Solve for $x$ in the following equation: $5(x - 2) - 3(2x + 1) = -4(x+3)$
$x = -1$
$x = -\frac{25}{3}$
$x = \frac{25}{3}$
$x = \frac{1}{3}$
Find the solution set for the inequality $\frac{2x-1}{3} \ge \frac{3x+2}{4}$.
$x \le 2$
$x \ge -10$
$x \le -10$
$x \ge 2$
Which of the following equations represents the line shown in the graph?
$y = -\frac{2}{3}x + 2$
$y = \frac{2}{3}x + 2$
$y = -\frac{3}{2}x + 3$
$y = \frac{3}{2}x + 2$
A line has the equation $5x - 2y = 20$. What are the coordinates of its x-intercept and y-intercept?
x-intercept: $(2,0)$, y-intercept: $(0,-5)$
x-intercept: $(4,0)$, y-intercept: $(0,-10)$
x-intercept: $(-4,0)$, y-intercept: $(0,10)$
x-intercept: $(0,4)$, y-intercept: $(-10,0)$
Solve the following system of simultaneous equations: $y = 2x - 1$ and $3x + 2y = 19$.
$(5, 3)$
$(2.5, 4)$
$(3, 5)$
$(1, 1)$
Solve the following system of simultaneous equations using the elimination method: $4x - 3y = 11$ and $3x + 2y = 21$.
$x=3, y=5$
$x=2, y=-1$
$x=-1, y=-5$
$x=5, y=3$
Simplify the expression: $(3a^4b^{-2})^3 \div (9a^5b^{-7})$
$18a^7b$
$3a^{-1}b^{-13}$
$3a^7b$
$\frac{1}{3}a^7b$
Evaluate the following expression: $81^{\frac{3}{4}} \times 16^{-\frac{1}{2}}$
$\frac{9}{2}$
$54$
$\frac{27}{4}$
$108$
Expand and simplify the polynomial: $(2x - 5)(3x + 1) - (x-4)^2$.
$5x^2 - 5x + 11$
$5x^2 - 21x + 11$
$7x^2 - 13x - 21$
$5x^2 - 5x - 21$
Simplify the following algebraic fraction: $\frac{x^2 - 4x - 12}{x^2 - 4}$.
$\frac{x-3}{x-1}$
$\frac{x+6}{x+2}$
$\frac{x-6}{x-2}$
$x - 3$
Factorise the quadratic trinomial $3x^2 - 10x - 8$ completely.
$(3x+2)(x-4)$
$(3x-2)(x+4)$
$(3x+4)(x-2)$
$(3x-4)(x+2)$
Factorise the expression $49y^2 - (x+3)^2$ completely using the difference of two squares method.
$(49y - x - 3)(y + x + 3)$
$(7y - (x+3))^2$
$(7y - x - 3)(7y + x + 3)$
$(7y - x + 3)(7y + x - 3)$
The solutions to the quadratic equation $2x^2 + 7x = 15$ are:
$x = -3, x = \frac{5}{2}$
$x = \frac{3}{2}, x = -5$
$x = -\frac{3}{2}, x = 5$
$x = 3, x = -\frac{5}{2}$
A closed cylinder has a radius of $5$ cm and a height of $12$ cm. What is its total surface area, in terms of $\pi$?
$120\pi \text{ cm}^2$
$170\pi \text{ cm}^2$
$220\pi \text{ cm}^2$
$145\pi \text{ cm}^2$
A triangular prism has a length of 20 cm. The triangular base is a right-angled triangle with side lengths 6 cm, 8 cm, and 10 cm. What is the volume of the prism?
$960 \text{ cm}^3$
$800 \text{ cm}^3$
$1600 \text{ cm}^3$
$480 \text{ cm}^3$
In a diagram, two parallel lines are intersected by a transversal. An angle corresponding to an angle of $(2x+15)^\circ$ is given as $(4x-35)^\circ$. Find the value of $x$.
$x=10$
$x=25$
$x=20$
$x=50$
The sum of the interior angles of a regular polygon is $1440^\circ$. How many sides does the polygon have?
12 sides
10 sides
9 sides
8 sides
An isosceles triangle has two equal sides of length 13 cm and a base of 10 cm. What is the perpendicular height of the triangle from the base?
10 cm
$\sqrt{269}$ cm
11 cm
12 cm
A rectangular prism has dimensions 4 cm by 7 cm by 8 cm. What is the length of the space diagonal, which connects opposite vertices of the prism? Give your answer as a simplified surd.
$\sqrt{65}$ cm
$\sqrt{113}$ cm
$19$ cm
$\sqrt{129}$ cm
From a point 40 metres from the base of a tree, the angle of elevation to the top of the tree is $35^\circ$. What is the height of the tree to the nearest metre? (Given $\tan(35^\circ) \approx 0.700$)
33 m
49 m
28 m
23 m
An amount of 5000 dollars is invested at a rate of 4% per annum, compounded annually. What is the total value of the investment after 3 years, to the nearest cent?
5612.16 dollars
5600.00 dollars
6243.20 dollars
5624.32 dollars
A bag contains 5 red marbles and 3 blue marbles. Two marbles are drawn at random without replacement. What is the probability that both marbles are the same colour?
$\frac{15}{64}$
$\frac{13}{28}$
$\frac{15}{28}$
$\frac{13}{32}$
The box plot below shows the test scores for a class. What is the interquartile range (IQR) of the scores?
20
75
10
48
The bar chart shows the number of goals scored by a soccer team in its last 15 matches. What is the median number of goals scored?
