SECONDARY 2 (GRADE 8) 2024 CONTEST PAPER
NAME: Index Number:
SCHOOL:
INSTRUCTIONS:
1. Please DO NOT OPEN the contest booklet until the Proctor has given permission to
start
2. TIME: 1 hour 30 minutes.
3. There are 25 questions:
Section A: Questions 1 to 15 score 2 points each, no points are deducted for an
unanswered question and 1 point is deducted for the wrong answer.
Section B: Questions 16 to 25 score 4 points each, no points are deducted for an
unanswered or wrong answer.
Section C: Questions 26 to 31 score 5 points each, no points are deducted for an
unanswered or wrong answer.
4. Shade your answers neatly using a 2B lead pencil in the Answer Entry Sheet.
5. PROCTORING: No one may help any student in any way during the contest.
6. No electronic devices capable of storing and displaying visual information are allowed
during the course of the exam.
7. Calculators are allowed into the exam.
8. All students must fill and shade their Name, School and Index Number in the
Answer Entry Sheet and Contest booklet.
9. MINIMUM TIME: Students must stay in the exam hall for at least 1 hour.
10. All students must show detailed workings in the contest booklet and transfer answers
to the Answer Entry Sheet.
11. No exam papers and written notes can be taken out by any contestant.
SMC 2024, Secondary 2 (Grade 8) Challenge
Rough Working
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SMC 2024, Secondary 2 (Grade 8) Challenge
Section (A) (Questions 1 to 15 carry 2 marks each. For each question, 4 options are given.
One of them is the correct answer. Make your choice (A, B, C or D). Shade the correct circle
on the Answer Entry Sheet (AES). The use of calculator is allowed in this section. No marks
will be deducted for wrong answers.)
Question 1
Find the smallest prime number 𝑥𝑥 satisfying the inequality 5 − 2𝑥𝑥 < 3𝑥𝑥 − 72.
A. 13
B. 15
C. 16
D. 17
Question 2
Calculate the value of 𝑘𝑘 if the line 3𝑥𝑥 + 4𝑦𝑦 = 𝑘𝑘 passes through the point (2, −1).
A. −5
B. −2
C. 2
D. 5
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SMC 2024, Secondary 2 (Grade 8) Challenge
Question 3
Factorise the expression 3𝑥𝑥 2 + 7𝑥𝑥 − 20 completely.
A. (3𝑥𝑥 − 5)(𝑥𝑥 + 4)
B. (3𝑥𝑥 − 4)(𝑥𝑥 + 5)
C. (3𝑥𝑥 + 4)(𝑥𝑥 − 5)
D. (3𝑥𝑥 + 5)(𝑥𝑥 − 4)
Question 4
Expand and simplify (3𝑥𝑥 − 2)(2𝑥𝑥 + 5) − (𝑥𝑥 + 3)(𝑥𝑥 − 4).
A. 5𝑥𝑥 2 + 10𝑥𝑥 − 22
B. 5𝑥𝑥 2 + 10𝑥𝑥 + 22
C. 5𝑥𝑥 2 + 12𝑥𝑥 − 2
D. 5𝑥𝑥 2 + 12𝑥𝑥 + 2
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SMC 2024, Secondary 2 (Grade 8) Challenge
Question 5
1
If the roots of the quadratic equation 2𝑥𝑥 2 + 𝑝𝑝𝑝𝑝 + 𝑞𝑞 = 0 are − and −4, find the value of 𝑝𝑝
2
and the value of 𝑞𝑞.
A. 𝑝𝑝 = −9, 𝑞𝑞 = −4
B. 𝑝𝑝 = −9, 𝑞𝑞 = 4
C. 𝑝𝑝 = 9, 𝑞𝑞 = −4
D. 𝑝𝑝 = 9, 𝑞𝑞 = 4
Question 6
A pair of simultaneous equations is given by 3𝑥𝑥 + 2𝑦𝑦 = 17 and 2𝑥𝑥 − 3𝑦𝑦 = −6. Solve the
simultaneous equations.
A. 𝑥𝑥 = 3, 𝑦𝑦 = 4
B. 𝑥𝑥 = 3, 𝑦𝑦 = 13
C. 𝑥𝑥 = 11, 𝑦𝑦 = −8
D. 𝑥𝑥 = 11, 𝑦𝑦 = 13
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SMC 2024, Secondary 2 (Grade 8) Challenge
Question 7
4𝑎𝑎2 −25 𝑎𝑎2 −𝑎𝑎−6
Simplify the expression − completely.
