Multiple Choice

1. Calculate the value of: $-15 + 3 \times (-4) \div 2 - (-8)$

   $-21$

   $-13$

   $-10$

   $13$

2. Evaluate: $5 - [12 \div (2 - 5) + 7]$

   $-6$

   $0$

   $16$

   $2$

3. What is the value of $24 \div (-3) + 7 \times (1 - 5)$?

   $-36$

   $-44$

   $20$

   $-20$

4. Simplify: $-9 \times (-2) - 40 \div (-8) + (-7)$

   $30$

   $16$

   $6$

   $18$

5. If $a = -3$, $b = 4$, and $c = -2$, find the value of $(ab - c) \div (a + b)$.

   $14$

   $-10$

   $10$

   $-14$

6. Simplify the expression: $7x - 4y + 2 - 3x + 9y - 6$

   $4x + 5y - 4$

   $4x - 5y - 4$

   $4x + 13y - 4$

   $10x + 5y - 4$

7. Combine like terms: $12ab - 5a + 7b - 3ab + 2a - 10b$

   $15ab - 3a - 3b$

   $9ab + 3a + 3b$

   $9ab - 3a - 3b$

   $9ab - 7a - 17b$

8. Simplify: $- (2m + 5) + 8m - 3 + 4m$

   $10m + 2$

   $10m - 8$

   $10m - 2$

   $6m - 8$

9. What is the simplified form of: $5p^2 + 3q - 2p^2 + q - 7$

   $5p^2 + 4q - 7$

   $3p^2 + 4q - 7$

   $7p^2 + 4q - 7$

   $3p^2 + 3q - 7$

10. If $A = 6x - 2y$ and $B = -3x + 5y$, find $A - B$.

    $3x + 3y$

    $9x - 7y$

    $3x - 7y$

    $9x + 3y$

11. Solve for x: $3x - 7 = 2x + 5$

    $x = -2$

    $x = 12$

    $x = 10$

    $x = 2$

12. Solve: $-5y + 12 = 2y - 9$

    $y = 3$

    $y = 7$

    $y = -7$

    $y = -3$

13. If $4x + 3 = 2x + 17$, find x.

    $x = 14$

    $x = 10$

    $x = 7$

    $x = -7$

14. Solve for y: $12 - 4y = 28$

    $y = 4$

    $y = 10$

    $y = -10$

    $y = -4$

15. If $(x/5) + 3 = 10$, what is the value of x?

    $x = 14$

    $x = 25$

    $x = 50$

    $x = 35$

16. Find the value of m: $-6m + 10 = -8$

    $m = -3$

    $m = -18$

    $m = 18$

    $m = 3$

17. What is the expanded and simplified form of: $6(p + 2q) - 3(2p - q)$?

    $-9q$

    $9q$

    $15q$

    $12p + 15q$

18. Expand and simplify: $-4(2a - 3b) + 5(a + b)$

    $-3a - 7b$

    $-3a + 7b$

    $13a + 17b$

    $-3a + 17b$

19. Which of the following is equal to $3(x - 4) + 2(x + 5)$?

    $5x - 22$

    $5x + 2$

    $5x + 1$

    $5x - 2$

20. Simplify completely: $-2(3y - 7) + 4(y + 5)$

    $-2y - 6$

    $2y + 34$

    $-10y + 34$

    $-2y + 34$

21. A recipe uses flour and sugar in the ratio 5:3. If 20 cups of flour are used, how many cups of sugar are needed?

    $20$

    $15$

    $12$

    $10$

22. The ratio of boys to girls in a class is 7:5. If there are 28 boys, how many girls are there?

    $25$

    $30$

    $20$

    $15$

23. If a map scale is $1:50{,}000$, what real distance does $3\,\text{cm}$ on the map represent (in km)?

    $150\,\text{km}$

    $0.15\,\text{km}$

    $1.5\,\text{km}$

    $15\,\text{km}$

24. A mixture contains red and blue beads in the ratio 4:9. If there are 52 beads in total, how many are red?

    $20$

    $13$

    $36$

    $16$

25. Two numbers are in the ratio 3:8. If their sum is 55, what is the larger number?

    $15$

    $40$

    $45$

    $30$

26. A rectangle has a perimeter of $40\,\text{cm}$. Its length is $3\,\text{cm}$ more than twice its width. Find the width of the rectangle.

