Multiple Choice

1. Evaluate the following expression: $\frac{-4 [3 - 2(5 - 9) + 1]}{8}$.

   $6$

   $-4$

   $-6$

   $10$

2. If $x = -2$ and $y = 3$, what is the value of the expression $3x^2 - 4(y - x)$?

   $4$

   $-8$

   $-16$

   $28$

3. When an unknown integer $N$ is multiplied by $-5$ and the result is then reduced by $12$, the final value is $18$. Determine the value of $N$.

   $-6$

   $-10$

   $6$

   $-4$

4. Evaluate the expression: $\frac{48}{-6} \times (-2 - 5) - (-10)$.

   $66$

   $46$

   $-54$

   $2$

5. Identify the statement below that is mathematically true.

   The expression $-3^2 + 10$ evaluates to $19$.

   $15 - [20 \div (-4) - 1] = 20$.

   If you calculate $(5 - 10) \times 4 \div 2$, the result is $10$.

   $-2(1 - 6) + 5 = 15$

6. Calculate the exact value of the expression: $3 \frac{1}{2} \div \left(1 \frac{1}{4} - \frac{5}{6}\right)$.

   $8 \frac{2}{5}$

   $16 \frac{4}{5}$

   $1 \frac{29}{30}$

   $7 \frac{4}{5}$

7. Evaluate the following expression using the correct order of operations (BIDMAS): $\frac{2}{5} + 2 \times \left(\frac{1}{2}\right)^2 - \frac{1}{10}$.

   $\frac{1}{2}$

   $\frac{7}{10}$

   $\frac{13}{10}$

   $\frac{4}{5}$

8. Simplify the expression: $3x + 10 - 5x + 7 - 2$.

   $8x + 15$

   $2x + 15$

   $-2x + 9$

   $-2x + 15$

9. Simplify the following expression by combining all like terms: $8a - 3b + 4a - 1b - 12a + 7b$.

   $24a + 11b$

   $12a + 4b$

   $3b - 8a$

   $3b$

10. Simplify the expression: $4y + 5x - 1 - 2y + 8 - 3x + 5y$.

    $2x + 7y + 7$

    $15xy + 7$

    $2x + 7y - 9$

    $8x + 7y + 7$

11. Simplify the algebraic expression: $-15k + 20 + 7k - 5 - 10k$.

    $-8k + 15$

    $-18k + 15$

    $-28k + 15$

    $-18k + 25$

12. Simplify the expression: $12m^2 + 6m - 4m^2 + 9 - 10m + 1$.

    $8m^2 - 16m + 10$

    $8m^2 + 16m + 8$

    $16m^2 + 4m + 10$

    $8m^2 - 4m + 10$

13. Simplify the expression $4(2x + 1) + 5x - 8 - 3x$.

    $10x - 3$

    $10x - 4$

    $10x + 12$

    $6x - 4$

14. Expand and simplify the expression $(5a + 6b - 2) - (2a - 4b + 1)$.

    $7a + 2b - 3$

    $3a + 10b - 1$

    $3a + 10b - 3$

    $3a + 2b - 3$

15. Simplify the expression $2(3k - 1) + 5k - 4(k + 3) + 10$.

    $7k - 14$

    $15k - 4$

    $7k - 4$

    $7k + 0$

16. Combine the like terms in the expression $-3m + 8n + 15 - 5m - 10n + 6m - 1$.

    $8m - 2n + 14$

    $-2m + 18n + 14$

    $-8m - 2n + 14$

    $-2m - 2n + 14$

17. Solve the equation for $x$: $3x + 7 - x = 15$.

    $x = 4$

    $x = 6$

    $x = 2$

    $x = 8$

18. Find the value of $y$ that satisfies the equation: $2(y - 5) + 3 = 19$.

    $y = 9$

    $y = 11$

    $y = 18$

    $y = 13$

19. What is the solution for $k$ in the equation $5k - 8 = 2k + 1$?

    $k = 3$

    $k = -3$

    $k = 4$

    $k = 1$

20. Solve for $z$: $4(z + 1) = z + 10$.

    $z = 2$

    $z = 3$

    $z = 6$

    $z = 1.5$

21. Sarah needs $\$150$ to buy a new bike. She currently has $\$85$. If $x$ represents the amount of money Sarah still needs, which equation correctly models this situation?

    $85 + x = 150$

    $150 - 85 = x + 1$

    $150 + x = 85$

    $150x = 85$

22. A farmer harvested $144$ apples. He wants to pack them into $x$ boxes, with exactly $12$ apples in each box. Which equation can be used to find $x$, the number of boxes?

