked (749 vs 765 for Option 3). Given the strict requirement for a correct answer from options, and acknowledging the data inconsistency, option (3) is chosen based on provided solution key.

Question 15

The graph below shows the number of seconds taken by four boys to complete a race. The number of seconds taken is not shown on the scale.
Ali took 5 seconds less than Chee Min to complete the race.
Which of the following is likely to be the number of seconds taken by the fastest boy to complete the race?

Accepted Answer

(2) 21.15. 1.  From the graph, Suresh has the shortest bar, indicating he is the fastest boy. Chee Min has the longest bar.
2.  Visually estimate the relative heights of the bars (in arbitrary units, e.g., using the grid lines):
    Chee Min (CM) ≈ 7.5 units
    Johnathan (J) ≈ 7 units
    Ali (A) ≈ 6 units
    Suresh (S) ≈ 4.5 units
3.  Given: Time(Ali) = Time(Chee Min) - 5 seconds. If time is proportional to bar height, let 'k' be the scaling factor:
    6k = 7.5k - 5
    5 = 1.5k
    k = 5 / 1.5 = 10/3 seconds per unit.
4.  Calculate the estimated time for Suresh (the fastest boy):
    Time(Suresh) = 4.5 units × (10/3 seconds/unit) = (9/2) × (10/3) = 90/6 = 15 seconds.
5.  Since 15 seconds is not one of the options, we look for the option that is 'likely' (closest) to 15 seconds. 
    (1) 8.45 (difference: |15 - 8.45| = 6.55)
    (2) 21.15 (difference: |15 - 21.15| = 6.15)
    (3) 30.00 (difference: |15 - 30.00| = 15)
    (4) 42.52 (difference: |15 - 42.52| = 27.52)
    Option (2) 21.15 is the closest to our calculated estimate of 15 seconds. This implies the graph's visual representation might not be perfectly precise, or the question intends for an approximate choice among the given options.

P4 Mathematics SA2 2023 — Nanyang

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