T EST

SMC 2025 Grade 4 Practice Paper 2

QUESTIONS

S EC TI O NS

1. Section A : MCQs - 15 Questions

2. Section B : Integer Type Open Ended Questions - 10 Questions

3. Section C : Integer Type Open Ended Questions - 6 Questions

Section 1 : Section A : MCQs - 15 Questions

S EC TI O N I N ST R UC T IO NS

MCQs

1 What is the value of the following sum?

2814 + 3700 + 4609 + 8211 + 9106 − 22900

4450

4540

5540

5450

None of the above

Correct: +2 · Incorrect: -1

2 If Gear A rotates anti-clockwise, which of the following options is true?

SMC 2025 Grade 4 Practice Paper 2 · Section A : MCQs · Questions Page 1 of 25

 Gears A and C rotate in opposite directions

Four gears rotate in the same direction

Four gears rotate in the same direction

Gear C rotates anti-clockwise

None of the above

Correct: +2 · Incorrect: -1

3 In the fictional ”Odd Island”, all the numbers contain only odd digits. The order of the counting numbers is
the following

1, 3, 5, 7, …, 19, 31, 33, …

What is the 55th counting number in the island?

99

101

197

199

SMC 2025 Grade 4 Practice Paper 2 · Section A : MCQs · Questions Page 2 of 25

 None of the above

Correct: +2 · Incorrect: -1

4 How many four-digit numbers are there such that if we add 2020 to each of the numbers, the results are still
four-digit numbers?

7020

6880

6980

7880

None of the above

Correct: +2 · Incorrect: -1

5 In the grid below, the first row and the first column have been filled up with numbers from 10 to 19. The
empty cells will be filled up with numbers by adding the topmost number in the column with the leftmost
number in the row. (For example, 𝐴 = 17 + 14 = 31 and 𝐵 = 19 + 18 = 37.) After filling up all the empty cells,
what will the sum of all the numbers in the grid be?

745

725

145

SMC 2025 Grade 4 Practice Paper 2 · Section A : MCQs · Questions Page 3 of 25

 135

None of the above

Correct: +2 · Incorrect: -1

6 Each of the numbers 138 and 243 has digits whose product is 24. How many threedigit numbers are there
whose digits have a product of 24?

12

18

None of the above

Correct: +2 · Incorrect: -1

7 The month of December of a certain calendar year has exactly 5 Saturdays and 4 Sundays. On which day of
the week does the first day of December fall?

Monday

Tuesday

Wednesday

Thursday

SMC 2025 Grade 4 Practice Paper 2 · Section A : MCQs · Questions Page 4 of 25

 Correct: +2 · Incorrect: -1

8 What is the missing number in the following pattern?

10

16

20

None of the above

Correct: +2 · Incorrect: -1

9 How many numbers are there in the list below?

25

26

38

SMC 2025 Grade 4 Practice Paper 2 · Section A : MCQs · Questions Page 5 of 25

 37

None of the above

Correct: +2 · Incorrect: -1

10 The five-digit number 25M48 is a multiple of 9. What digit does M represent?

None of the above

Correct: +2 · Incorrect: -1

11 In the figure below, 𝐴𝐵𝐶𝐷 and 𝑃𝑄𝑅𝑆 are rectangles. 𝐴𝐷 = 𝑃𝑆 = 6 cm and 𝐴𝐵 = 𝑃𝑄 = 10 cm. Compare the
areas of the shaded region of rectangle 𝐴𝐵𝐶𝐷 and 𝑃𝑄𝑅𝑆. Which of the following statements below is true?

The area of the shaded region of ABCD is equal to the area of the shaded region of PQRS.

The area of the shaded region of ABCD is greater than the area of the shaded region of PQRS.

SMC 2025 Grade 4 Practice Paper 2 · Section A : MCQs · Questions Page 6 of 25

 The area of the shaded region of ABCD is less than the area of the shaded region of PQRS

Cannot be determined

None of the above

Correct: +2 · Incorrect: -1

12 The time now is 16:56 and Archie’s 12-hour digital clock shows 4:56 P.M. He realizes that the digits of his
digital clock are in increasing consecutive order. When the time is 12:17 P.M. or A.M., the clock will show
12:17 P.M. or A.M. respectively. How many minutes later will Archie’s clock show digits again in increasing
consecutive order? A

507 minutes

458 minutes

467 minutes

407 minutes

None of the above

Correct: +2 · Incorrect: -1

13 Ali has 80 candles. He lights 1 candle every day. He can recycle the wax of four used candles to form a new
candle. After how many days will he need to buy more candles?

80

130

132

SMC 2025 Grade 4 Practice Paper 2 · Section A : MCQs · Questions Page 7 of 25

 1323

None of the above

Correct: +2 · Incorrect: -1

14 Among George, Helen and Irene, only one of them watched the movie ‘Avengers’. When they were asked
about the movie, they gave the following replies.

