CTJan27 Online JMSS - Mathematical Reasoning 13052026

The sum of three consecutive odd integers is $S$. Which of the following statements about $S$ must always be true?

The bar chart shows the number of books read by four students in Term 1. According to the chart, which statement is true?

A map has a scale of $1 : 50,000$. The distance on the map between Town A and Town B is $4.5$ cm. What is the actual distance between the towns in kilometres?

A shop advertised a sale giving a 20% discount on all items. After the sale, the shop owner increased the discounted price of a jacket by 20%. The final price is what percentage of the original, pre-sale price?

A rectangle has a length that is 2 cm less than three times its width. If the perimeter of the rectangle is 52 cm, what is its area?

Machine A can fill a container in 3 hours. Machine B can fill the same container in 6 hours. If both machines work together at their constant rates, how long will it take to fill the container?

Let the operation $\diamond$ be defined for two positive numbers $a$ and $b$ as $a \diamond b = \frac{a+b}{ab}$. What is the value of $(2 \diamond 3) \diamond 5$?

Point P has coordinates $(3, -4)$. It is first reflected across the y-axis to get point Q. Then, point Q is rotated 90 degrees counter-clockwise about the origin to get point R. What are the coordinates of point R?

The stacked bar chart shows a company's monthly sales for two product categories. Based on the chart, what was the percentage increase in sales for the 'Clothing' category from January to March?

In a group of 40 students, 25 play basketball and 20 play soccer. If 8 students play neither sport, how many students play both basketball and soccer?

A bag contains 5 red marbles and 3 blue marbles. Two marbles are drawn from the bag at random, one after the other, without replacement. What is the probability that both marbles are red?

A circle is perfectly inscribed inside a square. The radius of the circle is 10 cm. What is the area of the region inside the square but outside the circle? (Use the approximation $\pi \approx 3.14$)

In a sequence of figures made of dots, Figure 1 has 1 dot, Figure 2 has 4 dots, Figure 3 has 9 dots, and Figure 4 has 16 dots. A new pattern is created where the value of each term is the sum of the number of dots in the corresponding figure and the figure number itself. What is the value of the 10th term in this new pattern?

Two cyclists, Amy and Ben, start at the same point and travel in the same direction around a 400m circular track. Amy cycles at a constant speed of 8 m/s and Ben cycles at a constant speed of 6 m/s. How many seconds will it take for Amy to lap Ben for the first time?

Lily has a collection of stamps. She gives half of her stamps to her friend Maya. Then, she buys 12 more stamps. After that, she gives one-third of her new total to her brother, Sam. If Lily is left with 30 stamps, how many stamps did she have originally?

A linear function is defined as $f(x) = ax+b$. If $f(1) = 5$ and $f(3) = 11$, what is the value of $f(5)$?

When a positive integer $N$ is divided by 7, the remainder is 2. What is the remainder when $3N+5$ is divided by 7?

The two pie charts show a city's budget allocation for two different years. Which of the following statements correctly compares the funding between 2020 and 2023?

The chart shows the percentage composition of two metal alloys, A and B. A new alloy, C, is formed by mixing 50 kg of Alloy A with 150 kg of Alloy B. What is the percentage of zinc in Alloy C?

A number is trebled and then decreased by 8. The result is the same as if the number were increased by 12. What is the number?

If $\frac{3x-1}{2} = \frac{x+5}{3}$, what is the value of $x$?

The graph shows a straight line. Which of the following is the equation of this line?

Line $L_1$ passes through the points $(-4, 1)$ and $(2, 4)$. Line $L_2$ is perpendicular to $L_1$ and passes through the origin $(0,0)$. At which point do $L_1$ and $L_2$ intersect?

The area of a rectangle is given by the expression $x^2 + 8x + 15$. If the width of the rectangle is $x+3$, what is its length?

What is the value of $101^2 - 99^2$?

If $a^2 - b^2 = 60$ and $a+b=10$, where $a$ and $b$ are positive numbers, what is the value of $a-2b$?

Which integer coordinate point $(x,y)$ satisfies both $y < -x + 4$ and $y > 2x - 3$?

Which expression is equivalent to $\frac{(4x^3)^2}{2x^0 \times x^2}$?

If $3^{x-1} = 27$ and $4^{y+2} = 16$, what is the value of $x+y$?

Which of the following is the simplified form of $\sqrt{50} + \sqrt{18}$?

A rectangle has an area of exactly 4 square units. Its length is $\sqrt{7}+1$ units. What is its width in simplest form?