    $144 + 12 = x$

    $144 - x = 12$

    $12x = 144$

    $x + 12 = 144$

23. A taxi service charges a flat fee of $\$3$ for pickup plus $\$0.50$ for every kilometre traveled, $m$. If the total cost of a ride was $\$9$, which equation represents this situation?

    $3 + 9m = 0.50$

    $3m + 0.50 = 9$

    $3 + 0.50m = 9$

    $(3 + 0.50)m = 9$

24. Liam is $3$ years older than his sister, Maya. If the sum of their ages is $21$, and Maya's age is represented by $m$, which equation can be used to find Maya's age?

    $m + 3 = 21$

    $2m + 3 = 21$

    $3m = 21$

    $m + (m - 3) = 21$

25. After tripling the number of baseball cards he owned and then giving $7$ cards away, Ken had $29$ cards remaining. If $c$ represents the number of cards Ken started with, what is $c$?

    $10$

    $36$

    $8$

    $12$

26. A recipe requires $180$ grams of flour and $120$ grams of sugar. What is the ratio of flour to sugar, expressed in its simplest form?

    $4:3$

    $3:2$

    $2:3$

    $18:12$

27. The ratio of fiction books to non-fiction books in a library section is $4:7$. If there are $56$ non-fiction books, how many fiction books are there?

    $98$

    $14$

    $32$

28. Daniel and Emily share a bag of $84$ marbles in the ratio $5:2$, respectively. How many more marbles does Daniel have than Emily?

    $24$

    $12$

    $36$

    $60$

29. A school organized a trip where the ratio of teachers to students was $1:15$. If there were $6$ teachers who attended the trip, what was the total number of people (teachers and students) on the trip?

    $105$

    $90$

    $96$

30. A grocery store sells two types of coffee beans. Brand X costs $\$ 15.00$ for $3$ pounds. Brand Y costs $\$ 24.00$ for $5$ pounds. Which brand has the lower unit rate per pound?

    Brand Y; $\$ 4.80$ per pound

    Brand X; $\$ 4.80$ per pound

    Brand X; $\$ 5.00$ per pound

    Brand Y; $\$ 5.00$ per pound

31. A class has $40$ students. If $30$ students passed the math test, what percentage of the students passed the test?

    $70\%$

    $80\%$

    $65\%$

    $75\%$

32. A survey showed that $45\%$ of the $180$ respondents preferred cycling. How many respondents preferred cycling?

    $72$

    $81$

    $99$

    $90$

33. Last month, the price of a novel was $\$25$. This month, the price increased to $\$30$. What is the percent increase in the price?

    $5\%$

    $20\%$

    $25\%$

    $15\%$

34. A sporting goods store is offering a $35\%$ discount on all soccer balls priced at $\$60$. What is the amount of the discount (in dollars)?

    $\$39.00$

    $\$24.00$

    $\$15.00$

    $\$21.00$

35. A jeweler bought a watch for $\$80$ and decided to apply a $15\%$ markup before selling it. What is the final selling price of the watch?

    $\$95.00$

    $\$90.00$

    $\$81.50$

    $\$92.00$

36. Maria bought a jacket for $\$45$ during a sale. The sale offered a $25\%$ discount off the original price. What was the original price of the jacket?

    $\$60.00$

    $\$56.25$

    $\$63.00$

    $\$60.45$

37. The total cost of groceries, including an $8\%$ sales tax, was $\$108.00$. What was the cost of the groceries before the sales tax was applied?

    $\$100.08$

    $\$99.36$

    $\$104.00$

    $\$100.00$

38. The Pythagorean Theorem states that for any right-angled triangle, the square of the hypotenuse ($c$) is equal to the sum of the squares of the two legs ($a$ and $b$). Which equation correctly represents this relationship?

    $a^2 + b^2 = c$

    $a^2 * b^2 = c^2$

    $a + b = c$

    $a^2 + b^2 = c^2$

39. In a right-angled triangle, the legs measure 9 cm and 12 cm. What is the length of the hypotenuse?

    21 cm

    14 cm

    15 cm

    144 cm

40. The hypotenuse of a right triangle measures 25 inches, and one leg measures 7 inches. What is the length of the missing leg?

    18 inches

    26 inches

    24 inches

    $\sqrt{674}$ inches

41. In the equation $a^2 + b^2 = c^2$, the side labeled $c$ must always be located opposite which part of the triangle?

    One of the acute angles

    The right angle

    The shortest leg

    The side labeled $a$

42. Which of the following sets of numbers forms a Pythagorean Triple? (A set where $a^2 + b^2 = c^2$ uses integers.)

    4, 5, 6

    6, 7, 10

    5, 12, 13

    7, 8, 12

43. A builder needs to check if a corner wall forms a perfect right angle. She measures 6 feet along one wall and 8 feet along the adjacent wall. What should the diagonal distance between those two measured points be if the corner is exactly 90 degrees?

