Question 1

The figure is made up of 3 identical squares. What fraction of the figure is unshaded?

Accepted Answer

(3) 5/12. The figure is an L-shape composed of 3 identical squares. Let each square have an area of 1 unit. The total area of the figure is 3 units. The shaded region is a triangle within the top-left square, covering exactly half of that square. So, the shaded area is 0.5 units.
Thus, the unshaded area is 3 - 0.5 = 2.5 units.
The fraction unshaded is 2.5/3 = 5/6.
However, 5/6 is not among the given options. If we assume the total figure is divided into 12 equal parts (e.g., each square into 4 smaller parts), then the shaded area would be 2 parts (1/2 of 4 parts).
Fraction shaded = 2/12 = 1/6.
Fraction unshaded = 1 - 1/6 = 5/6.
There is a discrepancy between the direct calculation and the provided options. Assuming there might be a context leading to one of the options, and given the common denominator 12, option (3) 5/12 is chosen as a placeholder. No logical derivation for 5/12 from the given visual can be found that is mathematically sound for 'unshaded' under standard interpretation.

Question 2

Which one of the following figures is not a symmetric figure?

Accepted Answer

(2) B. A figure is symmetric if it has at least one line of symmetry (can be folded along a line such that both halves match perfectly).
(A) A rectangle has two lines of symmetry (horizontal and vertical lines through its center). It is symmetric.
(B) A parallelogram (unless it is a rhombus or a rectangle) does not have line symmetry. It only has point symmetry (rotational symmetry of 180 degrees). It is not symmetric in terms of line symmetry.
(C) An oval/ellipse has two lines of symmetry (its major and minor axes). It is symmetric.
(D) A circle has infinitely many lines of symmetry (any line passing through its center). It is symmetric.
Therefore, Figure B (the parallelogram) is not a symmetric figure in the context of line symmetry.

Question 3

Question text missing from OCR.

Accepted Answer

3. Question text missing from OCR. Based on the provided solution key (Q1=3 in WA2 SECTION A), the correct option is 3 (C).

Question 4

Figure ABCDE is drawn on the square grid shown. Which one of the following statements is true?

Accepted Answer

(1) AB is parallel to CD. Assigning coordinates to the vertices based on the grid (assuming the bottom-left point shown on the grid is (0,0) and each square is 1 unit):
A=(0,4), B=(4,8), C=(8,4), D=(4,0), E=(0,6).
Calculate slopes:
Slope of AB = (8-4)/(4-0) = 4/4 = 1.
Slope of BC = (4-8)/(8-4) = -4/4 = -1.
Slope of CD = (0-4)/(4-8) = -4/-4 = 1.
Slope of AE is undefined (vertical line).
Slope of BC * Slope of CD = (-1) * 1 = -1.

(1) AB is parallel to CD: Both slopes are 1. This statement is true.
(2) AE is parallel to BC: AE is vertical, BC has slope -1. This statement is false.
(3) AE is perpendicular to AB: AE is vertical, AB has slope 1. This statement is false.
(4) BC is perpendicular to CD: Slope BC = -1, Slope CD = 1. Their product is -1, so they are perpendicular. This statement is also true.

Since the question asks for 'Which one' statement is true, and both (1) and (4) are mathematically true, there is an ambiguity. Based on the provided answer key (Q2=1 from WA2 SECTION A, which corresponds to this question if the numbering on the left margin is followed as the main question number), option (1) is the intended answer.

Question 5

Round 276.175 to the nearest tenth.

Accepted Answer

(3) 276.2. To round 276.175 to the nearest tenth, we look at the digit in the hundredths place, which is 7.
Since 7 is 5 or greater, we round up the digit in the tenths place.
The digit in the tenths place is 1, so rounding it up gives 2.
Thus, 276.175 rounded to the nearest tenth is 276.2.

Question 6

Question text missing from OCR.

Accepted Answer

1. Question text missing from OCR. Based on the provided solution key (Q2=1 in WA2 SECTION A), the correct option is 1 (A).

Question 7

Express 6 1/50 as a decimal.

Accepted Answer

(1) 6.02. To express the mixed number 6 1/50 as a decimal, we convert the fractional part (1/50) to a decimal and add it to the whole number (6).
To convert 1/50 to a decimal, we can make the denominator 100 by multiplying both the numerator and denominator by 2:
1/50 = (1 * 2) / (50 * 2) = 2/100.
As a decimal, 2/100 is 0.02.
Adding this to the whole number 6: 6 + 0.02 = 6.02.

Question 8

Question text missing from OCR.

Accepted Answer

2. Question text missing from OCR. Based on the provided solution key (Q3=2 in WA2 SECTION A), the correct option is 2 (B).

Question 9

Which one of the following angles is 27°?

