Multiple Choice

1. Calculate the value of the expression: $15 - 3 \times (-4) + (18 \div 6)^2$.

   $30$

   $21$

   $36$

   $33$

2. Evaluate the expression: $\frac{1}{2} + (\frac{3}{4} - \frac{1}{8}) \times 4$.

   $3$

   $2\frac{1}{4}$

   $2\frac{1}{2}$

   $3\frac{1}{8}$

3. Simplify the expression: $-10 + 2 \times [5 - 3 \times (7 - 9)]$.

   $-4$

   $8$

   $24$

   $12$

4. A recipe uses flour and sugar in the ratio $5:2$. What percentage of the total mix is sugar? (Round to the nearest hundredth of a percent.)

   $28.00\%$

   $20.00\%$

   $25.00\%$

   $28.57\%$

5. Simplify the ratio $1.5$ hours to $45$ minutes in its simplest form.

   $3:1$

   $4:3$

   $1:3$

   $2:1$

6. If $35\%$ of a certain number is $70$, what is the number?

   $175$

   $200$

   $210$

   $245$

7. Simplify the algebraic expression: $5x^2 - 3x + 2 + 7x - x^2$.

   $6x^2 + 4x + 2$

   $5x^2 + 4x + 2$

   $4x^2 + 4x + 2$

   $4x^2 - 10x + 2$

8. Expand and simplify the expression: $4(2y - 3) - 5$.

   $8y + 17$

   $8y - 7$

   $8y - 17$

   $8y - 2$

9. Simplify the expression: $6(a + 2b) - 2(3a - b)$.

   $10b$

   $12a + 14b$

   $14b$

   $14b - a$

10. Simplify the expression: $3pq + 5q^2 - 2pq - 7q^2 + 4$.

    $pq - 12q^2 + 4$

    $pq - 2q^2 + 4$

    $5pq - 2q^2 + 4$

    $pq + 12q^2 + 4$

11. A right-angled triangle has legs of length $5$ cm and $12$ cm. What is the length of the hypotenuse?

    $12.5$ cm

    $13$ cm

    $15$ cm

    $17$ cm

12. If the hypotenuse of a right-angled triangle is $10$ m and one leg is $6$ m, what is the length of the other leg?

    $9$ m

    $16$ m

    $11.6$ m

    $8$ m

13. Find the median of the following data set: $12, 18, 15, 12, 20, 16$.

    $15.5$

    $15$

    $16$

    $15.83$

14. A local council surveys $500$ residents about a new park design. If the entire population of the town is $15,000$, which group represents the population?

    The $15,000$ residents of the town.

    The $500$ residents surveyed.

    The residents who voted in the last election.

    The park visitors.

15. A scientist calculated the mean height of a sample of $100$ sunflowers to be $1.8$ meters. What does the mean primarily represent in this context?

    The middle value when heights are ordered.

    The smallest height in the sample.

    The typical or average height of the sunflowers measured.

    The height that occurs most frequently.

16. A number $n$ is tripled, and then $5$ is subtracted. The result is $19$. What is the value of $n$?

    $42$

    $8$

    $14$

    $7$

17. A rectangle has a length that is $4$ cm longer than its width, $w$. If the perimeter is $40$ cm, what is the width, $w$?

    $8$ cm

    $9$ cm

    $10$ cm

    $12$ cm

18. What is the Greatest Common Factor (GCF) of $24$ and $40$?

    $8$

    $4$

    $120$

    $12$

19. Find the Least Common Multiple (LCM) of $9$ and $15$.

    $90$

    $45$

    $3$

    $135$

20. A car travels $240$ kilometers in $3$ hours. What is its average speed in kilometers per hour (km/h)?

    $60$ km/h

    $80$ km/h

    $70$ km/h

    $120$ km/h

21. A shirt originally costs $\$60$. It is on sale for $25\%$ off. What is the sale price of the shirt?

    $\$45$

    $\$15$

    $\$40$

    $\$35$

22. The price of a movie ticket increased from $\$8.00$ to $\$9.00$. What is the percentage increase?

    $12.5\%$

    $15\%$

    $10\%$

    $8\%$

23. Solve for $x$: $5x + 12 = 37$.

    $7$

    $4.5$

    $10$

    $5$

24. Solve for $y$: $3(y - 4) + 5 = 20$.

    $y=11$

    $y=9$

    $y=7$

    $y=8$

25. Calculate the value of the expression: $-2 + 12 \times (\frac{1}{2})^2 - 5$.

    $-4$

    $1$

    $-6$

    $-12$

26. A group of $\$80$ is divided between two friends in the ratio $3:5$. What percentage of the total amount did the friend with the larger share receive?

    $50\%$

    $60\%$

    $62.5\%$

    $37.5\%$

27. Simplify the algebraic expression: $3(2x - 5) + 4x + 10$.

    $6x - 5$

    $10x + 5$

    $10x - 25$

    $10x - 5$

28. A right-angled triangle has two shorter sides (legs) measuring $6 \text{ cm}$ and $8 \text{ cm}$. Use the Pythagorean theorem to find the length of the hypotenuse.

    $100 \text{ cm}$

    $14 \text{ cm}$

    $10 \text{ cm}$

    $5 \text{ cm}$

29. Calculate the mean (average) of the following data set: $\{5, 9, 12, 16, 3\}$.

    $10$

    $12$

    $8$

    $9$

30. Three times a number, $n$, decreased by $7$ is equal to $20$. Which equation represents this problem, and what is the value of $n$?

    $3n - 7 = 20$, $n=9$

    $3(n - 7) = 20$, $n = 7$

    $3n - 7 = 20$, $n=4$

    $3n = 20 + 7$, $n=27$

31. Find the Least Common Multiple (LCM) of $12$ and $18$.

    $6$

    $36$

    $216$

    $72$

32. A car travels a distance of $180 \text{ km}$ in $3$ hours. What is the car's average rate of speed in meters per minute?

    $1,000 \text{ meters per minute}$

    $1,800 \text{ meters per minute}$

    $300 \text{ meters per minute}$

    $60 \text{ meters per minute}$

33. Solve the following linear equation for $x$: $\frac{x}{3} + 5 = 11$.

    $x = 48$

    $x = 16$

    $x = 18$

    $x = 2$

34. A right-angled triangle has a hypotenuse of length $13$ and one leg of length $5$. What is the length of the other leg?

    $8$

    $18$

    $12$

    $16$

35. A survey researcher is studying the average height of students at a school with $500$ students. She measures the height of $100$ randomly selected students. What term best describes the $100$ students whose heights were measured?

    The sample

    The population

    The median

    The control group

36. Simplify the algebraic expression by combining like terms: $7a - 3b + 2a + 8b$.

    $17ab$

    $9a + 5b$

    $5a + 5b$

    $9a + 11b$

37. A jacket is originally priced at $\$40$. If the store offers a $20\%$ discount, what is the new price of the jacket?

    $\$32$

    $\$36$

    $\$8$

    $\$20$

38. Solve the multi-step linear equation for $y$: $2(y + 4) = 20$.

    $y = 8$

    $y = 7$

    $y = 6$

    $y = 12$