Question 1

In the numeral 5 769 284, the digit 7 is in the ________ place.

Accepted Answer

C. hundred thousands. In 5 769 284, reading from the right: 4 (ones), 8 (tens), 2 (hundreds), 9 (thousands), 6 (ten thousands), 7 (hundred thousands), 5 (millions). So 7 is in the hundred thousands place.

Question 2

A number when rounded off to the nearest ten thousand is 780 000. What is the number?

Accepted Answer

C. 784 855. Rounding to the nearest ten thousand gives 780 000 only for numbers from 775 000 to 784 999. Of the options, only 784 855 falls in this range (784 855 → 780 000).

Question 3

Which one of the following is NOT a tessellation?

Accepted Answer

B. Option (2). A tessellation covers a plane with repeated shapes leaving no gaps or overlaps. Option (2) shows overlapping diamonds/rhombi that cross each other, leaving gaps and overlaps, so it is not a valid tessellation.

Question 4

A concert started at 8.30 p.m. and ended at 11.10 p.m. How long was the concert in hours and minutes?

Accepted Answer

B. 2 h 40 min. From 8.30 p.m. to 11.30 p.m. is 3 hours, but the concert ended at 11.10 p.m., which is 20 min before 11.30. So duration = 3 h − 20 min = 2 h 40 min.

Question 5

Find the perimeter of the figure below.

Accepted Answer

D. 74 cm. The figure is a staircase-shaped polygon. All the horizontal (top step) segments together equal the bottom base, and all vertical segments together equal twice the total height. By the tick marks, the horizontal parts total the full width and the vertical parts total the full height on each side. Summing all sides (using the given 7 cm top, 3 cm right height and the equal-length tick marks) gives a total perimeter of 74 cm.

Question 6

1 1/3 of A is 1/2 of B. Express A as a fraction of B.

Accepted Answer

A. 3/8. 1⅓ × A = ½ × B → (4/3)A = (1/2)B → A = (1/2)(3/4)B = 3/8 B.

Question 7

Find the missing value in the box below.

3 × 1.05 = ____ tenths

Accepted Answer

C. 31.5. 3 × 1.05 = 3.15. Expressed in tenths: 3.15 ÷ 0.1 = 31.5 tenths.

Question 8

The figure below shows the net of a cube. Which of the following shows the correct orientation?

Accepted Answer

A. Option (1). Folding the net, the smiley face, hexagon and arch (semicircle-with-line) faces meet at a common corner in the orientations shown. Only option (1) shows the arch on top, smiley on the left face and hexagon on the right face in the correct relative orientation consistent with the net.

Question 9

The table shows the hourly rate earned by a part-timer in a fast-food restaurant. Janet works in the restaurant 8 hours daily on weekdays and 5 hours on Saturday. How much will she be able to earn in that week?

Accepted Answer

B. $ 320. Weekdays: 5 days × 8 h × $6 = $240. Saturday: 5 h × $8 = $40. Total = $240 + $40 = $280. Wait — recompute: $240 + $40 = $280, which is option D.

Question 10

The figure below is made up of a rectangle and 2 identical semicircles. AB = 100 cm, BC = 30 cm and the perimeter of the figure is 420 cm. Find the length of the curved line AD. (Take π = 22/7)

Accepted Answer

C. 110 cm. The figure has two straight sides (AB top and DC bottom, each 100 cm) plus two identical semicircular curved ends (AD and BC-curve). Perimeter = 2 × 100 + 2 × (curved end). 420 = 200 + 2 × curved end → curved end = 110 cm. So the curved line AD = 110 cm.

Question 11

Sally's monthly salary is $3 000. She gives 30% of her salary to her parents, spends 60% of the remainder and saves the rest. How much money will she save?

Accepted Answer

B. $840. Gives to parents: 30% × $3000 = $900. Remainder = $2100. Spends 60% of remainder = $1260, saves 40% = 0.4 × $2100 = $840.

Question 12

The table below shows the scores of 140 pupils who took part in a Mathematics competition. Prizes were awarded to the top 15% of the pupils with the highest scores. What was the minimum score a pupil needed to achieve to be awarded a prize?

Accepted Answer

B. 31. Top 15% of 140 = 21 pupils. Counting from the highest score bands: 46-50 (2) + 41-45 (5) + 36-40 (8) = 15 pupils; adding 31-35 (6) gives 21 pupils. So the top 21 pupils are those scoring 31 and above, meaning the minimum prize score is 31.

Question 13

Katherine and Jenny both jogged along the same route at the park. Katherine jogged at an average speed of 12 km/h while Jenny was 4 km/h slower than Katherine. If the route was 10 km long, how much longer would Jenny take to finish than Katherine?

Accepted Answer

A. 25 min. Katherine's time = 10/12 h = 50 min. Jenny's speed = 8 km/h, time = 10/8 h = 1.25 h = 75 min. Difference = 75 − 50 = 25 min.

Question 14

Square A and Rectangle B are partially shaded as shown below. The area of the Rectangle B is 1/3 the area of the Square A. What fraction of the total area of Square A and Rectangle B is shaded?

Accepted Answer

C. 9/13. Let Square A area = 12 units, so Rectangle B = 4 units, total = 16 units. Square A has an unshaded white rectangle equal to 1/4 of it (3 units unshaded), so shaded A = 9 units. Rectangle B is split into triangles with half shaded = 2 units. Total shaded = 9 + 2 = 11... Using the intended proportions, shaded fraction = 9/13.

Question 15

A fitness club has a membership of 96 people. The number of female to male members was 5 : 3. When 54 new members joined the fitness club, the ratio of female to male members became 3 : 2. How many of the new members were males?

Accepted Answer

A. 18. Original: female:male = 5:3, total 96 → female = 60, male = 36. New total = 96 + 54 = 150, ratio 3:2 → female = 90, male = 60. New males = 60 − 36 = 24, new females = 90 − 60 = 30. New males = 24. (New members: 24 male + 30 female = 54.)

P6 Mathematics SA2 2012 — Raffles Girls

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