George said: Helen watched it.

Helen said: I have not watched it.

Irene said: I have not watched it.

If two of them lied, who watched the movie?

George

Helen

Irene

Impossible to determine

None of the above

Correct: +2 · Incorrect: -1

15 Which one of the following options is a missing piece of the cube on the right?

SMC 2025 Grade 4 Practice Paper 2 · Section A : MCQs · Questions Page 8 of 25

 Correct: +2 · Incorrect: -1

Section 2 : Section B : Integer Type Open Ended Questions - 10 Questions

S EC TI O N I N ST R UC T IO NS

Integer Type Open Ended Questions

16 What is the value of 95 × 37 + 95 × 42 + 21 × 95?

Correct: +4

17 How many triangles are there in the figure below?

SMC 2025 Grade 4 Practice Paper 2 · Section B : Integer Type Open Ended Questions ·
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Questions
 Correct: +4

18 I am thinking of a number. If the number is added to 8, the sum is multiplied by 8, 8 is subtracted from the
product, and the difference is divided by 8, it yields a quotient of 80. What is this number?

Correct: +4

19 The graph below shows the number of guests who visited the National Museum during the first six months
of 2019. All the horizontal lines are equally spaced. If the total number of guests who visited in January and
May were 200 fewer than those in June, how many people visited the museum in total during the six
months?

Correct: +4

20 The following square is divided into four rectangles as shown. The sum of the perimeters of the four
rectangles is 72 cm. Find the side length (in cm) of the square.

SMC 2025 Grade 4 Practice Paper 2 · Section B : Integer Type Open Ended Questions ·
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Questions
 Correct: +4

21 One wants to colour the circles in the figure below such that any pair of circles connected by a line segment
shares different colours. What is the least number of colours needed for the colouring?

Correct: +4

22 Ronald McDonald, a farmer, has chickens, goats and cows in his farm. He has 40 chickens and goats
combined. He notices that 3 times the number of his chickens is 5 times the number of his cows. On the
other hand, 2 times the number of goats is 10 times the number of his cows. Help Ronald McDonald
determine the total number of animal feet in his farm.

Correct: +4

23

Correct: +4

24 A printer printed 237 digits for all the page numbers of a storybook. How many pages are there in the
storybook?

Correct: +4

25 In the following, all the different letters stand for different digits.

Find the value of the 4-digit number DBEC.

Correct: +4

Section 3 : Section C : Integer Type Open Ended Questions - 6 Questions

S EC TI O N I N ST R UC T IO NS

Integer Type Open Ended Questions

SMC 2025 Grade 4 Practice Paper 2 · Section C : Integer Type Open Ended Questions ·
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Questions
26 What is the value of the digit ‘6’ in the numeral 36 574?

Correct: +6

27 A number when rounded to the nearest 100 is 8000.

What is the greatest possible number?

Correct: +6

28 A van can transport 8 passengers.

How many passengers can 240 vans transport?

Correct: +6

29 The figure below is made up of 2 squares of different sizes.

AG is 8 cm and DE is 6 cm. What is the length of AD?

Give your answer in cm.

Correct: +6

30 Look at the figure below.

SMC 2025 Grade 4 Practice Paper 2 · Section C : Integer Type Open Ended Questions ·
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Questions
Which one of the following options will form a symmetric figure with the above?

Correct: +6

31 Rectangle PQRS is folded to form the figure below.

y is three times of  x.

Find  x

SMC 2025 Grade 4 Practice Paper 2 · Section C : Integer Type Open Ended Questions ·
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Questions
 Correct: +6

SMC 2025 Grade 4 Practice Paper 2 · Section C : Integer Type Open Ended Questions ·
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Questions
 TEST

SMC 2025 Grade 4 Practice Paper 2

ANSWERS

SECTIONS

1. Section A : MCQs - 15 Questions

2. Section B : Integer Type Open Ended Questions - 10 Questions

3. Section C : Integer Type Open Ended Questions - 6 Questions

Section 1 : Section A : MCQs - 15 Questions

1 5540

2 Gear C rotates anti-clockwise

3 199

4 6980

5 745

6 None of the above

7 Thursday

8 16

9 38

10 8

SMC 2025 Grade 4 Practice Paper 2 · Section A : MCQs · Answers Page 15 of 25

 11 The area of the shaded region of ABCD is equal to the area of the shaded region of PQRS.

12 458 minutes

13 None of the above

14 Irene

15

Section 2 : Section B : Integer Type Open Ended Questions - 10 Questions

16 9500

17 42

18 73

19 2000

20 9

21 2

22 164

23 306

24 115

25 9480

Section 3 : Section C : Integer Type Open Ended Questions - 6 Questions

26 6000

27 8049

SMC 2025 Grade 4 Practice Paper 2 · Section B : Integer Type Open Ended Questions · Answers Page 16 of 25
 28 1920

