Solve the following linear equation for $x$: $5(x - 3) - 2(4 - 3x) = 10$.
$x = \frac{23}{11}$
$x = -1$
$x = \frac{7}{11}$
$x = 3$
$x = -5$
Solve for $x$ in the equation: $\frac{2x+1}{3} - \frac{x-2}{4} = 2$.
$x = \frac{26}{5}$
$x = \frac{14}{11}$
$x = 2$
$x = \frac{14}{5}$
$x = \frac{34}{5}$
Which of the following equations represents the line shown in the graph?
$y = 2x + 3$
$y = -2x + 3$
$y = -2x - 3$
$y = 3x - 2$
$y = -\frac{1}{2}x + 3$
Expand and simplify the binomial product: $(3x - 5y)(2x + 3y)$.
$6x^2 - 15y^2$
$6x^2 - xy - 15y^2$
$5x - 2y$
$6x^2 - xy + 15y^2$
$6x^2 + 19xy - 15y^2$
Expand and simplify the expression $(4a - \frac{1}{2}b)^2$.
$16a^2 - \frac{1}{4}b^2$
$16a^2 - 4ab + \frac{1}{4}b^2$
$8a^2 - 4ab + \frac{1}{4}b^2$
$16a^2 + 4ab + \frac{1}{4}b^2$
$16a^2 - 8ab + \frac{1}{4}b^2$
Factorise the quadratic trinomial $x^2 - 5x - 24$.
$(x + 6)(x - 4)$
$(x - 6)(x + 4)$
$(x - 12)(x + 2)$
$(x + 8)(x - 3)$
$(x - 8)(x + 3)$
Factorise the quadratic trinomial $3x^2 + 10x - 8$.
$(3x - 8)(x + 1)$
$(3x - 2)(x + 4)$
$(3x + 2)(x - 4)$
$(3x + 4)(x - 2)$
$(x + 8)(3x - 1)$
A parabola has the equation $y = (x-4)(x+2)$. What are the coordinates of its turning point?
$(2, -8)$
$(3, -3)$
$(-1, -5)$
$(-2, 4)$
$(1, -9)$
Simplify the expression $(8a^6 b^{-3})^{\frac{2}{3}}$ assuming $a, b > 0$.
$\frac{16a^4}{b^2}$
$4a^4 b^2$
$\frac{4a^4}{b^2}$
$\frac{4a^9}{b^{\frac{1}{3}}}$
$\frac{8a^4}{b^2}$
Simplify the expression $\frac{(2x^2 y^{-1})^3}{4xy^3}$ completely, expressing your answer with positive indices.
$\frac{2x^5}{y^6}$
$2x^5$
$\frac{4x^5}{y^6}$
$\frac{2x^6}{y^3}$
$\frac{x^5}{2y^6}$
Simplify the following expression involving surds: $\sqrt{72} - \sqrt{50} + \sqrt{18}$.
$4\sqrt{6}$
$2\sqrt{2}$
$\sqrt{40}$
$4\sqrt{2}$
$14\sqrt{2}$
Express $\frac{6}{3 - \sqrt{7}}$ with a rational denominator.
$9 + 3\sqrt{7}$
$\frac{18 + 6\sqrt{7}}{16}$
$\frac{9+3\sqrt{7}}{8}$
$3(3 - \sqrt{7})$
$9 - 3\sqrt{7}$
An amount of 5000 dollars is invested for 3 years at an interest rate of 4% per annum, compounded annually. What is the total value of the investment after 3 years, to the nearest cent?
5616.00 dollars
5200.00 dollars
5600.00 dollars
5624.32 dollars
624.32 dollars
How many years would it take for 8000 dollars to earn 1200 dollars in simple interest at a rate of 5% per annum?
3.5 years
3 years
2.5 years
4 years
2 years
A regular polygon has an interior angle of $156^\circ$. How many sides does it have?
14
16
12
15
18
In the diagram, line AB is parallel to line CD. Angle BAE = $45^\circ$ and Angle DCE = $60^\circ$. What is the size of the reflex angle AEC?
$75^\circ$
$105^\circ$
$255^\circ$
$240^\circ$
$270^\circ$
A right-angled triangle has a hypotenuse of length 17 cm and one of the shorter sides is 8 cm. What is the perimeter of the triangle?
40 cm
30 cm
25 cm
18.8 cm
15 cm
A rectangular prism has side lengths of 4 cm, 5 cm, and 7 cm. What is the length of the space diagonal, correct to one decimal place?
9.5 cm
9.0 cm
8.1 cm
16.0 cm
10.5 cm
In a right-angled triangle, the angle of elevation to the top of a tower from a point 50 metres from its base is $28^\circ$. What is the height of the tower to the nearest metre?
