The price of a concert ticket was increased by 20%. After a week, the new price was then discounted by 25%. The final price is what percentage of the original price?
$95%$
$100%$
$90%$
$105%$
In a bag of marbles, the ratio of red to blue marbles is $3:5$. The ratio of blue to green marbles is $2:3$. If there are more than 100 marbles in total, what is the minimum possible number of marbles in the bag?
$155$
$110$
$124$
$104$
If $x$ is an odd integer and $y$ is an even integer, which of the following expressions must always result in an odd integer?
$x-y$
$x+y+1$
$2x+y$
$xy$
The integer $K$ is a two-digit number greater than 50. The product of its digits is 24 and the sum of its digits is 10. What is $K$?
$83$
$38$
$46$
$64$
A sequence of figures is generated where Figure 1 is formed by the sum of the first two consecutive square numbers ($0^2+1^2=1$), Figure 2 is the sum of the next two ($1^2+2^2=5$), Figure 3 is ($2^2+3^2=13$), and so on. What is the value of Figure 5?
$25$
$50$
$34$
$41$
Consider the sequence: $2, 6, 12, 20, 30, \dots$. The 10th term of this sequence is added to the 11th term. What is the result?
$220$
$242$
$264$
$200$
At a fruit stand, 3 apples and 2 bananas cost a total of 780 cents. At the same stand, 2 apples and 3 bananas cost a total of 720 cents. What is the total cost of one apple and one banana?
300 cents
320 cents
280 cents
150 cents
In the figure, a square ABCD and an equilateral triangle ABE share the side AB. The triangle is drawn inside the square. The diagonal AC of the square is drawn, intersecting the side BE of the triangle at point F. What is the size of angle BFC?
$105^\circ$
$75^\circ$
$120^\circ$
$90^\circ$
The figure shown is a large square with side length 10 cm, from which a smaller square with side length 4 cm has been removed from one corner. What is the perimeter of the resulting L-shape?
32 cm
84 cm
36 cm
40 cm
Two identical squares, each with an area of $100 \text{ cm}^2$, overlap. The area of the overlapping region, which is also a square, is a quarter of the area of one of the original squares. What is the perimeter of the combined shape?
80 cm
50 cm
60 cm
A cyclist travels from Town A to Town B, a distance of 30 km. For the first 12 km, she cycles at a speed of 24 km/h. She then increases her speed for the remainder of the journey. If the total journey takes 1.5 hours, what was her speed for the second part of the journey?
12 km/h
18 km/h
20 km/h
24 km/h
At a market, 3 mangoes and 2 apples cost 13 dollars. 1 mango and 2 apples cost 7 dollars. What is the cost of one mango?
3 dollars
3.50 dollars
4 dollars
2 dollars
A bag contains 20 cards, numbered from 1 to 20. A card is drawn at random. What is the probability that the number on the card is a multiple of 3 and also a multiple of 4?
$1/12$
$11/20$
$1/2$
$1/20$
Alice and Ben are running a 400-metre race. They start at the same time. Alice runs at a constant speed of 8 m/s. Ben runs at a constant speed of 6 m/s. When Alice finishes the race, how far is Ben from the finish line?
50 m
300 m
100 m
133 m
A mobile phone company offers two monthly plans as shown in the table. Additionally, any data used above the plan's inclusion is charged at 10 dollars per GB.
In a particular month, a user on the Basic plan and a user on the Plus plan both paid exactly 65 dollars. How much more data did the Plus user use than the Basic user?
13.5 GB
16.5 GB
15 GB
1.5 GB
The grid below follows two rules:
4
1
3
2
A box of 4 cups and 3 plates weighs 1.7 kg. A box of 2 cups and 5 plates weighs 1.9 kg. All cups have the same weight, and all plates have the same weight. What is the weight of a single plate?
0.5 kg
0.2 kg
0.25 kg
0.3 kg
A bag contains 5 red marbles and 3 blue marbles. Two marbles are drawn from the bag one after another, without replacement. What is the probability that both marbles drawn are the same colour?
$13/28$
$15/28$
$17/32$
The table shows checkpoints of a delivery van's journey from its depot. The depot is at the 0 km mark.
What was the van's average speed for the entire period it was moving?
60 km/h
$73\frac{1}{3}$ km/h
80 km/h
55 km/h
A sequence of five boxes is filled with numbers. The number in any box is the sum of the numbers in the two boxes immediately to its left. The first box contains the number 3, and the fourth box contains the number 13.
[ 3 ] [ ? ] [ ? ] [ 13 ] [ ? ]
What is the number in the fifth box?
16
26
18
21
The sum of two numbers is 30. One-third of the first number is equal to one-half of the second number. What is the positive difference between the two numbers?
10
6
15
5
A plane flies from City X to City Y, a distance of 1800 km, in 3 hours, flying against a constant headwind. The return journey from Y to X, with the same wind now as a tailwind, takes 2.5 hours. What is the speed of the wind?