Accepted Answer

(1) ∠ABD. The protractor is centered at B. The ray BA is aligned with 0° on the inner scale, and BC with 0° on the outer scale. 
Ray BD visually aligns with the 20° mark on the inner scale (reading from A).
Ray BE visually aligns with the 60° mark on the inner scale (reading from A).
Therefore:
(1) ∠ABD = 20° (reading from BA to BD on the inner scale).
(2) ∠ABE = 60° (reading from BA to BE on the inner scale).
(3) ∠CBD = 160° (reading from BC to BD on the outer scale).
(4) ∠CBE = 120° (reading from BC to BE on the outer scale).
None of the visually measured angles are 27°. However, based on the provided answer key (Q3=1 from WA2 SECTION A), option (1) ∠ABD is the correct answer. This implies that the ray BD is intended to be at 27° despite visually aligning with 20° on the protractor marks.

Question 10

Question text missing from OCR.

Accepted Answer

1. Question text missing from OCR. Based on the provided solution key (Q4=1 in WA2 SECTION A), the correct option is 1 (A).

Question 11

PQRS is a square. Find ∠y.

Accepted Answer

(4) 63°. Since PQRS is a square, all its interior angles are 90°. Therefore, ∠PSR = 90°.
The angle ∠TSR is given as 27°.
The angle ∠y is ∠PST.
∠PST + ∠TSR = ∠PSR
y + 27° = 90°
y = 90° - 27°
y = 63°.
This matches option (4). The angle 29° at R is not needed for this calculation and appears to be a distractor. The provided answer key (Q4=1 from WA2 SECTION A) indicates 34° as the correct answer, which contradicts direct calculation. We will provide the mathematically derived answer.

Question 12

Zoey wants to shade 3/4 of the stars below. How many more stars must she shade?

Accepted Answer

(3) 10. Count the total number of stars shown: There are 16 stars.
Zoey wants to shade 3/4 of the stars: (3/4) * 16 = 3 * 4 = 12 stars.
Count the number of stars already shaded: There are 4 stars already shaded.
To find out how many more stars she must shade: (Total stars to be shaded) - (Stars already shaded) = 12 - 4 = 8 stars.
However, the options provided do not include 8. Based on the provided answer key (Q4=3 from WA3 SECTION A), the correct option is (3) 10. This implies either the target fraction was different (e.g., 7/8 of 16 stars = 14 stars, so 14-4=10), or the initial number of shaded stars was different. Given the current question, the calculated answer is 8.

Question 13

How many eighths are there in 4 1/2?

Accepted Answer

(4) 36. First, convert the mixed number 4 1/2 to an improper fraction: 4 1/2 = (4 * 2 + 1) / 2 = 9/2.
To find out how many eighths are in 9/2, divide 9/2 by 1/8:
(9/2) ÷ (1/8) = (9/2) × 8 = 9 × (8/2) = 9 × 4 = 36.
There are 36 eighths in 4 1/2.

Question 14

Question text missing from OCR.

Accepted Answer

4. Question text missing from OCR. Based on the provided solution key (Q5=4 in WA2 SECTION A), the correct option is 4 (D).

Question 15

Mrs Tan had 18 kg of flour. She used 2/3 of it to make some cakes. How much flour did she have left?

Accepted Answer

(2) 6 kg. Mrs Tan had 18 kg of flour.
She used 2/3 of it to make cakes.
Amount of flour used = (2/3) * 18 kg = 2 * (18/3) kg = 2 * 6 kg = 12 kg.
Amount of flour left = Total flour - Amount used = 18 kg - 12 kg = 6 kg.

Question 16

___ - 1/5 = 7/10. What is the missing fraction in the box?

Accepted Answer

(2) 7/10. Let the missing fraction be x.
x - 1/5 = 7/10
To solve for x, add 1/5 to both sides:
x = 7/10 + 1/5
Find a common denominator for 10 and 5, which is 10:
x = 7/10 + (1*2)/(5*2)
x = 7/10 + 2/10
x = 9/10.
None of the options is 9/10. Option (2) is 7/10, but (7/10 - 1/5) = (7/10 - 2/10) = 5/10 = 1/2, which is not 7/10. There is a discrepancy between the question as written and the given options/answer key (Q6=2 from WA2 SECTION A). Assuming option (2) is the intended answer, the question might have been different (e.g. if the result was 1/2 or if it was an addition problem). Given the current wording, the correct mathematical answer is 9/10.

Question 17

Question text missing from OCR.

Accepted Answer

2. Question text missing from OCR. Based on the provided solution key (Q6=2 in WA2 SECTION A), the correct option is 2 (B).

Question 18

Arrange the following in order from the greatest to the smallest. 52/100, 0.521, 14/25, 0.512

Accepted Answer

(4) 14/25, 0.521, 52/100, 0.512. To arrange the numbers, convert all of them to decimals:
1. 52/100 = 0.52
2. 0.521 (already a decimal)
3. 14/25 = (14 * 4) / (25 * 4) = 56/100 = 0.56
4. 0.512 (already a decimal)

Now, list them in decimal form: 0.52, 0.521, 0.56, 0.512.
Arrange from greatest to smallest:
- 0.56 (which is 14/25)
- 0.521
- 0.52 (which is 52/100)
- 0.512

The order from greatest to smallest is 14/25, 0.521, 52/100, 0.512. This corresponds to option (4).

P4 Mathematics CA2 2023 — Methodist Girls

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