2𝑎𝑎−5 𝑎𝑎+2
A. 𝑎𝑎 − 8
B. 𝑎𝑎 − 3
C. 𝑎𝑎 + 3
D. 𝑎𝑎 + 8
Question 8
The ratio of the length to the breadth of a rectangle is 4: 3 and the perimeter is 56 cm. Find
the area of the rectangle in cm2.
A. 56 cm2
B. 96 cm2
C. 112 cm2
D. 192 cm2
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SMC 2024, Secondary 2 (Grade 8) Challenge
Question 9
The sum of the ages of Alice and Bob is 51 years. Alice is 6 years older than twice of Bob's
age. How old is Alice?
A. 15
B. 21
C. 22.5
D. 36
Question 10
A chemist needs to prepare 600 ml of a 15% saline solution. She has a 25% saline solution
and a 10% saline solution. Find the volume of the 25% saline solution she should use.
A. 200 ml
B. 250 ml
C. 300 ml
D. 400 ml
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SMC 2024, Secondary 2 (Grade 8) Challenge
Question 11
The first three terms of a sequence are 5, 8 and 11.
𝑥𝑥 is a term in the sequence and 𝑥𝑥 is a four-digit number. What is the smallest possible value
of 𝑥𝑥?
A. 1000
B. 1001
C. 1002
D. 1003
Question 12
A student writes down three consecutive odd numbers. All three numbers are positive. The
sum of the squares of three numbers is 371. Find the sum of the three numbers.
A. 19
B. 27
C. 33
D. 123
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SMC 2024, Secondary 2 (Grade 8) Challenge
Question 13
Find the number of sides of a regular polygon if each exterior angle is 24°.
A. 10
B. 15
C. 24
D. 36
Question 14
A right-angled triangle has base 9 m and area 54 m2. Find the length of the hypotenuse.
A. 7.94 cm
B. 10.4 cm
C. 10.8 cm
D. 15 cm
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SMC 2024, Secondary 2 (Grade 8) Challenge
Question 15
The volume of a solid cylinder is 1570 cm³. If the height of the cylinder is 10 cm, find its
approximate surface area in cm2.
A. 89 cm2
B. 628 cm2
C. 3140 cm2
D. 3584 cm2
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SMC 2024, Secondary 2 (Grade 8) Challenge
Section (B) (Questions 16 to 25 carry 4 marks each. Shade your answers in the Answer
Entry Sheet (AES) provided. The use of calculator is allowed in this section. No marks will be
deducted for wrong answers.)
Question 16
A cylindrical tank of height 0.8 m is being filled with water at a rate of 1.5 litres per minute.
The tank is completely filled after 2.1 minutes. Find the base radius of the tank in
centimeters. Give your answer correct to the nearest whole number.
Question 17
The mean of five numbers is 14. If one of the numbers is removed, the mean of the
remaining four numbers becomes 15. Find the removed number.
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SMC 2024, Secondary 2 (Grade 8) Challenge
Question 18
The following frequency table shows the number of books read by students in a month. The
median number of books read is 2. Find the greatest possible value of 𝑥𝑥.
No. of books 0 1 2 3 4 5 6 7 8
Frequency 17 25 20 𝑥𝑥 14 10 5 2 1
Question 19
The area of a park is represented by 80 cm² on a map. If the scale of the map is 1: 25,000,
find the actual area of the park in square kilometers.
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SMC 2024, Secondary 2 (Grade 8) Challenge
Question 20
The number of workers required to complete a task is inversely proportional to the time
taken. If 9 workers can complete the task in 4 days, how many days will it take for 6
workers to complete the same task?
Question 21
The line 𝑦𝑦 = 𝑚𝑚𝑚𝑚 + 18 cuts the positive 𝑥𝑥-axis and the positive 𝑦𝑦-axis and passes through the
point (−5, 𝑝𝑝). It makes an angle of 45° with the 𝑥𝑥-axis. Find the value of 𝑚𝑚 + 𝑝𝑝.
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SMC 2024, Secondary 2 (Grade 8) Challenge
Question 22
In a survey, the number of books read by 10 persons is recorded and the results are shown
in the stem-and-leaf diagram below. Find the greatest possible value of the median of this
data set.