120 km/h
30 km/h
660 km/h
Three boys (B) and two girls (G) are to be seated in a row of five chairs. If they are seated randomly, what is the probability that no two boys are sitting next to each other?
$2/5$
$1/10$
A company needs to print 3000 flyers. They can use Printer X or Printer Y.
160 dollars
240 dollars
180 dollars
220 dollars
Four positive whole numbers, A, B, C, and D, are all different and have a sum of 25. They satisfy the following conditions:
13
9
12
11
Leo thinks of a number. He doubles it, subtracts 14, then divides the result by 4. The final answer is 8. What was the original number?
$15$
$23$
$9$
$30$
A parallelogram ABCD has vertices at A(1, 2), B(5, 4), and C(7, 8). What are the coordinates of vertex D?
$(3, 6)$
$(-1, -2)$
$(11, 10)$
$(4, 5)$
A mobile plan 'TalkMore' costs 20 dollars per month plus 10 cents per minute of calls. A second plan 'CallEasy' costs 40 dollars per month which includes 300 free minutes, with no charge for calls up to this limit. For a particular month, a user's bill is the same on both plans. How many minutes of calls did they use?
$200$ minutes
$300$ minutes
$400$ minutes
$100$ minutes
At a market stall, 3 apples and 2 bananas cost 5.40 dollars. At the same stall, 2 apples and 3 bananas cost 5.10 dollars. What is the cost of one apple and one banana together?
$0.30 \text{ dollars}$
$2.10 \text{ dollars}$
$1.20 \text{ dollars}$
$2.25 \text{ dollars}$
A cyclist travels from Town A to Town B. For the first half of the distance, she travels at 20 km/h. For the second half of the distance, she travels at 30 km/h. What is her average speed for the entire journey?
$24.5 \text{ km/h}$
$25 \text{ km/h}$
$26 \text{ km/h}$
$24 \text{ km/h}$
The chart shows the number of new houses built per quarter in a town over two years. The accompanying table shows the average number of occupants per new house for each of those years.
What was the total increase in the town's population from new houses built from the start of Year 1 to the end of Year 2?
$1500$
$1398$
$600$
$1410$
Three friends share a box of cookies. Anika takes half of the cookies. Ben then takes one-third of the remaining cookies. Finally, Chloe takes the last 8 cookies. How many cookies were in the box originally?
$24$
$36$
$18$
$48$
A line segment connects point P(2, 8) and point Q(10, 2). Which of the following points lies on the perpendicular bisector of the segment PQ?
$(7, 7)$
$(9, 8)$
$(3, 1)$
$(5, 9)$
The graph shows the cost of printing flyers at two different companies, 'PrintFast' and 'CopyKing'. Which statement is best supported by the graph?
CopyKing is always more expensive than PrintFast.
For an order of 500 flyers, PrintFast is cheaper.
PrintFast has a higher cost per flyer, but no setup fee.
It is cheaper to use CopyKing for small orders, but cheaper to use PrintFast for large orders.
A collection of 36 coins consists only of 10-cent, 20-cent, and 50-cent coins. There are three times as many 20-cent coins as 10-cent coins. The total value of the collection is 11.50 dollars. How many 50-cent coins are there?
$12$
$5$
$16$
Two trains start at the same time from two stations 420 km apart and travel towards each other on parallel tracks. Train A travels at a constant speed of 90 km/h. Train B travels at a constant speed of 120 km/h. How far from Train A's starting station will they meet?
$210 \text{ km}$
$240 \text{ km}$
$180 \text{ km}$
$200 \text{ km}$
A survey asked 95 Year 8 students about their favorite sport. The results were: Soccer (35 students), Basketball (25 students), Netball (20 students), Swimming (10 students), and Other (5 students). To the nearest whole percent, what percentage of students chose Soccer?
$50%$
$26%$
$37%$
$35%$
A straight line is described by the equation $2y + 4x = 8$. What is the sum of its x-intercept and y-intercept?
$-2$
$2$
$6$
$8$
What is the value of $50 - 5 \times 2 + (8 - 4) \div 2$?
$47$
$42$
$22$
Given that $x, y, z$ are positive real numbers, simplify the following expression completely. The final answer should contain only positive exponents.
$$\frac{(3x^{1/2}y^{-2}z^2)^{-2}}{(6x^{-1}y^{3/2}z^{-1})^{-1}}$$
$\frac{3y^{11/2}}{2x^2z^5}$
$\frac{2x^{1/2}z^2}{3y^{9/2}}$
$\frac{2y^{11/2}}{3x^2z^5}$
$\frac{2y^{5/2}}{3z^3}$
Assuming $x>0$ and $y>0$, which of the following expressions is equivalent to $\frac{\sqrt{48x^5y^3}}{2\sqrt{3xy^7}}$?