29 14

30 1

31 18

SMC 2025 Grade 4 Practice Paper 2 · Section C : Integer Type Open Ended Questions · Answers Page 17 of 25
 TEST

SMC 2025 Grade 4 Practice Paper 2

SOLUTIONS

SECTIONS

1. Section A : MCQs - 15 Questions

2. Section B : Integer Type Open Ended Questions - 10 Questions

3. Section C : Integer Type Open Ended Questions - 6 Questions

Section 1 : Section A : MCQs - 15 Questions

2814 + 9106 = 11920

4609 + 8211 = 12820

11920 + 12820 + 3700 − 22900 = 𝟓𝟓𝟒𝟎

If gear A rotates anti-clockwise, gear B will rotate clockwise, gear C will rotate anticlockwise, gear D will
rotate clockwise, gear E will rotate anti-clockwise, and gear F will rotate clockwise. The only statement
that fits our observations is the statement in option D.

The first 55 counting numbers are:

1, 3, 5, 7, 9,

11, 13, 15, 17, 19,

31, 33, 35, 37, 39,

51, 53, 55, 57, 59,

71, 73, 75, 77, 79,

91, 93, 95, 97, 99,

111, … … , 119,

131, … … , 139,

151, … … , 159

SMC 2025 Grade 4 Practice Paper 2 · Section A : MCQs · Solutions Page 18 of 25

171, … … , 179

191, … … , 199

Thus, the 55th counting number is 199.

The largest four-digit number is 9999.

Hence, the largest possible four-digit number, which will still be a four-digit number after being added to
2020, is 9999 − 2020 = 7979.

The smallest possible such four-digit number is 1000.

From 1000 to 7979, there are 7979 − 1000 + 1 = 𝟔𝟗𝟖𝟎 numbers.

Write down the expressions of the remaining numbers in the grid, to facilitate calculation:

ince each column is added 5 times and each row number added 6 times, the sum of all the numbers equals
to:

10 + 5 × 11 + 6 × 12 + 5 × 13 + 6 × 14 + 5 × 15 + 6 × 16 + 5 × 17 + 6 × 18 + 5 × 19

= 10 + 5 × (11 + 13 + 15 + 17 + 19) + 6 × (12 + 14 + 16 + 18)

= 10 + 5 × 75 + 6 × 60

= 10 + 375 + 360

= 𝟕𝟒𝟓

When the hundreds place is 1:

There are 4 numbers whose product of digits is 24: 138, 146, 164, 183.

Similarly, we construct the following table.

SMC 2025 Grade 4 Practice Paper 2 · Section C : Integer Type Open Ended Questions ·
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Solutions
Thus, there are 4 × 4 + 3 + 2 = 𝟐𝟏 three-digit numbers whose digits have a product of 24.

Since there are exactly 5 Saturdays and 4 Sunday, then there is no Sunday after 5th Saturday which
means that the last Saturday is December 31st. Thus, the first day of this December falls on Thursday.

Observe that the number 1 is inscribed in a rectangle with 4 sides.

The pattern would be: (Number of sides of the shape a number is inscribed in − number) squared.

For example, the number 6 is inscribed in an 8-sided shape, so (8 − 6)2 = 4

Hence, the missing number is (5 − 1)2 = 16

Since all fractions now have the same denominator, then counting them is the same as counting the
number on the numerators, or the number of numbers in the list: 19, 21, 23, … 93. It can be counted using
SMC 2025 Grade 4 Practice Paper 2 · Section C : Integer Type Open Ended Questions ·
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Solutions
the formula:

(𝑙𝑎𝑠𝑡 𝑛𝑢𝑚𝑏𝑒𝑟 − 𝑓𝑖𝑟𝑠𝑡 𝑛𝑢𝑚𝑏𝑒𝑟) ÷ 𝑐𝑜𝑚𝑚𝑜𝑛 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 + 1

Thus, there are (93 − 19) ÷ 2 + 1 = 𝟑𝟖 numbers in the list.

10

According to the Divisibility Rule of 9, the sum of digits: 2 + 5 + M + 4 + 8 = 19 + M is a multiple of 9.

The next multiple of 9 greater than 19 is 27.

Hence M must be 27 − 19 = 𝟖.

11

In both ABCD and PQRS, their shaded regions and unshaded regions have the same base and the same
height. In each of the rectangles ABCD and PQRS, the area of shaded regions and area of unshaded
regions are the same. Hence, area of shaded regions in both ABCD and PQRS is half the area of the whole
rectangle i.e., they are the same.

