Multiple Choice

1. Evaluate: $25 - [3 \times (-4) + (20 \div (-5))^2] - 10$.

   $11$

   $12$

   $-7$

   $5$

2. The line passing through points $(p, 7)$ and $(6, 11)$ has a slope of $\frac{4}{3}$. Find the value of $p$.

   $3$

   $2$

   $3$

   $5$

3. A group of 70 students were surveyed about their favourite subjects. 35 liked Math, 42 liked Science, and 18 liked both. How many students liked neither Math nor Science?

   $11$

   $11$

   $15$

   $13$

4. Solve the inequality: $3(2x - 5) - 4x \ge 7x + 10$.

   $x \ge -5$

   $x \le -1$

   $x \le -5$

   $x \le -5$

5. A shop bought an item for $\$120$ and marked it up by $40\%$. During a sale, they offered a $25\%$ discount on the marked price. What was the final selling price of the item?

   $\$108$

   $\$126$

   $\$132$

   $\$112$

6. The ratio of boys to girls in a class is $5\!:\!3$. If 12 more girls join the class, the new ratio of boys to girls becomes $5\!:\!6$. How many students were originally in the class?

   $24$

   $32$

   $32$

   $40$

7. A car travels at an average speed of $80 \text{ km/h}$ for the first $120 \text{ km}$ of a journey. It then travels at $60 \text{ km/h}$ for the remaining $180 \text{ km}$. What is the average speed of the car for the entire journey?

   $\dfrac{200}{3}\ \text{km/h}$

   $72 \text{ km/h}$

   $70 \text{ km/h}$

   $68 \text{ km/h}$

8. A rectangular garden has a perimeter of $40 \text{ meters}$. If the length is $4 \text{ meters}$ more than the width, what is the area of the garden?

   $96 \text{ m}^2$

   $100 \text{ m}^2$

   $84 \text{ m}^2$

   $92 \text{ m}^2$

9. A line passes through $(2, -3)$ and is parallel to the line $y = \frac{1}{2}x + 5$. Find the equation of this line.

   $y = \frac{1}{2}x - 2$

   $y = -\frac{1}{2}x - 2$

   $y = 2x - 7$

   $y = \frac{1}{2}x - 4$

10. In a survey of 100 people, 55 read newspaper A, 45 read newspaper B, and 20 read neither. How many people read exactly one newspaper?

    $70$

    $55$

    $80$

    $60$

11. Simplify the expression: $\frac{3}{4} + \frac{1}{3} \times \left( \frac{5}{2} - \frac{1}{6} \right)$.

    $\frac{7}{4}$

    $\frac{17}{12}$

    $\frac{55}{36}$

    $\frac{11}{6}$

12. Simplify: $\frac{(x^3 y^{-2})^4}{(x^{-2} y^5)^{-1}}$.

    $x^{10} y^{-3}$

    $x^{14} y^{-3}$

    $x^{10} y^{13}$

    $x^{14} y^{-13}$

13. A rectangular field has a length that is twice its width. If the length is increased by $5 \text{ meters}$ and the width is decreased by $2 \text{ meters}$, the area remains the same. What was the original area of the field?

    $150 \text{ m}^2$

    $100 \text{ m}^2$

    $120 \text{ m}^2$

    $200 \text{ m}^2$

14. If $A = \{x \in \mathbb{Z} \mid -3 < x \le 2\}$ and $B = \{x \in \mathbb{N} \mid x \le 4\}$, find the number of elements in $A \cup B$. ($\mathbb{Z}$ is integers, $\mathbb{N}$ is natural numbers starting from 1).

    $8$

    $7$

    $9$

    $6$

15. Solve for $x$: $7 - 2(3x - 1) < 4x + 15$.

    $x > -\frac{3}{5}$

    $x > -1$

    $x > -0.5$

    $x < -1$

16. A jacket is on sale for $30\%$ off its original price. If the sale price is $\$84$, what was the original price?

    $\$105$

    $\$109.20$

    $\$117.60$

    $\$120$

17. Two towns, A and B, are $300 \text{ km}$ apart. A cyclist leaves town A travelling towards town B at $20 \text{ km/h}$. At the same time, another cyclist leaves town B travelling towards town A at $30 \text{ km/h}$. How far from town A will they meet?

    $100 \text{ km}$

    $120 \text{ km}$

    $150 \text{ km}$

    $180 \text{ km}$

18. The sum of three consecutive odd integers is $207$. What is the largest of these integers?

    $69$

    $73$

    $67$

    $71$

19. A line passes through the points $(-1, 5)$ and $(3, k)$. If the slope of the line is $-2$, what is the value of $k$?

    $13$

    $7$

    $1$

    $-3$

20. In a class of 30 students, 18 play football, 15 play basketball, and 8 play both. How many students play exactly one sport?