$6x^3y^5$
$\frac{4x^2}{y^2}$
$2x^2y^2$
$\frac{2x^2}{y^2}$
Line A passes through the points $(1, 3)$ and $(5, k)$. Line B has the equation $2y = 6x - 5$. If Line A and Line B are parallel, what is the value of $k$?
$7$
$27$
$-9$
What is the value of $1 - \frac{1}{2} \div (1 - \frac{1}{2} \div (1 - \frac{1}{3}))$?
$-1$
$\frac{1}{3}$
$\frac{7}{8}$
Given that $x, y > 0$, fully simplify the expression $\left(\frac{27x^{9}y^{-6}}{8x^{-3}y^{3/2}}\right)^{-2/3}$.
$\frac{4y^5}{9x^8}$
$\frac{9y^5}{4x^8}$
$\frac{4x^8}{9y^5}$
$\frac{9x^{12}}{4y^4}$
Given that $x > 0$ and $x \neq 2$, what is the simplified form of the expression $\frac{x\sqrt{48x^3} - \sqrt{75x^5}}{x\sqrt{3x} - \sqrt{12x}}$?
$\frac{x^2}{x-2}$
$4x - \frac{5x^2}{2}$
$\frac{x^2}{2-x}$
$\frac{x^2}{4-x}$
Which of the following is equivalent to the expression $\frac{(3x^{-4}y^2)^{-2}}{(9x^2y^{-3})^{-1}}$ for all positive values of $x$ and $y$?
$\frac{x^6}{y^7}$
$\frac{x^{10}}{81y^7}$
$\frac{x^{10}}{y^7}$
$\frac{x^{10}}{y}$
The line $y = mx - 1$ passes through the first quadrant. Which of the following statements about the gradient $m$ must be true? (The first quadrant is where $x>0$ and $y>0$).
$m > 1$
$m > 0$
$m < 0$
$m = 1$
For which integer value of $k$ is the expression $24 \div (8 - 2 \times k)$ undefined?
$4$
$0$
$-8$
The expression $\frac{(2x^2 y^{-1})^3}{4x^{-2} y}$ simplifies to the form $ax^m y^n$. What is the value of $m+n$?
The expression $\frac{12}{\sqrt{3}} + \sqrt{75}$ can be written in the form $k\sqrt{3}$. What is the value of $k$?
$29$
$17$
A rectangle has a length of $(\sqrt{5} + \sqrt{20})$ cm and a width of $\sqrt{5}$ cm. What is the area of the rectangle in cm$^2$?
$5+2\sqrt{5}$
$3\sqrt{5}$
$5\sqrt{5}$
The quadratic equation $3x^2 - 11x - 4 = 0$ has two real roots. What is the sum of the squares of these roots?
$145/9$
$97/9$
$145/3$
$121/9$
For what range of values of $k$ does the quadratic equation $kx^2 - 4x + 2 = 0$ have two distinct real roots?
$k > 2$
$k < 2$ and $k eq 0$
$k > -2$
$k < 2$
Which of the following equations represents the quadratic function $f(x)$ in vertex form, given that its standard form is $f(x) = -2x^2 + 12x - 11$?
$f(x) = -2(x-3)^2 + 7$
$f(x) = -2(x+3)^2 + 7$
$f(x) = -2(x-6)^2 - 11$
$f(x) = -2(x-3)^2 - 7$
A parabola has a vertex at $(-4, 5)$ and passes through the point $(-2, -7)$. What is its axis of symmetry and the direction of opening?
Axis of symmetry: $x = -4$; Opens upwards
Axis of symmetry: $x = -4$; Opens downwards
Axis of symmetry: $y = 5$; Opens downwards
Axis of symmetry: $x = 5$; Opens upwards
The graph of a quadratic function is shown below. Which of the following equations best represents the function?
$y = (x-2)^2 + 1$
$y = -\frac{1}{2}(x-2)^2 + 1$
$y = -\frac{1}{2}(x+2)^2 + 1$
$y = -2(x+2)^2 + 1$
A motorboat, whose speed in still water is 15 km/h, travels 30 km downstream and then returns to its starting point. The total time taken for the entire journey is 4 hours and 30 minutes. What is the speed of the stream in km/h?
7.5 km/h
6 km/h
4 km/h
5 km/h
Pipe A can fill a cistern in 12 hours and Pipe B can fill it in 15 hours. A third pipe, C, fitted at the bottom, can empty the full cistern in 10 hours. If all three pipes are opened simultaneously, in how many hours will the cistern be full?
20 hours
18 hours
24 hours
30 hours
The product of an individual's age in years five years ago and their age in years nine years from now is 15. What is the individual's present age?
5 years
9 years
6 years
10 years
A motorboat travels 30 kilometres down a river and then returns to its starting point. The entire trip takes 8 hours. If the speed of the river current is 2 km/h, what is the speed of the motorboat in still water?
$8$ km/h
$9.5$ km/h
$7.5$ km/h
$5.5$ km/h
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