Stem Leaf
0 0 4 5 6
1 0 𝑦𝑦 2𝑦𝑦 − 3
2 3 5 9
Key: 2 | 3 means 23
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SMC 2024, Secondary 2 (Grade 8) Challenge
Question 23
In a bookstore, the numbers of books sold per day in a week are listed below.
85, 𝑎𝑎, 𝑏𝑏, 82, 90, 𝑐𝑐
The mean number of books sold is 84.5, the median is 84.5, and the mode is 85.
Given that 𝑎𝑎 < 𝑏𝑏 < 𝑐𝑐, find the value of 𝑎𝑎 + 2𝑏𝑏 + 3𝑐𝑐.
Question 24
A box contains blue, red, and yellow balls. The total number of balls is more than 100. The
5
probability of choosing a blue ball at random from the box is , and the probability of
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2
choosing a red ball is . Find the minimum possible number of yellow balls in the box.
9
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SMC 2024, Secondary 2 (Grade 8) Challenge
Question 25
Three fair six-sided dice are rolled. The probability that the product of the numbers rolled is
𝑝𝑝 𝑝𝑝
a prime number is , where is a fraction in the simplest form. Find the value of 𝑝𝑝 + 2𝑞𝑞.
𝑞𝑞 𝑞𝑞
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SMC 2024, Secondary 2 (Grade 8) Challenge
Section (C) (Questions 26 to 31 carry 5 marks each. Shade your answers in the Answer
Entry Sheet (AES) provided. The use of calculator is allowed in this section. No marks will be
deducted for wrong answers.)
Question 26
In a right-angled triangle, the size of one of the interior angles is 26° and the length of the
shortest side is 29.3 cm. Find the length of the longest side in centimeters. Give your
answer correct to the nearest whole number.
Question 27
The curved surface area of a cone is 150 cm2. If the slant height of the cone is 10 cm, find
the volume of the cone in cm3. Give your answer correct to the nearest whole number.
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SMC 2024, Secondary 2 (Grade 8) Challenge
Question 28
The greatest possible distance between any two points on the surface of a solid hemisphere
is 17.5 cm. Find the total surface area of the solid hemisphere in cm2. Give your answer
correct to the nearest whole number.
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SMC 2024, Secondary 2 (Grade 8) Challenge
Question 29
In the diagram, 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 and 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 are congruent rectangles. 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 is symmetrical about the
𝑦𝑦-axis. 𝐶𝐶𝐶𝐶𝐶𝐶 is a horizontal line. The coordinates of 𝐵𝐵 are (−4, 7), the coordinates of 𝐷𝐷 are
(𝑝𝑝, 𝑞𝑞) and the 𝑥𝑥-coordinate of 𝐹𝐹 is 9. Find the value of 𝑝𝑝 + 2𝑞𝑞.
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SMC 2024, Secondary 2 (Grade 8) Challenge
Question 30
In the diagram, 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 and 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 are rectangles, 𝑄𝑄 lies on 𝐴𝐴𝐴𝐴 and 𝐷𝐷 lies on 𝑃𝑃𝑃𝑃. 𝐵𝐵𝐵𝐵 =
43 cm, 𝐶𝐶𝐶𝐶 = 82 cm, 𝐶𝐶𝐶𝐶 = 47 cm and 𝑅𝑅𝑅𝑅 = 𝑥𝑥 cm. Find the value of 𝑥𝑥. Give your answer
correct to the nearest whole number.
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SMC 2024, Secondary 2 (Grade 8) Challenge
Question 31
The diagram shows first three rows of an array of numbers. Rectangles consisting of four
numbers are selected as shown. 𝑇𝑇𝑛𝑛 is defined to be the sum of the numbers in the
rectangle, where 𝑛𝑛 is the number in the top left corner. For example, 𝑇𝑇1 = 1 + 2 + 8 + 9 and
𝑇𝑇12 = 12 + 13 + 19 + 20. If 𝑇𝑇𝑘𝑘 is at least 321, find the smallest possible value of 𝑘𝑘.
~~ End of Grade 8 Paper ~~
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SMC 2024, Secondary 2 (Grade 8) Challenge
Rough Working
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SMC 2024, Secondary 2 (Grade 8) Challenge
Rough Working
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SMC 2024, Secondary 2 (Grade 8) Challenge
Rough Working
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