Question 1

In which of the following numbers does the digit 7 stand for 700?

Accepted Answer

(3) 5740. The digit 7 stands for 700 when it is in the hundreds place. In the number 5740, the digit 7 is in the hundreds place.

Question 2

27 358 rounded to the nearest hundred is

Accepted Answer

(4) 27 400. To round 27 358 to the nearest hundred, look at the tens digit, which is 5. Since 5 is 5 or greater, round up the hundreds digit. The hundreds digit 3 becomes 4. So, 27 358 rounded to the nearest hundred is 27 400.

Question 3

In the number 68.59, the digit ____ is in the tenths place.

Accepted Answer

(3) 5. In a decimal number, the tenths place is the first digit immediately to the right of the decimal point. In 68.59, the digit 5 is in the tenths place.

Question 4

Which of the following is not a factor of 56?

Accepted Answer

(1) 6. A factor of a number divides the number exactly without a remainder.
- 56 ÷ 2 = 28 (2 is a factor)
- 56 ÷ 8 = 7 (8 is a factor)
- 56 ÷ 4 = 14 (4 is a factor)
- 56 ÷ 6 = 9 with a remainder of 2 (6 is not a factor).

Question 5

2/9 = ____/45 What is the missing number in the box?

Accepted Answer

(1) 10. To find the missing number, determine the relationship between the denominators. 45 ÷ 9 = 5. So, the denominator 9 was multiplied by 5 to get 45. To keep the fraction equivalent, multiply the numerator 2 by the same factor: 2 × 5 = 10. The missing number is 10.

Question 6

Find the value of 5/12 - 1/4

Accepted Answer

(1) 1/6. To subtract fractions, they must have a common denominator. The least common multiple of 12 and 4 is 12. Convert 1/4 to an equivalent fraction with a denominator of 12: 1/4 = (1 × 3) / (4 × 3) = 3/12. Now subtract: 5/12 - 3/12 = (5-3)/12 = 2/12. Simplify the fraction by dividing both numerator and denominator by 2: 2/12 = 1/6.

Question 7

Express 3/4 as a decimal.

Accepted Answer

(3) 0.75. To express 3/4 as a decimal, divide the numerator by the denominator: 3 ÷ 4 = 0.75.

Question 8

Which of the following is a multiple of both 3 and 7?

Accepted Answer

(4) 42. A number that is a multiple of both 3 and 7 must be divisible by both 3 and 7. This means it must be a multiple of their least common multiple, which is 3 × 7 = 21.
- 10 is not a multiple of 21.
- 27 is not a multiple of 21 (27 ÷ 3 = 9, but 27 ÷ 7 is not an integer).
- 35 is not a multiple of 21 (35 ÷ 7 = 5, but 35 ÷ 3 is not an integer).
- 42 is a multiple of 21 (42 ÷ 21 = 2). Also, 42 ÷ 3 = 14 and 42 ÷ 7 = 6.

Question 9

In the figure below, which angle is greater than a right angle?

Accepted Answer

(2) ∠f. A right angle measures 90 degrees. An angle greater than a right angle is an obtuse angle.
- ∠e, ∠g, and ∠h appear to be acute angles (less than 90 degrees).
- ∠f appears to be an obtuse angle (greater than 90 degrees).

Question 10

Arrange these numbers from the smallest to the greatest. 0.204, 0.402, 0.24, 0.42

Accepted Answer

(1) 0.204, 0.24, 0.402, 0.42. To arrange decimals, compare them digit by digit from left to right. It's helpful to ensure all numbers have the same number of decimal places.
0.204
0.402
0.240 (0.24 can be written as 0.240)
0.420 (0.42 can be written as 0.420)
Comparing the tenths digit: 0.2... are smaller than 0.4...
Among 0.204 and 0.240, 0.204 is smaller.
Among 0.402 and 0.420, 0.402 is smaller.
So, the order from smallest to greatest is 0.204, 0.24, 0.402, 0.42.

Question 11

Julia bought a book for $18.90 and a pencil box for $7.50. She gave the cashier $50. How much change did she get?

Accepted Answer

(2) $23.60. First, calculate the total cost of the items:
Cost of book = $18.90
Cost of pencil box = $7.50
Total cost = $18.90 + $7.50 = $26.40
Next, calculate the change received:
Change = Amount paid - Total cost = $50.00 - $26.40 = $23.60.

Question 12

The table below shows the duration of different activities held at a children's workshop. Rachel started an activity at 09 35 and ended at 11 50. Which activity did she participate in at the workshop?