    $6\,\text{cm}$

    $\frac{17}{3}\,\text{cm}$

    $5\,\text{cm}$

    $7\,\text{cm}$

27. If a car travels $180\,\text{km}$ in 3 hours, what is its average speed?

    $50\,\text{km}\,\text{per}\,\text{hour}$

    $60\,\text{km}\,\text{per}\,\text{hour}$

    $70\,\text{km}\,\text{per}\,\text{hour}$

    $183\,\text{km}\,\text{per}\,\text{hour}$

28. A tap fills a tank in 6 hours. How much of the tank is filled in 2 hours?

    $\frac{2}{3}$

    $\frac{1}{4}$

    $\frac{1}{3}$

    $\frac{1}{2}$

29. A cyclist covers $45\,\text{km}$ in $1.5\,\text{hours}$. What is the speed in km/h?

    $45\,\text{km}\,\text{per}\,\text{hour}$

    $40\,\text{km}\,\text{per}\,\text{hour}$

    $25\,\text{km}\,\text{per}\,\text{hour}$

    $30\,\text{km}\,\text{per}\,\text{hour}$

30. A car consumes 8 liters of fuel to travel $120\,\text{km}$. What is the fuel efficiency in km per liter?

    $10\,\text{km}\,\text{per}\,\text{liter}$

    $12\,\text{km}\,\text{per}\,\text{liter}$

    $15\,\text{km}\,\text{per}\,\text{liter}$

    $20\,\text{km}\,\text{per}\,\text{liter}$

31. If a runner completes a $400\,\text{m}$ lap in $50\,\text{seconds}$, what is the average speed in m/s?

    $20\,\text{m}\,\text{per}\,\text{s}$

    $8\,\text{m}\,\text{per}\,\text{s}$

    $10\,\text{m}\,\text{per}\,\text{s}$

    $5\,\text{m}\,\text{per}\,\text{s}$

32. A right-angled triangle has legs of length $9\,\text{cm}$ and $12\,\text{cm}$. What is the length of its hypotenuse?

    $15\,\text{cm}$

    $21\,\text{cm}$

    $13\,\text{cm}$

    $10\,\text{cm}$

33. The hypotenuse of a right-angled triangle is $25\,\text{units}$, and one of its legs is $7\,\text{units}$. What is the length of the other leg?

    $18\,\text{units}$

    $24\,\text{units}$

    $20\,\text{units}$

    $26\,\text{units}$

34. A ladder is $10\,\text{meters}$ long and leans against a wall. The base is $6\,\text{meters}$ away from the wall. How high up the wall does the ladder reach?

    $7\,\text{meters}$

    $8\,\text{meters}$

    $12\,\text{meters}$

    $9\,\text{meters}$

35. A rectangular field is $16\,\text{meters}$ long and $12\,\text{meters}$ wide. What is the distance from one corner of the field to the opposite corner?

    $18\,\text{meters}$

    $20\,\text{meters}$

    $28\,\text{meters}$

    $24\,\text{meters}$

36. A TV screen is measured by its diagonal length. If a $32$-inch TV has a diagonal of $32\,\text{inches}$ and a height of $18\,\text{inches}$, what is its approximate width to the nearest inch?