56 m
94 m
23 m
44 m
27 m
A bag contains 5 red and 3 blue marbles. A marble is drawn at random, its colour is noted, and it is NOT replaced. A second marble is then drawn. What is the probability that the two marbles are of different colours?
$\frac{15}{64}$
$\frac{30}{64}$
$\frac{15}{28}$
$\frac{15}{56}$
$\frac{13}{28}$
A box-and-whisker plot summarises the results of a test, as shown in the chart. The minimum score was 45, the lower quartile (Q1) was 60, the median was 75, the upper quartile (Q3) was 85, and the maximum score was 100. Which statement must be true?
The mean score was 75.
The distribution of scores is symmetrical.
The interquartile range is 25.
Exactly 25% of students scored 85.
No student scored 70.
Solve the following pair of simultaneous equations for $x$ and $y$: \begin{cases} 3x + 2y = 4 \ 4x - y = 9 \end{cases}
$x=3, y=-2.5$
$x=-2, y=5$
$x=4, y=7$
$x=1, y=0.5$
$x=2, y=-1$
The graph shows two linear equations. What is the solution to the simultaneous equations represented by these lines?
$(0, 2)$
The equations have no solution.
$(2.25, 0)$
$(-1, 3.5)$
$(2, -1)$
A line segment has endpoints A(-3, 8) and B(5, -2). What is the length of the segment and the coordinates of its midpoint M?
Length = $2\sqrt{41}$, Midpoint = (2, 6)
Length = $\sqrt{68}$, Midpoint = (4, 5)
Length = $2\sqrt{41}$, Midpoint = (1, 3)
Length = 18, Midpoint = (-4, -5)
Length = $6$, Midpoint = (1, 3)
The bar chart shows the number of pets owned by students in a class. What is the total number of pets owned by all students in the class?
45
1.5
4
30
A sequence of numbers starts with 5, 8, 11, 14, ... . If $n$ represents the position of a term in the sequence, which algebraic rule correctly describes this pattern?
$5n$
$3n + 2$
$3n - 1$
$4n + 1$
$n + 4$
A school is organising a trip for 86 students and 4 teachers. They need to hire buses that can each hold a maximum of 30 people. The cost to hire one bus is 250 dollars. What is the total cost to transport everyone on the trip?
500 dollars
1000 dollars
1250 dollars
750 dollars
600 dollars
In a survey of 200 students, $\frac{2}{5}$ chose soccer as their favourite sport. Of the remaining students, 25% chose basketball. Of the students who did not choose soccer or basketball, $\frac{1}{3}$ chose tennis. How many students chose tennis?
60
20
40
80
Liam has a collection of comic books. His friend Maya has 5 more than double the number of comic books Liam has. Together, they have a total of 80 comic books. If $L$ represents the number of comic books Liam has, which equation correctly represents this situation?
$L + \frac{L}{2} + 5 = 80$
$L + 2(L + 5) = 80$
$2L + 5 = 80$
$L + (2L - 5) = 80$
$L + (2L + 5) = 80$
What is the value of the expression $x(3y - z) - y^2$ when $x=4$, $y=-2$, and $z=5$?
$48$
$40$
$-40$
$-36$
$-48$
The bar chart shows the number of hours students in a class spent on homework in one week. What percentage of students spent 4 hours or more on homework?
$50%$
$40%$
$60%$
$25%$
$30%$
A car is travelling at a constant speed of 80 km/h. How many metres does the car travel in 45 seconds?
1500 m
2000 m
1000 m
1200 m
1800 m
In a number puzzle, a circle, a square, and a triangle each represent a unique positive whole number. The following statements are true:
What is the value of the Circle?
8
2
6
A train is scheduled to depart at 10:45 AM. However, it is delayed by 80 minutes. The journey itself takes 3 hours and 50 minutes. What time does the train arrive at its destination?
4:15 PM
3:55 PM
3:15 PM
4:35 PM
4:05 PM
Anna and Ben share the profit from a small business in the ratio 3:5. If the total profit for a month is 2400 dollars, how much more money does Ben receive than Anna?
900 dollars
1500 dollars
400 dollars
300 dollars
A number is chosen. When it is divided by 3, then 8 is subtracted from the result, the answer is -2. What was the original number?
24
An input-output machine follows a specific rule. The table shows some values. What is the output when the input is 7?
29
27
25
35
A concert hall has its seats arranged in a pattern. The first row has 15 seats, the second row has 18 seats, and the third row has 21 seats. If this pattern continues, how many seats are in the 20th row?
78
68
75
81
72
A rectangular garden measuring 12 m by 16 m is surrounded by a path of uniform width. The area of the path itself is $128 \text{ m}^2$. What is the width of the path?
3 m
2 m
3.5 m
1.5 m
2.5 m
The price of a bicycle is increased by 10%. A month later, the new price is decreased by 10%. The final price is what percentage of the original price?
