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CTJan27 Online JMSS Mathematics Practice Test
Student Name
Student Email
1
Solve the linear equation for $x$: $3(x - 2) = 5x + 4$.
-5
-2
5
1
2
Find the $y$-intercept of the line given by the equation $2x - 5y = 10$.
(0, -2)
(-2, 0)
(5, 0)
(0, 10)
3
Solve the inequality: $7 - 2x < 15$.
$x < -4$
$x > -4$
$x < 4$
$x > 4$
4
Which ordered pair $(x, y)$ is a solution to both inequalities $x + y \le 4$ and $x > 1$?
(1, 3)
(3, 0)
(0, 5)
(2, 3)
5
What is the distance between the points $A(-1, 5)$ and $B(2, 1)$ in the Cartesian plane?
3
5
$\sqrt{10}$
$\sqrt{34}$
6
A line passes through the point $(4, 3)$ and has a slope (gradient) of $-2$. What is the equation of the line?
$y = 2x + 5$
$y = -2x + 11$
$y = -2x + 5$
$y = 4x + 3$
7
If the function is defined by $f(x) = x^2 - 3x$, find the value of $f(-2)$.
10
2
-10
4
8
Simplify the expression using index laws: $\frac{12a^5 b^2}{(4a^2 b^3)^{-1}}$
$3a^7 b^5$
$48 a^3 b^{-1}$
$48 a^7 b^5$
$3 a^3 b^{-1}$
9
Simplify the surd $\sqrt{72}$.
$36\sqrt{2}$
$6\sqrt{2}$
$8\sqrt{9}$
$12\sqrt{6}$
10
Evaluate the expression $8^{2/3}$.
2
4
16
$8/3$
11
A map uses a scale of $1: 50,000$. If a road measures $4 \text{ cm}$ on the map, what is its actual length in kilometers?
$2 \text{ km}$
$0.2 \text{ km}$
$20 \text{ km}$
$50 \text{ km}$
12
If $5$ workers can paint a fence in $12$ hours, how long would it take $3$ workers to paint the same fence, assuming they work at the same rate?
$7.2 \text{ hours}$
$10 \text{ hours}$
$20 \text{ hours}$
$60 \text{ hours}$
13
A store purchased an item for $\$150$ and marked it up by $40\%$. What is the selling price?
$\\$190$
$\\$210$
$\\$154$
$\\$180$
14
Calculate the simple interest earned on $\$5000$ invested at $6\%$ per annum for $4$ years.
$\\$120$
$\\$300$
$\\$1200$
$\\$5300$
15
A price of a jacket was reduced from $\$80$ to $\$64$. What is the percentage decrease?
$16\%$
$20\%$
$25\%$
$80\%$
16
Convert $3.5 \text{ square meters}$ ($m^2$) to $\text{square centimeters}$ ($cm^2$).
$350 \text{ cm}^2$
$3500 \text{ cm}^2$
$35000 \text{ cm}^2$
$350000 \text{ cm}^2$
17
Calculate the area of a trapezoid with parallel sides of $6 \text{ cm}$ and $10 \text{ cm}$ and a height of $5 \text{ cm}$.
$30 \text{ cm}^2$
$40 \text{ cm}^2$
$50 \text{ cm}^2$
$80 \text{ cm}^2$
18
What is the surface area of a cube with side length $3 \text{ cm}$?
$27 \text{ cm}^2$
$36 \text{ cm}^2$
$54 \text{ cm}^2$
$9 \text{ cm}^2$
19
A right-angled triangle has legs of length $5 \text{ cm}$ and $12 \text{ cm}$. What is the length of the hypotenuse?
$15 \text{ cm}$
$13 \text{ cm}$
$17 \text{ cm}$
$\sqrt{119} \text{ cm}$
20
A ladder $10 \text{ m}$ long leans against a wall. The base of the ladder is $6 \text{ m}$ from the wall. How high up the wall does the ladder reach?
$4 \text{ m}$
$8 \text{ m}$
$16 \text{ m}$
$\sqrt{136} \text{ m}$
21
In a right-angled triangle, the angle $\theta$ has an opposite side of length $8$ and an adjacent side of length $15$. What is the value of $\tan(\theta)$?
$15/8$
$8/17$
$15/17$
$8/15$
22
If $\sin(A) = 0.5$ in a right-angled triangle, what is the measure of angle $A$ in degrees?