    100 feet

    10 feet

    14 feet

    48 feet

44. A flag pole 15 feet tall is supported by a wire anchored 8 feet away from the base of the pole on the ground. Assuming the pole is perfectly vertical, what is the length of the support wire (the hypotenuse)?

    18 feet

    23 feet

    289 feet

    17 feet

45. What is the resulting number when you square the number 11?

    121

    22

    1

    110

46. A rectangular swimming pool is 8 meters wide and 15 meters long. If a swimmer swims diagonally from one corner to the opposite corner, how far do they swim?

    16 meters

    17 meters

    23 meters

    120 meters

47. Determine if a triangle with side lengths 6, 8, and 12 is a right-angled triangle using the Converse of Pythagoras ($a^2 + b^2 = c^2$).

    No, because $6^2 + 8^2 = 100$, and $12^2 = 144$, which means $100 \neq 144$.

    Yes, because $6^2 + 8^2 = 12^2$.

    Yes, because $6+8$ is close to 12.

    No, because 12 is the largest side.

48. Which of the following questions is a statistical question?

    How many text messages do Grade 7 students typically send in a day?

    What time did the bus arrive today?

    What is the favorite color of Ms. Smith?

    How tall is the principal of the school?

49. A survey wants to determine the average number of hours Grade 7 students in Texas spend on homework weekly. A researcher surveys $100$ randomly selected Grade 7 students across $5$ different schools in Texas. What is the population for this study?

    The $100$ randomly selected Grade $7$ students.

    All students in Texas.

    All Grade $7$ students in Texas.

    The $5$ different schools in Texas.

50. The principal wants to know the average number of books read last summer by the $450$ students at Northwood Middle School. She surveys $45$ students whose names were drawn from a hat. What is the sample in this scenario?

    All students who read books last summer.

    The $450$ students at Northwood Middle School.

    The principal of the school.

    The $45$ students whose names were drawn from a hat.

51. Five students reported the number of pets they own: $1, 3, 0, 4, 2$. What is the mean number of pets owned by these students?

    $10$

    $2$

    $1.5$

    $2.5$

52. Calculate the median for the following data set representing daily high temperatures (in degrees Celsius): $18, 25, 20, 15, 22, 25$.

    $21$

    $25$

    $20$

    $21.5$

53. A track team recorded the following times (in seconds) for a $100$-meter sprint: $12.3, 11.9, 13.1, 12.0$. What is the range of these times?

    $1.2$ seconds

    $1.0$ seconds

    $0.8$ seconds

    $13.1$ seconds

54. A company wants to randomly select $50$ employees from a list of $1000$. They assign each employee a number and use a random number generator to select the $50$ numbers. What type of sampling method is this?

    Stratified sampling

    Simple random sampling

    Systematic sampling

    Convenience sampling

55. A quality control inspector checks products coming off an assembly line. He decides to check every $20^{th}$ item produced, starting with the third item. What type of sampling method is the inspector using?

    Stratified sampling

    Systematic sampling

    Cluster sampling

    Simple random sampling

56. A school wants to survey $10\%$ of its students. They separate the student body into three groups (Grade 6, Grade 7, Grade 8) and then take a $10\%$ random sample from *each* grade level. What sampling technique is this?

    Systematic sampling

    Simple random sampling

    Convenience sampling

    Stratified sampling

57. A local newspaper asks readers to call a phone number or vote online to share their opinion on a new local tax bill. What type of bias is most likely present in the collected data?

    Voluntary response bias

    Systematic bias

    Undercoverage bias

    Response bias

58. Find the Interquartile Range (IQR) for the following data set: $10, 12, 14, 15, 18, 20, 25$.

    $10$

    $8$

    $9$

    $15$

59. A data set lists test scores: $80, 85, 90, 95, 100$. A new score, $40$, is added. How does the addition of the score $40$ primarily affect the mean and the median?

    The mean will increase, but the median will decrease.

    Both the mean and the median will increase significantly.

    The mean will decrease significantly, while the median changes less.

    The median will decrease significantly more than the mean.

60. The Mean Absolute Deviation (MAD) for the number of goals scored by Team A is $1.5$ goals, and the MAD for Team B is $0.5$ goals. What does this indicate about the teams' scoring consistency?

    Team A has a higher average number of goals than Team B.

    Team B's scoring is more consistent (less variable) than Team A's scoring.

    Team A has a higher range of goals than Team B.

    Team B scored more goals overall during the season.