CTJan27 Online JMSS - Mathematical Reasoning 18032026

A bookstore orders 15 boxes of books. Each box contains 24 books. The total cost for the order is 5400 dollars. The store sells each book for 20 dollars. If they sell all the books except for 18 that were damaged, what is their total profit?

Sarah has 240 dollars. She spends $\frac{1}{4}$ of it on a concert ticket. Then she spends 45 dollars on a t-shirt. With the remaining money, she buys 3 identical books. How much did each book cost?

A tank contains 600 litres of water. $\frac{1}{5}$ of the water is used for gardening. Then, 25% of the remaining water is used for washing a car. How much water is left in the tank?

In a school of 800 students, 0.35 of the students play soccer. 40% of the students play basketball. The remaining students play tennis. If $\frac{1}{4}$ of the tennis players are girls, how many boys play tennis?

A jacket is sold for 120 dollars after a 20% discount. The shopkeeper still made a 25% profit on the cost price. What was the original cost price of the jacket?

A farmer buys 500 apples for 200 dollars. 10% of the apples were rotten and had to be thrown away. He sold the remaining apples in bags of 5, with each bag selling for 3 dollars. What is his percentage profit?

A cyclist travels from Town A to Town B, a distance of 90 km. For the first third of the journey, the cyclist travels at a speed of 30 km/h. For the remaining two-thirds of the journey, the cyclist travels at 20 km/h. What is the total time taken for the journey?

Tom leaves his house at 8:00 AM, cycling at a constant speed of 15 km/h. His brother, Jerry, leaves the same house at 8:30 AM, cycling along the same route at a constant speed of 20 km/h. At what time will Jerry catch up to Tom?

A rectangular water tank measures 2 metres by 1.5 metres by 1 metre. The tank is full of water. If the water is used to fill cylindrical bottles each with a capacity of 750 millilitres, how many bottles can be filled completely? (Note: $1 \text{ m}^3 = 1000 \text{ litres}$ and $1 \text{ litre} = 1000 \text{ mL}$).

A rectangular room has a floor area of 12 square metres. If you want to tile this floor with square tiles that are 20 cm by 20 cm, how many tiles will you need?

A composite shape is formed by a rectangle and a semicircle. The rectangle has a length of 10 cm and a width of 14 cm. The semicircle is attached to one of the 14 cm sides. What is the perimeter of the entire shape? (Use $\pi \approx \frac{22}{7}$)

A large rectangular garden measures 20 m by 15 m. A smaller rectangular swimming pool measuring 8 m by 5 m is built in the center of the garden. The rest of the area is covered with grass. What is the area of the grass?

The ratio of red marbles to blue marbles in a bag is 3:5. After 12 more red marbles are added to the bag, the ratio becomes 3:4. How many blue marbles are in the bag?

A mixture of juice and water is in the ratio 7:2. The total volume of the mixture is 45 litres. How much water must be added to the mixture to make the ratio of juice to water 1:1?

A supermarket sells coffee in two sizes. A small jar of 150g costs 7.50 dollars. A large jar of 400g costs 18.00 dollars. Which is the better buy and by how much per 100g?

A single chocolate bar costs 2.40 dollars. Three special offers are available.

• Offer A: 25% off the price of a single bar.
• Offer B: Buy two, get a third one free.
• Offer C: A pack of 4 bars for 7.20 dollars. Which offer gives the lowest price per chocolate bar?

A number is multiplied by 4, then 15 is subtracted from the result. The new result is then divided by 3. The final answer is 25. What was the original number?

On Monday, a fish tank was half full. On Tuesday, the owner added 6 litres of water. On Wednesday, one-third of the total water in the tank was removed. If the tank now contains 12 litres, what is the total capacity of the tank?

The average score of five tests is 88. After the sixth test is taken, the average score for all six tests becomes 90. What was the score on the sixth test?

The average height of 24 students in a class is 150 cm. When the teacher's height is included, the average height of the 25 people becomes 152 cm. What is the teacher's height?

Below is a partial bus timetable. A person arrives at the Market St stop at 09:35. They take the next available bus to the Station. How long is their total journey time, including waiting time?

A train operates according to the scheduled departure times shown 

below.

The travel time between any two stations is always the same. However, due to ongoing track maintenance, any journey that commences after 

14:00 has its total travel time increased by 7 minutes. A passenger is travelling from Eastwood to an office building, which is a 5-minute walk from Southpine station. If their appointment at the office is at 16:30, what is the absolute latest time they must depart from Eastwood station?

