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- Given the equation 20π₯ β [4(π¦ β 3π₯) + 9π₯] + 5π₯ = π(π π₯ + π‘π¦), π > 3 and π, π , and π‘ are integers, find the sum of π, π , and π‘.
- Find the smallest possible integer π such that 120π is a perfect square.
- Consider a sequence where the π-π‘β term is given by $π_π = (3π + 2)^3$. Find the difference between the 6th and 5th term of the sequence.
- A sum of money was divided among Alice, Bob, and Carol in the ratio of 7:3:10. If Bob received $\$$80 less than Carol, find the average amount of money received per person, in dollars. Round off the answer to the nearest integer.
- Emily, travelling at an average speed of 5 km/h, takes 40 minutes to walk to the library. If she left her house for the library at 08:30 AM, calculate the average speed, in m/s, at which she must travel if she is to reach the library by 09:00 AM. Round off the answer to the nearest integer.
- Find the gradient of the graph shown. Round off the answer to the nearest integer.
- Given that β5 β€ π₯ β€ 3, 3 β€ π¦ < 15 and 2 β€ π§ β€ 10, and π₯, π¦, and π§ are natural numbers, find the smallest value of $π = 4π₯^3 β 2π¦^2 + 3π§^4$. If π is negative number, express your answer of π as a positive integer.
- Estimate $\frac{\sqrt{125}+5.5552}{3.33\times 4.444}$ and round off the answer to the nearest integer.
- Solve the equation: $$36(x+\frac{9}{2})+24(x+3)=120x$$ Round off the answer to the nearest integer.
- The diagram shows an isosceles triangle where ππ = π
π. Find the value of π₯. Round off the answer to the nearest integer.
- In 2022, a company spent 25% of its budget on research, 15 on marketing, and 10% of the remaining budget on employee benefits. The total expenditure was $\$$4,689,000. In 2023, the company's budget increased by 20% . The total expenditure on research, marketing, and employee benefits increased by 18%. If the marketing budget increased by 15%, and the spending on employee benefits decreased by 8%, by what percentage did the spending on research change? Round the answer to the nearest percentage.
- A cyclist rides from Point π to Point π at an average speed of π£ km/h for 30 minutes. She then rides back from Point π to Point π at an average speed of π€ km/h. The ratio π£ : π€ is 7 : 8. Find the total time (in minutes) taken for the entire journey. Round off the answer to the nearest integer.
- The diagram shows a semicircle where ππ = 12 is a diameter. π
is the point on the semicircle such that ππ
= ππ
. Find the area of the shaded region. Round off the answer to the nearest integer.
- The diagram shows a prism. The base of the prism is in the shape of a trapezium. The lengths shown are in centimeters. Find the volume of the prism in $\text{cm}^3$.
- The ratio of $p:q=2\frac{2}{3}:\frac{4}{7}$ and $q:r=1:3$. Given that $\frac{p}{r}=\frac{x}{y}$ in its simplest form, find the sum of $x$ and $y$.
- In the figure πππ
ππ, find the sum of all reflex angles.
- The total number of employees hired by Bluebird Corporation and Starlight Enterprises from 2014 to 2017 is detailed below. Determine the percentage of employees hired in 2016 out of the total number of employees hired over these four years. Round your answer to the nearest percentage.
- Greenland Park has decided to repurpose a circular area with a circumference of 40π π into an outdoor concert stage. The stage, shaped like a trapezium, will be constructed on this land, with the longer of its parallel sides matching exactly the diameter of the circle.
The lengths of the trapezium's parallel sides are in the ratio of 3:4, and the the distance between the parallel sides is 14.2π. If the cost of flooring per square metre is $\$$20, calculate the total cost for the stage flooring. (Figure not drawn to scale) - The rectangle shown in Figure 1 is cut along its diagonal to obtain two triangles. The two triangles are then rearranged as shown in Figure 2. ππ
π is a straight line and a line is drawn to joined π and π. Find the value of π₯.