    $18$

    $22$

    $17$

    $25$

21. What is $1 \frac{1}{2}$ divided by $\left( \frac{3}{4} - \frac{1}{3} \right)$?

    $\dfrac{9}{2}$

    $\dfrac{2}{3}$

    $\dfrac{18}{5}$

    $\dfrac{13}{5}$

22. Simplify: $(2x^2 y^3)^3 \times (x^{-1} y^2)^{-2}$.

    $8x^8 y^{13}$

    $8x^8 y^5$

    $8x^6 y^5$

    $8x^4 y^{13}$

23. A sum of money is divided between A, B, and C in the ratio $2\!:\!3\!:\!5$. If C receives $\$150$ more than A, what is the total sum of money?

    $\$300$

    $\$250$

    $\$450$

    $\$500$

24. If $P = \{ \text{prime numbers less than 15} \}$ and $Q = \{ \text{odd numbers less than 12} \}$, find $P \cap Q$.

    $\{3, 5, 7, 11\}$

    $\{3, 5, 7, 13\}$

    $\{2, 3, 5, 7, 11, 13\}$

    $\{1, 3, 5, 7, 11, 13\}$

25. Which of the following numbers is a solution to $5(x+2) - 3x \le 12$ and $2x+1 > -3$?

    $0$

    $1.5$

    $-3$

    $2$

26. A store offers a $20\%$ discount on all items. If a customer has a coupon for an additional $10\%$ off the discounted price, what is the total percentage discount the customer receives?

    $32\%$

    $29\%$

    $30\%$

    $28\%$

27. A car travels $150 \text{ km}$ at a speed of $x \text{ km/h}$. If it had travelled $10 \text{ km/h}$ faster, it would have saved $30 \text{ minutes}$. What is the value of $x$?

    $60 \text{ km/h}$

    $50 \text{ km/h}$

    $75 \text{ km/h}$

    $40 \text{ km/h}$

28. The product of two consecutive positive even integers is $168$. What is the sum of these integers?

    $24$

    $28$

    $22$

    $26$

29. A line segment connects the points $(1, -2)$ and $(5, 6)$. What is the slope of a line perpendicular to this segment?

    $-2$

    $2$

    $\dfrac{1}{2}$

    $-\dfrac{1}{2}$

30. In a class of 40 students, 25 play football and 18 play hockey. If 5 students play neither sport, how many students play both football and hockey?

    $3$

    $8$

    $13$

    $10$

31. Evaluate: $\dfrac{5}{6} \times \left( \dfrac{1}{2} + \dfrac{2}{3} \right) - \dfrac{1}{4}$.

    $\dfrac{5}{6}$

    $\dfrac{1}{3}$

    $\dfrac{13}{18}$

    $\dfrac{23}{24}$

32. If $m = 2^{-3}$ and $n = (2^2)^{-1}$, what is the value of $\dfrac{m}{n}$?

    $2$

    $1/2$

    $4$

    $1/4$

33. An item's price increased by $20\%$ and then decreased by $20\%$. If the final price is $\$480$, what was the original price?

    $\$480$

    $\$460$

    $\$500$

    $\$520$

34. Set $A = \{x \mid x \text{ is an integer, } -5 < x \le 1\}$ and Set $B = \{x \mid x \text{ is an even integer, } -2 \le x < 4\}$. Find the number of elements in $A \cap B$.

    $3$

    $4$

    $5$

    $2$

35. Solve for $x$: $\dfrac{x}{3} - \dfrac{x-1}{2} \ge 1$.

    $x \le -3$

    $x \ge 3$

    $x \ge -3$

    $x \le 3$

36. A rectangular field has a perimeter of $72 \text{ m}$. If its length is $6 \text{ m}$ less than twice its width, what is the width of the field?

    $12 \text{ m}$

    $15 \text{ m}$

    $18 \text{ m}$

    $14 \text{ m}$

37. Two runners are $100 \text{ meters}$ apart. They start running towards each other. Runner A runs at $6 \text{ m/s}$ and Runner B runs at $4 \text{ m/s}$. How long will it take for them to meet?

    $8 \text{ seconds}$

    $15 \text{ seconds}$

    $10 \text{ seconds}$

    $12 \text{ seconds}$

38. The temperature at 6 AM was $-5^\circ \text{C}$. By noon, it had risen to $7^\circ \text{C}$. What was the average rate of temperature increase per hour?

    $2.5^\circ \text{C/hour}$

    $1^\circ \text{C/hour}$

    $1.5^\circ \text{C/hour}$

    $2^\circ \text{C/hour}$

39. Simplify: $\left( \dfrac{a^5 b^{-2}}{a^{-3} b^4} \right)^{-2}$.

    $\dfrac{a^{12}}{b^{16}}$

    $\dfrac{a^{16}}{b^{12}}$

    $a^{16} b^{12}$

    $\dfrac{b^{12}}{a^{16}}$

40. In a survey, $40\%$ of people prefer tea, $30\%$ prefer coffee, and $15\%$ prefer both. What percentage of people prefer neither tea nor coffee?

    $40\%$

    $50\%$

    $30\%$

    $45\%$