$100%$
$90%$
$99%$
$101%$
$110%$
A video streaming service offers a monthly plan that costs 15 dollars for a base allowance equivalent to 10 hours of standard definition (SD) streaming. Any usage beyond this allowance incurs a charge of 2.50 dollars per SD hour equivalent. High definition (HD) streaming consumes data 1.5 times faster than SD streaming. A customer streams exclusively in HD for $H$ hours, exceeding the base allowance. Which equation models the total monthly cost, $C$, in dollars, as a function of $H$?
$C = 15 + 3.75(H - \frac{20}{3})$
$C = 15 + 2.50(H - 10)$
$C = 15 + 3.75(H - 10)$
$C = 15 + 2.50(H - \frac{20}{3})$
$C = 2.50H + 15$
The stacked bar chart shows the revenue sources for a company in two different years. What was the approximate percentage increase in revenue from 'Services' from 2022 to 2023?
$33%$
$20%$
The formula for the volume of a sphere is $V = \frac{4}{3}\pi r^3$. If the radius of a sphere is doubled, by what factor does its volume increase?
3
A sequence of numbers starts with 3. To get the next number, you double the current number and then subtract 4. What is the 5th number in this sequence?
36
132
In the number grid, each box is the sum of the two boxes directly above it. The top row contains 5, a, and 8. The bottom box has value 31. What is the value of a?
5
7
9
10
Three friends, Alex, Ben, and Chloe, have an average of 20 marbles each. Alex has 15 marbles and Ben has 18 marbles. Chloe then gives half of her marbles to Alex. What is the new average number of marbles for Alex and Ben?
30.5
23.5
26.5
A digital clock uses 24-hour time in HH:MM format. A palindromic time reads the same forwards and backwards. For example, 12:21 is palindromic. How many minutes until the next one after 15:51?
251
74
321
84
62
A baker uses $\frac{1}{3}$ of his flour to make bread and $\frac{1}{4}$ of the remaining flour to make cakes. After this, he has 15 kilograms of flour left. How much flour did the baker have initially?
35 kg
30 kg
25 kg
45 kg
40 kg
A shop offers a 20% discount on a jacket. After the discount, a 10% Goods and Services Tax (GST) is added to the discounted price. If the final price paid is 176 dollars, what was the original price of the jacket before any discount or tax?
210 dollars
220 dollars
200 dollars
180 dollars
190 dollars
A 'Number Transformer' machine follows a two-step rule. It takes a number as input, first multiplies it by a certain value, and then adds another value to get the output. If an input of 3 gives an output of 13, and an input of 5 gives an output of 21, what is the output for an input of 8?
31
37
33
Let the operation $\oplus$ be defined as $a \oplus b = 2a - b^2$. What is the value of $(5 \oplus 3) \oplus 2$?
1
-3
-2
0
Four identical squares are arranged to form a larger rectangle. The perimeter of this large rectangle is 50 cm. What is the area of one of the identical squares?
36 cm$^2$
50 cm$^2$
20 cm$^2$
25 cm$^2$
16 cm$^2$
A rectangular garden has a length of 12 metres and a width of 8 metres. A path of uniform width is built around the outside of the garden. If the area of the path is equal to the area of the garden, what is the width of the path?
1 metre
2 metres
1.5 metres
3 metres
2.5 metres
A tap fills a 300-litre tank at a rate of 250 millilitres per second. At the same time, a leak at the bottom of the tank drains water at a rate of 6 litres per minute. Starting with an empty tank, how long will it take to fill the tank completely?
33.3 minutes
30 minutes
40 minutes
25 minutes
50 minutes
The mean of five distinct positive integers is 10. The median of these five integers is 11. What is the maximum possible value for the largest of these integers?
26
Liam has a collection of red, blue, and green pens. The ratio of red pens to blue pens is 2:3. The ratio of blue pens to green pens is 4:5. If there are 70 pens in total, how many blue pens does Liam have?
32
A snail is at the bottom of a 21-metre well. Each day, it climbs up 5 metres. Each night, it slides down 2 metres. On which day will the snail first reach the top of the well?
Day 8
Day 7
Day 5
Day 9
Day 6
A large cube is painted blue on all six faces. It is then cut into 125 smaller, identical cubes. How many of these smaller cubes have exactly two faces painted blue?
48
54
Solve the quadratic equation $x^2 - 3x - 40 = 0$ for $x$.
$x = -8$ or $x = -5$
$x = -8$ or $x = 5$
$x = 8$ or $x = 5$
$x = 8$ or $x = -5$
$x = 10$ or $x = -4$
A 13-metre ladder rests against a vertical wall with its base 5 metres from the wall. The base of the ladder is then pulled away from the wall so that its base is now 12 metres from the wall. How far down the wall does the top of the ladder slide?
8 m
7 m
1 m
12 m
5 m
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