$60^\circ$
$30^\circ$
$45^\circ$
$90^\circ$
23
A bag contains $3$ red marbles and $7$ blue marbles. If two marbles are selected at random without replacement, what is the probability that both are red?
$1/10$
$9/100$
$1/15$
$3/50$
24
What is the probability of rolling a number greater than $4$ on a standard six-sided die?
$1/6$
$1/3$
$1/2$
$2/3$
25
Given sets $A = \\{1, 3, 5, 7\\}$ and $B = \\{5, 7, 9, 11\\}$. What is the intersection $A \cap B$?
$\\{1, 3, 5, 7, 9, 11\\}$
$\\{1, 3, 9, 11\\}$
$\\{5, 7\\}$
$\\{1, 3\\}$
26
In a class of $30$ students, $18$ study Math (M) and $15$ study Science (S). If $5$ students study neither subject, how many students study both Math and Science?
3
8
13
23
27
A car travels $300 \text{ km}$ at an average speed of $60 \text{ km/h}$. How long did the journey take?
$4 \text{ hours}$
$5 \text{ hours}$
$6 \text{ hours}$
$50 \text{ hours}$
28
A runner completes a $1000 \text{ m}$ race. They run the first $600 \text{ m}$ at $5 \text{ m/s}$ and the remaining distance at $4 \text{ m/s}$. What is the average speed for the entire race?
$4.5 \text{ m/s}$
$50/11 \text{ m/s}$
$4.8 \text{ m/s}$
$4.0 \text{ m/s}$
29
Find the equation of a line perpendicular to $2x - 3y = 5$ that passes through the point $(4, 1)$.
$3x + 2y = 14$
$2x - 3y = 5$
$3x - 2y = 10$
$2x + 3y = 11$
30
If the equation $3(x - 2) + kx = 10$ has the solution $x = 4$, what is the value of $k$?
$k = 1$
$k = 3$
$k = 4$
$k = -2$
31
Solve the simultaneous inequality system: $2x - 3 > 5$ and $4 - x \geq -3$.
$4 < x \leq 7$
$x > 4$
$x \leq 7$
$4 \leq x < 7$
32
The perimeter of a rectangle must be no more than $40 \text{ cm}$. If the length $L$ is three times the width $W$, find the maximum possible integer value for the width $W$.
$W = 4$
$W = 5$
$W = 6$
$W = 7$
33
A line segment has endpoints $A(-2, 5)$ and $B(x, y)$. If the midpoint $M$ is $(1, 2)$, what is the distance $AB$?
$6\sqrt{2} \text{ units}$
$\sqrt{52} \text{ units}$
$10 \text{ units}$
$\sqrt{68} \text{ units}$
34
What is the area of the triangle formed by the $x$-axis, the $y$-axis, and the line $5x + 2y = 20$?
$20 \text{ square units}$
$10 \text{ square units}$
$40 \text{ square units}$
$50 \text{ square units}$
35
A relation is defined by the set of ordered pairs $\{(-3, 4), (-1, 0), (0, 4), (2, 8)\}$. If a new pair $(k, 5)$ is added such that the resulting set is still a function, which value of $k$ is NOT allowed?
$k = -3$
$k = 5$
$k = 1$
$k = 3$
36
Simplify the expression: $\frac{18x^{-3}y^4}{(3x^2y^{-1})^2}$.
$2x^{-7}y^6$
$6x^{-7}y^6$
$2x^{-1}y^5$
$\frac{2y^2}{x^7}$
37
If $4\sqrt{27} - \sqrt{48} = k\sqrt{3}$, what is the value of $k$?
$k = 8$
$k = 16$
$k = 20$
$k = 4$
38
Solve for $n$: $2^{2n+1} \cdot 4^n = \frac{1}{16}$.
$n = -5/4$
$n = -1$
$n = -3/2$
$n = -2$
39
If $A$ is inversely proportional to $B$, and $A=6$ when $B=4$, what is the value of $A$ when $B=1.5$?
$A = 16$
$A = 9$
$A = 24$
$A = 4$
40
A shopkeeper marks up a product by $40\%$ on the cost price. If the shopkeeper then offers a $10\%$ discount on the marked price, what is the overall profit percentage?
$26\%$
$30\%$
$36\%$
$4\%$
41
A principal of $\$5000$ is invested at $8\%$ p.a. compounded quarterly. What is the value of the investment after 9 months? (Round to the nearest cent.)