12

Since 5.67 P.M. is not an actual time, he next time after 4.56 P.M. when the digits of

his digital clock are in increasing consecutive order is 12.34 A.M.

12.34 A.M. is 7 hours 38 minutes or 7 × 60 + 38 = 𝟒𝟓𝟖 minutes after 4.56 P.M.

13

80 candles take 80 days to be used up, and will give 80 pieces of wax to form 20 new candles.

20 candles take another 20 days to be used up, and will give 20 pieces of wax to form 5 new candles.

5 candles take another 5 days to be used up, and 4 out of the 5 pieces of wax can be used to form one last
candle.

One candle will be used up in 1 day.

Total number of days = 80 + 20 + 5 + 1 = 106

14

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Solutions
15

The missing piece must have 3 faces shown below to match the cube.

Only options B and E have all the 3 faces, but Option B has the correct orientation.

Section 2 : Section B : Integer Type Open Ended Questions - 10 Questions

16

95 × 37 + 95 × 42 + 21 × 95

= 95 × (37 + 42 + 21)

= 95 × 100

SMC 2025 Grade 4 Practice Paper 2 · Section C : Integer Type Open Ended Questions ·
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Solutions
= 𝟗𝟓𝟎𝟎

17

18

Working backwards:

80 × 8 = 640

640 + 8 = 648

648 ÷ 8 = 81

81 − 8 = 𝟕𝟑

19

According to the diagram, there are 2 units of guests in January, 4 units in February, 5 units in March, 3
units in April, 1 unit in May and 5 units in June. In total, there are 2 + 4 + 5 + 3 + 1 + 5 = 20 units Total
number of guests who visited the museum in January and May were 200 fewer than those in June:

There are altogether 2 + 1 = 3 units in January and May while 5 units in June.

Thus, 5 − 3 = 2 𝑢𝑛𝑖𝑡𝑠 = 200

1 𝑢𝑛𝑖𝑡 = 100

Total number of guests during the six months

= 20 × 100

= 𝟐𝟎𝟎𝟎

SMC 2025 Grade 4 Practice Paper 2 · Section C : Integer Type Open Ended Questions ·
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Solutions
Note that the vertical side of the square is counted 4 times in vertical side lengths of the 4 rectangles.
Similarly, the horizontal side of the square is also counted 4 times in horizontal sides lengths of the 4
rectangles. Thus, the sum of the perimeters of the four rectangles = 8 x length of square = 72 cm and the
length of the square = 9 cm.

21

Let us colour all the circles with 2 colours, say yellow (Y) and green (G).

The diagram below shows one possible way to colour all the circles with just yellow and green:

22

Let the number of chickens Ronald McDonald has be 5 units.

Then the number of cows he has = 5 units × 3 ÷ 5 = 3 units.

Then the number of goats he has = 3 units × 10 ÷ 2 = 15 units.

Number of chickens and goats = (5 + 15) units = 20 units = 40

Thus, 1 unit = 2, the number of chickens is 5 × 2 = 10 , the number of cows is 3 × 2 = 6, and the number of
goats is 15 × 2 = 30

Since a chicken has 2 feet, each cow and goat has 4 feet, then the total number of feet is 10 × 2 + 6 × 4 +
30 × 4 = 164.

23

Let the number of candies Kate bought be 3 𝑢𝑛𝑖𝑡𝑠.

3 − 1 = 2 𝑢𝑛𝑖𝑡𝑠

2 𝑢𝑛𝑖𝑡𝑠 = 26 × 7 + 22 = 204

1 𝑢𝑛𝑖𝑡 = 204 ÷ 2 = 102

𝑇𝑜𝑡𝑎𝑙 = 3 𝑢𝑛𝑖𝑡𝑠 = 102 × 3 = 𝟑𝟎𝟔

SMC 2025 Grade 4 Practice Paper 2 · Section C : Integer Type Open Ended Questions ·
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Solutions
24

Page 1 to Page 9: 9 digits Pages 10 to 99: 90 × 2 = 180 digits (99 − 10 + 1 = 90 2-digit numbers) The
remaining pages have 237 − 9 − 180 = 48 digits 48 digits belong to the 3-digit numbers, starting from
Page 100.

48 ÷ 3 = 16 99 + 16 = 115

The book has 115 pages.

25

A four-digit number plus a four-digit number can only result in a five-digit number that starts with 1.
Hence A must be 1.

Since A is 1, D can only be 8 or 9. If D=8, then C = 0, E = D – A = 7 which is impossible since the last digit of
B + B must be even.

Thus D = 9, C = 0, E = D – F = 8, 8 = B + B or B = 4 and DBEC is 9480.

Section 3 : Section C : Integer Type Open Ended Questions - 6 Questions

26

27

28

29

30

31

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Solutions