In a right-angled triangle, the hypotenuse is 15 cm long and one of the shorter sides is 9 cm long. What is the perimeter of the triangle?

A 13-metre ladder leans against a vertical wall. The base of the ladder is 5 metres from the base of the wall. If the base of the ladder is pulled 7 metres further away from the wall, how far does the top of the ladder slide down the wall?

What is the length of the longest straight line that can be drawn inside a rectangular box with dimensions 4 cm, 5 cm, and 20 cm? (Answer in simplest surd form if necessary).

In the right-angled triangle ABC, the right angle is at B. Side AB = 8 cm and side BC = 15 cm. What is the value of $\sin(C)$?

A support wire is attached to the top of a vertical pole. The wire is 20 metres long and makes an angle of $60^\circ$ with the ground. What is the height of the pole?

An isosceles triangle has two equal sides of length 15 cm and a base of length 18 cm. What is the size of the angle at the apex (the angle between the two equal sides), to the nearest degree?

From the top of a 120-metre-tall lighthouse, the angle of depression to a ship is $45^\circ$. A second ship is in a direct line behind the first ship, and its angle of depression is $30^\circ$. How far apart are the two ships, to the nearest metre?

The sum of the squares of two consecutive positive odd integers is 202. What is the sum of the two integers?

The price of a book is increased by 50%. The new price is then decreased by 50%. What is the final price as a percentage of the original price?

A positive integer $N$ has exactly three factors: 1, $x$, and $N$. Which of the following must be true about $N$?

In a school, the ratio of teachers to students is $1:15$. The ratio of non-teaching staff to teaching staff is $2:5$. If there are 1200 students, what is the number of non-teaching staff?

If $2^x = 5$, what is the value of $2^{x+3}$?

A rectangle's length is 5 cm more than its width, $w$. If the perimeter of the rectangle is $P$, which equation correctly represents the relationship between $P$ and $w$?

Consider the sequence: $3, 6, 11, 18, 27, ...$. What is the next term in this sequence?

Machine A can produce 100 widgets in 40 minutes. Machine B can produce 100 widgets in 20 minutes. If both machines work together, how many minutes will it take them to produce 150 widgets?

At a fruit stand, 3 apples and 2 bananas cost 480 cents. At the same stand, 2 apples and 3 bananas cost 470 cents. What is the cost of one apple and one banana combined?

The shape below is made of a square with side length 10 cm and a semicircle attached to one of its sides. What is the perimeter of the composite shape?

A ladder leans against a vertical wall. The base of the ladder is 1.5 metres from the wall and the top of the ladder reaches 2 metres up the wall. A second ladder, which is twice as long as the first, is placed with its base 2.4 metres from the wall. How high up the wall does the second ladder reach?

A square is rotated 45° clockwise about its centre. What is the shape of the overlapping region between the original square and the rotated square?

Point $A$ is at $(2, 3)$. Point $B$ is the reflection of point $A$ in the y-axis. Point $C$ is the reflection of point $B$ in the x-axis. What are the coordinates of point $C$?

In a right-angled triangle, one of the acute angles is $\theta$. If $\sin(\theta) = \frac{5}{13}$, what is the value of $\cos(\theta)$?

The graph shows the number of members in the school's Coding Club and Chess Club from 2020 to 2024. In which 1-year period did the Chess Club have the greatest percentage increase in members?

A bag contains red and blue marbles. The probability of picking a red marble is $\frac{1}{3}$. After 6 more red marbles are added to the bag, the probability of picking a red marble becomes $\frac{1}{2}$. How many blue marbles are in the bag?

The bar chart shows the results of a test for a class of students. The score for one student, who scored 12 marks, is missing from the chart. If the mean score for the entire class was exactly 6, how many students are in the class?

The pie chart shows the favourite sports of 240 students. How many more students chose Soccer than chose Tennis?

Four friends, A, B, C, and D, are standing in a line. A is not at either end. B is to the left of A (but not necessarily next to A). C is at the first position. D is not next to C. Which of the following is the correct order of the friends from first to fourth?

The graph shows a cyclist's journey from home to a park. What was the cyclist's average speed for the entire journey, including the rest stop?

Completely factorise the quadratic trinomial $6x^2 - 13x + 6$.

In a right-angled triangle PQR, the right angle is at Q. S is a point on the hypotenuse PR such that QS is perpendicular to PR. If the length of PQ is 8 cm and $\angle QPR = 60^\circ$, what is the length of QS?