In 4 years, Maria will be twice as old as she was 6 years ago. How old is Maria now?

The sum of the current ages of a father and his son is 60 years. Six years ago, the father was three times as old as his son was then. What will be the father's age in 5 years?

What is the next number in the sequence: 3, 7, 15, 31, 63, ...?

A pattern is made using matchsticks to form a row of connected squares. The first figure has 1 square and uses 4 matchsticks. The second figure has 2 squares and uses 7 matchsticks. The third figure has 3 squares and uses 10 matchsticks. How many matchsticks are needed for the 20th figure?

Alex invests 4000 dollars in a savings account that pays simple interest at a rate of 5% per annum. How much money will be in the account in total after 3 years?

Sarah has 2500 dollars and wants to earn 500 dollars in simple interest. If her bank offers an interest rate of 4% per year, how many years will she need to keep the money in the account?

A farm has only chickens and cows. In a count of all the animals, there are a total of 50 heads and 140 legs. How many chickens and how many cows are on the farm?

The cost for two adults and three children to watch a movie is 54 dollars. The cost for three adults and one child is 53 dollars. What is the total cost for one adult and one child?

The graph shows a cyclist's journey. The cyclist travels away from home for 30 minutes covering 12 km, rests for 30 minutes, and then travels back to the start in 60 minutes. What was the cyclist's average speed for the entire journey, including the rest period?

The speed-time graph below represents a car's motion. It accelerates uniformly from rest to 20 m/s in 10 seconds, then travels at a constant speed for 20 seconds, and finally decelerates uniformly to rest in 5 seconds. What is the total distance travelled by the car?

A line $L_1$ has the equation $2y - 4x = 6$. A second line, $L_2$, is perpendicular to $L_1$ and passes through the point $(4, 1)$. What is the equation of $L_2$?

A straight line passes through the points $(-2, 10)$ and $(4, -2)$. What is the y-intercept of this line?

Simplify the expression $\sqrt{50} - \sqrt{18} + \sqrt{72}$ completely.

Expand and simplify $(\sqrt{7} - 2\sqrt{3})^2$.

Rationalise the denominator and simplify the expression $\frac{10}{3 - \sqrt{2}}$.

Simplify $\frac{\sqrt{5}}{\sqrt{5} + \sqrt{3}}$ by rationalising the denominator.

The solutions to the quadratic equation $2x^2 - 5x - 3 = 0$ are the x-intercepts of the parabola shown. What are the solutions?

What are the coordinates of the vertex of the parabola with the equation $y = x^2 + 6x + 5$?

A ladder of length 5 metres leans against a vertical wall. The base of the ladder is 2 metres from the base of the wall. What is the angle the ladder makes with the ground, correct to the nearest degree?

An isosceles trapezium has parallel sides of length 10 cm and 20 cm. The sloping non-parallel sides are each 13 cm long. What is the perpendicular height of the trapezium?

A circle with radius 5 cm is perfectly inscribed within a square. A point P is at the centre of the circle, and a point Q is at one of the vertices of the square. What is the exact distance PQ?

A rectangular prism has side lengths of 3 cm, 4 cm, and 12 cm. What is the length of the longest diagonal that can be drawn inside the prism, connecting opposite vertices?

Three triangles have the following side lengths:

• Triangle 1: 9 cm, 12 cm, 15 cm
• Triangle 2: 7 cm, 24 cm, 25 cm
• Triangle 3: 8 cm, 15 cm, 18 cm

Using the converse of Pythagoras' theorem, which of these triangles are right-angled?

The distance-time graph shows a car's journey from home. What was the car's speed during the first 2 hours of the journey?

A parabola has x-intercepts at $x=-4$ and $x=2$, and passes through the point $(0, -8)$ which is its y-intercept. Which of the following is the correct equation for this parabola?

In a right-angled triangle $ABC$, the right angle is at vertex $B$. If the length of side $AB$ is 8 units and the length of side $BC$ is 15 units, what is the value of $\sin(C)$?

In a right-angled triangle $PQR$, the right angle is at $Q$. The hypotenuse $PR$ has a length of 25, and side $PQ$ has a length of 7. What is the value of $\tan(R)$?

In a right-angled triangle $LMN$, the right angle is at $M$. If $\tan(L) = \frac{20}{21}$, what is the value of $\cos(L)$?

The line graph tracks the strength of a signal over distance. At a certain point, an antenna forms a right-angled triangle with the ground. The angle of elevation, $\theta$, from a point on the ground to the top of the antenna has $\tan(\theta) = \frac{33}{56}$. What is the value of $\sin(\theta)$?