- The time zone in Sydney, Australia is GMT +10, while the standard time zone in Los Angeles, USA is GMT β8. A flight departs from Los Angeles at 2200 β local time on 15 August 2023 and arrives in Sydney at 0630 β local time on 17 August 2023. Calculate the duration of the flight in minutes.
- Consider the number pattern:
$1^{π π‘}\text{ π‘πππ}: 1^2 β 0^2 + 2 = 3$
$2^{ππ}\text{ π‘πππ}: 2^2 β 1^2 + 5 = 8$
$3^{ππ}\text{ π‘πππ}: 3^2 β 2^2 + 8 = 13$
$4^{π‘β}\text{ π‘πππ}: 4^2 β 3^2 + 11 = 18$
$π^{π‘β}\text{ π‘πππ}: π₯^2 β π¦^2 + π§ = 268$
Find the sum of π₯, π¦ and π§.
(π»πππ‘: $(π β 1)^2 = π^2 β 2π + 1$) - A sequence of patterns is formed using matchsticks. The first three patterns are shown below. The dots indicate where two or more matchsticks meet.
The table below describes some information about the sequence of patterns:
What is the sum of T and D in Pattern 45? - Segment AB is parallel to segment EF and segment AC is parallel to DE. If the β BAC = 113Β°, what is the value (in degrees) of β DEF?
- In the figure below, there is a right cone with a base radius of πΆπ = 5 metres and a height of πΆπ = 6 metres. What is the total surface area of the cone, including the base, in square metres? Give your answer correct to the nearest integer.
- A rectangular piece of paper is such that its breadth is 65% as long as its length. It is cut into two equal pieces by cutting along a line parallel to the breadth. One of the pieces is then rotated by 90Β° and placed beside the other piece to obtain a new figure. Find the percentage increase in the perimeter compared to the original piece of paper. Give your answer correct to the nearest integer.
- James ran 40% of a track at 4 km/h. He then increased his speed by 20% for the remainder of the track. He took 1 hour 14 minutes to run the entire track. Find the length of the track correct to the nearest kilometre.
- Two inlet pipes can fill up an empty water tank in 2 hours and 4 hours, respectively. An outlet pipe can empty the same tank filled fully by with water tank in 8 hours. If all the pipes are turned on at the same time, how many minutes will it take to fill up the empty water tank fully?
- If $\frac{6}{(x^2-4)}-\frac{1}{(x+2)}+\frac{1}{(x-2)}=2\frac{(px+q)}{(x^2-4)}$, find the value of $p^2+q^2$.
- Consider the following pattern. How many complete triangles are there in Figure 90?
- A solid cuboid has the dimensions as shown in the diagram below. Two identical solids are removed from the cuboid. The cross section of each of the solids removed is the biggest possible quadrant that can be removed from the 12 cm by 4 cm face. Find the total surface area of the remaining solid in $\text{cm}^2$, giving your answer correct to the nearest integer.
- In the following figure, points πΈ and π· are the midpoints of π΄π΅ and π΄πΆ , respectively. πΆπΈ and π΅π· intersect at point π. πΊπΆ is parallel to π΄π΅, intersecting the extension of π΅π· ππ‘ πΊ. If π΅π = 14 cm, what is the length of π΅πΊ in cm?
- Written as a product of its prime factors, 88 200 = $2^3 Γ 3^2 Γ 5^2 Γ 7^2$. The number π is a factor of 88 200 and its last digit is 5. If it is not a perfect square, find the greatest possible value of π.
- A cylindrical container with base diameter of 40 cm is filled with water to a depth of 10 cm. A cube with side of length 14 cm is placed on the base of the container and is partially immersed in the water. What is the percentage of the cube that is submerged in the water? Give your answer correct to the nearest integer.
- In a survey, some students were asked to choose their favourite colour from Yellow, Red and Green. Each student chose exactly one colour. The results are represented on the pie chart as shown.
What is the minimum number of students who chose Red? - The area of the square base of a pyramid is 2880 $\text{cm}^2$. The triangular faces of the pyramid are identical and each has an area of 840 cm2. What is the height of the pyramid, in cm? Round off the answer to the nearest integer.
Posted : 26/06/2026 7:55 am
