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- When expressed as a product of its prime factors, 18200 = $2^π Γ 5^π Γ 7^π Γ π$. Find the value of π + π + π + π.
- A map is drawn to a scale of 1 : 2700. What is the distance, in cm, between two buildings on the map which are 6750 metres apart?
- $15π₯^2 + 14π₯ β 8$ can be expressed as (ππ₯ + π)(ππ₯ + π), where π, π, π and π are constants. Find the value of π + π + π + π.
- The length of the diagonal of the square is 95 cm. What is the length of a side of the square, in cm? Round off the answer to the nearest integer.
- Solve the equation 5π₯ β 17 = 39 β 2π₯.
- Estimate the value of $(\sqrt{226.5} β 5.7)^2$, correct to 1 significant figure.
- π is the largest integer and π is the smallest integer satisfying $$-2\le\frac{6+2y}{5}<4$$ Find the value of π β π.
- When Tom sold his toy for $\$$225, he incurred a loss of 25%. At what price should he have sold the toy to make a 37% profit instead? Round off the answer to the nearest integer.
- Given the sequence: $$4, 11, 30, 67, 128, π, π, β¦$$ Find the sum of π and π.
- In parallelogram π΄π΅πΆπ· below, π΄πΈ is perpendicular to π·πΆ and π·πΉ is perpendicular to π΅πΆ. If π΄π· = 10, πΆπ· = 15 and π΄πΈ = 6, find the length of π·πΉ.
- Amy and Ben live in different cities, and they are in different time zones. When it is 6:00 AM on June 1st in Ben's city, it is 10:30 PM on May 31st in Amy's city. Amy decides to take a train from her city to Ben's city. The train departs from Amy's city at 11:20 PM on June 1st and arrives in Ben's city at 9:05 AM on June 2nd. The distance covered during the train journey is 850 kilometres. What was the average speed of the train, in km/h, during this journey? Give your answer correct to the nearest integer.
- The sum of three consecutive even numbers is 1386. Find the largest number among these 3 numbers.
- In the figure, π΄π΅, πΆπ·, and πΈπΉ are straight lines. Find the value of π₯.
- Given that π is a positive number, find the value of π if 1 : π = 2π : 288.
- 5π + 3π = $\frac{7-2m}{n}$ can be expressed as π = $\frac{an^2+bn+c}{dn+e}$. If π < 0 and π is fraction in simplest form. Find the value of π + π + π + π + π.
- Solve the equation $\frac{81}{3^{3-a}}+7^3=2530$.
- The line π has a gradient of β18. It intersects the positive π¦-axis at point π and the positive π₯-axis at point π. The area of triangle πππ is 36 $\text{units}^2$. Find the length of ππ. Give your answer correct to the nearest integer.
- Solve the simultaneous equations and find the sum of π + π. $$\frac{4}{3}a+7b=239$$ $$\frac{23}{3}a-466=3b$$
- A quadratic graph has the line of symmetry π₯ = 10.5. It passes through points (1, 7) and (π, 7). Find the value of π.
- Find the smallest positive integer value of π for which 700π is a multiple of 125.
- In the cube below, the diagonals of the face intersect at point Q and R is a vertex. Given that the length of the edge is 4, find the length of QR. Round off the answer to the nearest integer.
- Given that $m=\frac{3n+7}{5-3n}$, when $n$ is the expressed in terms of $m,n=\frac{am+b}{cm+d}$. Find the sum of $a,b,c$ and $d$.
- The π₯-coordinates of the points of intersection of the graphs $π¦ = ππ₯ + π$ and $π¦ = 3π₯^2 β 7π₯ + 2$ are the solutions to the equation $π₯^2 β 6π₯ β 13 = 0$. Find the value of $π + π$.
- There are some blue, white and orange socks in a drawer. A sock is randomly chosen.
- The probability that the sock is blue or white is $\frac{4}{7}$.
- The probability that the sock is white is $\frac{9}{28}$.
- The probability that the sock is blue or orange is $\frac{m}{n}$, where the fraction $\frac{m}{n}$ is in the simplest form.
Find the value of π + π. - An π-gon is such that 4 of its interior angles are each equal to 105Β° and the remaining interior angles are each equal to 170Β°. Find the value of π.
- A data set has eight integer data values: 5, 12, 11, 3, 2, π, π and 10, where π < π. The mean is 7.75, the median is 8 and there is no mode. Find the value of π + 3π.
- Given that $ππ = 4$ and $π^2 + π^2 = 41$, find the value of $(π + π)^4$.
- In the diagram below, square ABCD with side length 4 is inscribed in a circle. Semicircular arcs are drawn on each side of the square. What is the area of the shaded region outside the circle and inside the semi-circles?
- $$\sqrt{56+\sqrt{56+\sqrt{56+\sqrt{56+\cdots}}}}=x$$ Find the value of π₯.
- In right-angled triangle π΄π΅πΆ, point π· is on side π΅πΆ and π΄π΅ = 10 cm, π΄πΆ = 20.6 ππ, π΄π· = 11.7 cm. Find the length of π·πΆ in cm, leaving the answer to the nearest integer.
- Cylindrical container A has a height of 10 metres and a radius of 4 metres. Cylindrical container B has a height of 7 metres and a radius of 6 metres. Tom filled container A with water to its brim and then transferred the water from container A to container B until both containers had the same depth of water. Given that container B was empty at first, what was the depth of water in each container, in metres, after the transfer? Round off the answer to the nearest integer.
- 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 $\text{cm}^2$. What is the height of the pyramid, in cm? Round off the answer to the nearest integer.
- The table below shows the number of toys that 100 children purchased in a store.
If the median is given to be 5.5, find the mean of this distribution. Round your answer to the nearest integer. - In triangle π΄π΅πΆ below, π΄π΅ = 10 m, β π΄πΆπ΅ = 65Β° and β πΆπ΄π΅ = 40Β°, find the area of βπ΄π΅πΆ. Round off the answer to the nearest integer.
- In the diagram below, three identical small circles of radius 10 are tangent to each other and the rectangle, as shown. The rectangle is inscribed in a large circle as shown. What is the area of the large circle, in cm? Round off the answer to the nearest integer.
Posted : 27/06/2026 12:54 am