    $28\,\text{inches}$

    $25\,\text{inches}$

    $20\,\text{inches}$

    $26\,\text{inches}$

37. Calculate the value of: $(-7) \times (15 - 9) + 48 \div (-6)$

    $50$

    $-34$

    $-50$

    $40$

38. Evaluate: $25 - [18 + (5 - 9)^2]$

    $3$

    $9$

    $-9$

    $-11$

39. What is the result of $(3^3 - 7) \times (-2) + (-120) \div 4$?

    $-70$

    $-50$

    $10$

    $-10$

40. If $a = -4$ and $b = 5$, what is the numerical value of the expression $(6a - 3b) - (2a + b)$ after simplifying?

    $-40$

    $-32$

    $-36$

    $-26$

41. Evaluate $7x - 2y + x + 5y$ when $x = -3$ and $y = -1$.

    $-21$

    $-29$

    $-30$

    $-27$

42. What is the simplified form of the expression: $-4p + 3q - 2p - 5q + 12$?

    $-2p - 2q + 12$

    $-6p + 8q + 12$

    $-6p - 8q + 12$

    $-6p - 2q + 12$

43. If $5x - 7 = 3x + 9$, solve for x.

    $x = 8$

    $x = 4$

    $x = 1$

    $x = 2$

44. Solve the equation: $-2y + 14 = 4y - 2$.

    $y = 2$

    $y = 3$

    $y = \frac{16}{3}$

    $y = \frac{8}{3}$

45. A and B are variables where $A = 2x - 3y$ and $B = -x + 4y$. Find $A + 2B$.

    $2x + y$

    $5y$

    $-5y$

    $4x + 5y$

46. Simplify the expression: $3a - 2b + 5 - (a + 4b - 7)$

    $2a - 6b + 12$

    $2a - 6b - 2$

    $4a + 2b - 2$

    $2a + 2b - 2$

47. The ratio of red to blue marbles is 5:7. If there are 84 marbles total, how many are red?

    $49$

    $35$

    $28$

    $42$

48. In a class, the ratio of students who like basketball to those who like soccer is 3:4. If 21 students like basketball, how many like soccer?

    $35$

    $24$

    $28$

    $32$

49. A recipe calls for sugar and butter in the ratio 2:5. If $30\,\text{grams}$ of butter are used, how much sugar is needed?

    $20\,\text{grams}$

    $12\,\text{grams}$

    $10\,\text{grams}$

    $15\,\text{grams}$

50. A car travels $150\,\text{km}$ in $2.5\,\text{hours}$. What is the average speed?

    $50\,\text{km}\,\text{per}\,\text{hour}$

    $100\,\text{km}\,\text{per}\,\text{hour}$

    $60\,\text{km}\,\text{per}\,\text{hour}$

    $75\,\text{km}\,\text{per}\,\text{hour}$

51. A pipe can fill a tank in 4 hours. How much of the tank is filled in 45 minutes?

    $\frac{3}{4}$

    $\frac{1}{4}$

    $\frac{1}{2}$

    $\frac{3}{16}$

52. A runner covers $1{,}200\,\text{meters}$ in 4 minutes. What is the average speed in m/s?

    $20\,\text{m}\,\text{per}\,\text{s}$

    $5\,\text{m}\,\text{per}\,\text{s}$

    $10\,\text{m}\,\text{per}\,\text{s}$

    $300\,\text{m}\,\text{per}\,\text{s}$

53. A square has a side length of $10\,\text{cm}$. What is the length of its diagonal?

    $20\,\text{cm}$

    $5\sqrt{2}\,\text{cm}$

    $10\sqrt{2}\,\text{cm}$

    $10\,\text{cm}$

54. A right-angled triangle has a hypotenuse of length $13\,\text{units}$ and one leg of length $12\,\text{units}$. What is the length of the other leg?

    $1\,\text{unit}$

    $7\,\text{units}$

    $5\,\text{units}$

    $10\,\text{units}$

55. The base of a right triangle is $8\,\text{cm}$, and the hypotenuse is $17\,\text{cm}$. Find the height.

    $9\,\text{cm}$

    $13\,\text{cm}$

    $15\,\text{cm}$

    $16\,\text{cm}$

56. A wire is stretched from the top of a $15\,\text{m}$ pole to a point $9\,\text{m}$ from the base. Find the length of the wire.

    $3\sqrt{34}\,\text{m}$

    $24\,\text{m}$

    $12\,\text{m}$

    $18\,\text{m}$

57. The sides of a right triangle are in the ratio 3:4:5. If the hypotenuse is $20\,\text{cm}$, what are the other sides?

    $15\,\text{cm}$ and $20\,\text{cm}$

    $9\,\text{cm}$ and $12\,\text{cm}$

    $12\,\text{cm}$ and $16\,\text{cm}$

    $6\,\text{cm}$ and $8\,\text{cm}$

58. What is the value of: $-48 \div 6 + 2 \times (5 - 9)$

    $0$

    $-24$

    $-8$

    $-16$

59. Evaluate: $18 - 6 \times (4 - 7) + 12 \div (-3)$

    $-4$

    $22$

    $32$

    $18$

60. Compute: $(2^4 - 3^2) \times (-1) + 7$

    $7$

    $0$

    $14$

    $-14$

61. Evaluate: $-3 \times (2 - 7) + 4 \times (-5)$

    $5$

    $-5$

    $-35$

    $35$

62. Calculate: $[10 - 3 \times (8 - 6)] \div 2 - 9$

    $1$

    $-1$

    $7$

    $-7$