$\$5306.04$
$\$5300.00$
$\$5308.23$
$\$5400.00$
42
A design consists of a rectangle $8 \text{ cm} \times 6 \text{ cm}$ with two semicircles of diameter $6 \text{ cm}$ attached to the $6 \text{ cm}$ sides. What is the total area of the design? (Use $\pi \approx 3.14$)
$76.26 \text{ cm}^2$
$48.00 \text{ cm}^2$
$66.84 \text{ cm}^2$
$57.42 \text{ cm}^2$
43
A tank holds $450 \text{ litres}$ of water. If water flows out at a rate of $25 \text{ millilitres}$ per second, how long (in hours) will it take for the tank to empty completely? (Round to the nearest whole hour.)
$5 \text{ hours}$
$3 \text{ hours}$
$8 \text{ hours}$
$7 \text{ hours}$
44
A cuboid has dimensions $4 \text{ cm}$ by $3 \text{ cm}$ by $12 \text{ cm}$. What is the length of the longest internal diagonal?
$13 \text{ cm}$
$17 \text{ cm}$
$\sqrt{225} \text{ cm}$
$15 \text{ cm}$
45
An isosceles triangle has two sides of length $13 \text{ cm}$ and a base of $10 \text{ cm}$. What is its area?
$60 \text{ cm}^2$
$65 \text{ cm}^2$
$120 \text{ cm}^2$
$30 \text{ cm}^2$
46
In a right-angled triangle, the hypotenuse is $15 \text{ units}$ and one acute angle is $37^\circ$. What is the length of the side adjacent to the $37^\circ$ angle, rounded to two decimal places?
$11.98 \text{ units}$
$9.03 \text{ units}$
$10.51 \text{ units}$
$11.23 \text{ units}$
47
A person standing $50 \text{ m}$ away from the base of a tower measures the angle of elevation to the top of the tower as $28^\circ$. How tall is the tower (to the nearest meter)?
$27 \text{ m}$
$23 \text{ m}$
$44 \text{ m}$
$15 \text{ m}$
48
A bag contains 5 red balls and 3 blue balls. If two balls are drawn without replacement, what is the probability that they are of different colors?
$\frac{15}{28}$
$\frac{13}{28}$
$\frac{15}{32}$
$\frac{5}{14}$
49
The probability of rain on Monday is $0.6$, and the probability of rain on Tuesday is $0.4$. Assuming the weather on these two days is independent, what is the probability that it rains on exactly one of the two days?
$0.52$
$0.48$
$0.24$
$1.00$
50
Two pipes fill a tank. Pipe A alone takes 6 hours to fill the tank. Pipe B alone takes 9 hours. If both pipes are opened simultaneously, how long (in minutes) will it take to fill $\frac{2}{3}$ of the tank?
$144 \text{ minutes}$
$150 \text{ minutes}$
$100 \text{ minutes}$
$180 \text{ minutes}$
51
If the universal set $U = \\{1, 2, 3, 4, 5, 6, 7, 8, 9\\}$, $A = \\{1, 3, 5, 7, 9\\}$ and $B = \\{2, 3, 5, 8\\}$, what is the cardinality of the set $A \cup B$?
$7$
$9$
$6$
$2$
52
In a class of 30 students, 18 study Mathematics ($M$), 15 study Science ($S$), and 7 study neither. How many students study both Mathematics and Science?
$10$
$23$
$7$
$5$
53
A car travels $120 \text{ km}$ at an average speed of $80 \text{ km/h}$. It then travels $100 \text{ km}$ at $50 \text{ km/h}$. What is the average speed for the entire $220 \text{ km}$ journey, rounded to two decimal places?
$62.86 \text{ km/h}$
$65.00 \text{ km/h}$
$60.00 \text{ km/h}$
$63.33 \text{ km/h}$
54
Train A leaves Station P at $10:00 \text{ am}$ traveling towards Station Q at $60 \text{ km/h}$. Train B leaves Station Q at $10:00 \text{ am}$ traveling towards Station P at $90 \text{ km/h}$. If the distance between P and Q is $300 \text{ km}$, at what time do they meet?
$12:00 \text{ pm}$
$11:30 \text{ am}$
$12:30 \text{ pm}$
$1:00 \text{ pm}$
55
For the linear function $f(x) = mx + c$, if $f(2) = 7$ and $f(5) = 16$, what is the value of $f(-1)$?
$-2$
$1$
$4$
$-5$
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