1
2
3
1.93
The graph of the quadratic function $y = x^2 - 4x + 3$ is shown. What are the coordinates of its vertex?
$(2, -1)$
$(1, 0)$
$(-2, 15)$
$(3, 0)$
Solve the following linear equation for $x$: $5(x - 3) = 2(x + 6)$
$x = 1$
$x = 7$
$x = 9$
Which of the following inequalities is the solution to $7 - 2x \le 15$?
$x \ge 4$
$x \le 4$
$x \le -4$
$x \ge -4$
The graph of a linear relationship is shown below. What is the equation of the line?
$y = 2x + 4$
$y = -2x + 4$
$y = -\frac{1}{2}x + 4$
$y = -2x - 2$
What are the coordinates of the x-intercept for the linear equation $3x - 5y = 15$?
$(-3, 0)$
$(0, -3)$
$(0, 5)$
$(5, 0)$
Solve the following system of simultaneous equations: \begin{cases} y = 2x - 1 \ 3x + 2y = 12 \end{cases}
$x=-2, y=-5$
$x=2, y=3$
$x=1, y=4.5$
Solve the following system of simultaneous equations: \begin{cases} 4x + 3y = 10 \ 4x - y = 2 \end{cases}
$x=-1, y=-6$
$x=1, y=2$
$x=3, y=-1$
$x=2, y=1$
Simplify the expression $\frac{(a^4b)^3}{a^5b^2}$ completely.
$a^{12}b$
$a^2b$
$a^7b^5$
$a^7b$
Expand and simplify the polynomial expression: $(3x - 1)(x + 4)$.
$3x^2 + 13x - 4$
$3x^2 + 11x - 4$
$3x^2 + 12x + 4$
$3x^2 - 11x - 4$
Which of the following is the fully factorised form of the quadratic trinomial $x^2 - 3x - 18$?
$(x + 9)(x - 2)$
$(x - 6)(x + 3)$
$(x + 6)(x - 3)$
$(x - 9)(x + 2)$
Factorise the expression $16x^2 - 81y^2$ using the difference of two squares.
$(4x - 9y)^2$
$(8x - 9y)(2x + 9y)$
$(16x - 9y)(x + 9y)$
$(4x - 9y)(4x + 9y)$
What are the solutions to the quadratic equation $x^2 - 8x + 15 = 0$?
$x = -3, x = 5$
$x = 3, x = 5$
$x = 2, x = 6$
$x = -3, x = -5$
A cylinder has a radius of 5 cm and a height of 10 cm. What is its volume? (Leave your answer in terms of $\pi$)
$100\pi$ cm$^3$
$500\pi$ cm$^3$
$50\pi$ cm$^3$
$250\pi$ cm$^3$
Calculate the total surface area of a rectangular prism with length 10 cm, width 5 cm, and height 4 cm.
$110$ cm$^2$
$260$ cm$^2$
$200$ cm$^2$
$220$ cm$^2$
In a pair of parallel lines cut by a transversal, one of the obtuse angles formed is $115^\circ$. What is the measure of a co-interior angle to this angle?
$245^\circ$
$75^\circ$
$65^\circ$
$115^\circ$
What is the sum of the interior angles of a regular decagon (a 10-sided polygon)?
$144^\circ$
$1440^\circ$
$1620^\circ$
$1800^\circ$
A rectangle measures 9 cm by 12 cm. What is the length of its diagonal?
$15$ cm
$21$ cm
$\sqrt{63}$ cm
$10.5$ cm
A rectangular box (cuboid) has dimensions 3 cm, 4 cm, and 12 cm. What is the length of the longest diagonal (the space diagonal) that can fit inside the box?
$\sqrt{153}$ cm
$13$ cm
$5$ cm
In a right-angled triangle, the hypotenuse is 20 cm long and one of the angles is $30^\circ$. What is the length of the side opposite this angle?
$10$ cm
$10\sqrt{3}$ cm
$17.32$ cm
$20\sqrt{2}$ cm
In a right-angled triangle, the side opposite angle $\theta$ is 5 cm and the side adjacent to angle $\theta$ is 12 cm. What is the value of $\theta$ to one decimal place?
$22.6^\circ$
$67.4^\circ$
$24.6^\circ$
$0.4^\circ$
An amount of 2000 dollars is invested at a simple interest rate of 5% per annum. How much interest is earned after 3 years?
2300 dollars
100 dollars
300 dollars
150 dollars
An amount of 5000 dollars is invested for 2 years at an interest rate of 4% per annum, compounded annually. What is the total value of the investment after 2 years?
5408 dollars
408 dollars
5400 dollars
5416 dollars
A fair six-sided die is rolled and a fair coin is tossed. What is the probability of rolling a number greater than 4 AND tossing a head?
$\frac{1}{12}$
$\frac{1}{3}$
$\frac{1}{6}$
$\frac{5}{6}$
The box plot below shows the distribution of test scores for a class. What is the interquartile range (IQR) of the scores?
12
15
22
25
Consider the data set: {4, 5, 5, 6, 7, 8, 25}. The histogram shows the distribution. How does the mean of the data compare to the median?
The mean is equal to the median.
The mean is less than the median.
The mean is greater than the median.
It cannot be determined from the data.
Simplify the following expression involving negative indices: $(2x^{-3}y^2)^{-2}$.
$\frac{x^6}{4y^4}$
$-4x^6y^{-4}$
$\frac{y^4}{4x^6}$
$\frac{4x^6}{y^4}$
Great effort! Check the detailed feedback above.
Incorrect password