Accepted Answer

(4) Dino Dash. First, calculate the duration of Rachel's activity:
End time: 11 50
Start time: 09 35
Duration = 11 h 50 min - 09 h 35 min.
Subtracting minutes: 50 - 35 = 15 minutes.
Subtracting hours: 11 - 9 = 2 hours.
So, the activity lasted 2 hours and 15 minutes.
Compare this duration to the table:
- Art Jamming: 2 h 45 min
- Build-A-Bear: 1 h 45 min
- Creative Music: 1 h 15 min
- Dino Dash: 2 h 15 min
Rachel participated in Dino Dash.

Question 13

Henry has some stamps. John has 3 times as many stamps as Henry. They have 2700 stamps altogether. How many stamps does Henry have?

Accepted Answer

(1) 675. Let Henry's stamps be represented by 1 unit.
John has 3 times as many as Henry, so John has 3 units.
Together, they have 1 unit (Henry) + 3 units (John) = 4 units.
These 4 units represent 2700 stamps.
To find 1 unit (Henry's stamps), divide the total by 4: 2700 ÷ 4 = 675 stamps.
Henry has 675 stamps.

Question 14

The table below shows the number of chicken wings eaten by a group of children at a party. What was the total number of chicken wings eaten by the children at the party?

Accepted Answer

(3) 55. To find the total number of chicken wings, multiply the number of wings eaten by each child by the number of children who ate that amount, then sum the results:
- 5 children ate 0 wings: 5 × 0 = 0 wings
- 3 children ate 1 wing: 3 × 1 = 3 wings
- 8 children ate 2 wings: 8 × 2 = 16 wings
- 12 children ate 3 wings: 12 × 3 = 36 wings
Total wings = 0 + 3 + 16 + 36 = 55 wings.

Question 15

Thomas went for a movie which ended at 18 00. The movie lasted 2 h 15 min. What time did the movie start?

Accepted Answer

(1) 15 45. To find the start time, subtract the duration from the end time.
End time: 18 00 (which is 18 hours 00 minutes)
Duration: 2 h 15 min
Subtract 15 minutes from 18 00: (18 h 00 min) - 15 min = 17 h 45 min.
Then subtract 2 hours: (17 h 45 min) - 2 h = 15 h 45 min.
The movie started at 15 45.

Question 16

The length of a bus is 12.1 m when rounded to 1 decimal place. Which of the following is the greatest possible length of the bus?

Accepted Answer

(3) 12.14 m. When a number is rounded to 1 decimal place to get 12.1, the original number must be between 12.05 (inclusive) and 12.15 (exclusive).
- 12.05 m rounds up to 12.1 m.
- 12.09 m rounds up to 12.1 m.
- 12.14 m rounds down to 12.1 m.
- 12.15 m rounds up to 12.2 m.
The greatest possible length from the options that rounds to 12.1 m is 12.14 m.

Question 17

The following figures are made up of identical squares. Which of the following figures is symmetrical?

Accepted Answer

(4) [Figure 4]. A figure is symmetrical if it can be divided by a line of symmetry into two identical mirror-image halves.
Figure (4) has both a horizontal and a vertical line of symmetry (passing through the center of the figure). The other figures do not possess such symmetry.

Question 18

In the figure shown, ABCD is a square. Find ∠y.

Accepted Answer

(1) 16°. In a square, the diagonal bisects the corner angles. Therefore, ∠BDC (the angle formed by the diagonal BD and side DC) is 45°.
From the figure, we can see that ∠BDC is composed of two adjacent angles: ∠y and 29°.
So, ∠y + 29° = 45°.
To find ∠y, subtract 29° from 45°: ∠y = 45° - 29° = 16°.

Question 19

The perimeter of rectangle ABCD is 50 cm. Its breadth is 8 cm. What is the length of rectangle ABCD?

Accepted Answer

(2) 17 cm. The formula for the perimeter of a rectangle is P = 2 × (length + breadth).
Given: Perimeter (P) = 50 cm, Breadth (b) = 8 cm.
50 = 2 × (length + 8)
Divide both sides by 2: 50 ÷ 2 = length + 8
25 = length + 8
Subtract 8 from both sides: length = 25 - 8 = 17 cm.

Question 20

Aaron and Brandon had a total of $567 at first. After Aaron gave Brandon $33, Aaron had twice as much money as Brandon. How much money did Brandon have at first?

Accepted Answer

(1) $156. The total amount of money ($567) remains the same after Aaron gives Brandon $33.
After the transaction:
Let Brandon's money be 1 unit.
Aaron's money is twice Brandon's, so Aaron has 2 units.
Total units = 1 unit + 2 units = 3 units.
These 3 units equal the total money: 3 units = $567.
So, 1 unit = $567 ÷ 3 = $189.
After the transaction, Brandon had $189.
To find how much Brandon had at first, subtract the money Aaron gave him:
Brandon's money at first = Brandon's money after - $33 = $189 - $33 = $156.

P4 Mathematics SA2 2023 — Catholic High

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