Multiple Choice

1. A friend claims that $3/4 \div (1/2 + 1/4)^2 \times 5/3$ simplifies to a value greater than $2$. Are they correct? Justify your answer with calculations.

   No, the simplified value is $15/16$.

   Yes, the simplified value is $20/9$.

   Yes, but the simplified value is $5/3$.

   No, the simplified value is $4/3$.

2. Evaluate $10 - [ 2^3 \div (1/5 \times 20) + 6 ]$.

   $2$

   $12$

   $0$

   $4$

3. Which expression has a greater value? A: $5/2 + 3/2 \times 1/3$ or B: $(5/2 + 3/2) \times 1/3$.

   Expression B is greater.

   Expression B has a value of $4$, which is greater than Expression A's value of $3$.

   Expression A has a value of $3$, which is greater than Expression B's value of $4/3$.

   Both expressions have the same value.

4. Insert brackets into the expression $4 \times 5 + 6 \div 2 - 1$ to make the result equal to $12$.

   $4 \times (5 + 6) \div (2 - 1)$

   $4 \times 5 + (6 \div 2 - 1)$

   $(4 \times 5 + 6) \div 2 - 1$

   $4 \times (5 + 6 \div 2) - 1$

5. A number is increased by $2^3$, then multiplied by $3/4$, and the result is $30$. What was the original number?

   $40$

   $22$

   $32$

   $28$

6. Simplify the expression $3x(x - 2y) - (y - x^2) + 2xy$. What is the coefficient of the $xy$ term?

   $6$

   $4$

   $-4$

   $-2$

7. The area of a rectangle is given by $(5a - 2)(3a + 4)$ and the area of a smaller rectangle is $3a(a-1)$. Find a simplified expression for the remaining area if the smaller rectangle is cut out from the larger one.

   $18a^2 + 17a - 8$

   $12a^2 + 11a - 8$

   $18a^2 + 11a - 8$

   $12a^2 + 17a - 8$

8. If $P = 2x - 3$ and $Q = x + 5$, find an expression for $P^2 - Q$ in its simplest form.

   $4x^2 - 13x + 4$

   $4x^2 - 13x + 14$

   $4x^2 - 11x + 14$

   $4x^2 - 12x + 4$

9. Simplify $5[2(x-1) - 3(x-2)]$.

   $5x + 10$

   $5x + 20$

   $-5x + 20$

   $-5x - 10$

10. The perimeter of a triangle is $15p + 9q$. Two of its sides are $4p + 2q$ and $7p - q$. What is the length of the third side?

    $4p + 8q$

    $11p + q$

    $26p + 8q$

    $4p + 10q$

11. Solve for $x$: $(3x - 1)/4 = (x + 5)/2$.

    $x = 11$

    $x = -9$

    $x = 6$

    $x = 3$

12. Five less than three times a number is the same as the number plus seven. What is the number?

    $6$

    $-1$

    $1$

    $4$

13. Solve the equation $5(a - 3) - 2(a - 4) = 11$.

    $a = 8$

    $a = 4$

    $a = 6$

    $a = 2$

14. The sum of three consecutive odd integers is $81$. What is the largest of these integers?

    $28$

    $27$

    $29$

    $25$

15. Solve for $y$: $0.2(y - 5) = 0.3(y + 2) - 1.2$.

    $y = 1$

    $y = -28$

    $y = -4$

    $y = 28$

16. Simplify $((3a^4b^{-2})/c^3)^{-2}$. Express your answer with only positive exponents.

    $(9a^8b^4)/c^6$

    $(b^4c^6)/(9a^8)$

    $(b^4c^6)/(3a^8)$

    $(9a^8)/(b^4c^6)$

17. Find the value of $x$ if $2^{x-3} \times 2^{x+1} = 64$.

    $x = 2$

    $x = 4$

    $x = 3$

    $x = 5$

18. Which is larger: $(5^2)^3$ or $5^{2^3}$?

    They are equal.

    $5^{2^3}$ is larger.

    It depends on the base.

    $(5^2)^3$ is larger.

19. If $x^2 = 36$ and $y^3 = -27$, what is the maximum possible value of $x-y$?

    $3$

    $-3$

    $9$

    $-9$

20. Simplify $((2x^5y^2)^3)/(4x^7y^9)$.

    $(2x^8)/y^3$

    $2x^8y^3$

    $(8x^8)/y^3$

    $2x^{22}y^{15}$

21. Given $U = \{\text{integers from } 1 \text{ to } 10\}$, $A = \{\text{prime numbers}\} $, and $B = \{\text{even numbers}\}$. What is the set $(A \cup B)'$? ($U$ - Universal Set)

    $\{1, 9\}$

    $\{1\}$

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

    $\{9\}$

22. Let $U = \{\text{letters in the word 'MATHEMATICS'}\} $, $P = \{\text{vowels}\} $, and $Q = \{\text{letters in the word 'STATIC'}\} $. Find $n(P \cap Q')$.

    $0$

    $3$

    $2$

    $1$

23. In a class of $30$ students, $18$ play hockey, $15$ play basketball, and $5$ play neither. How many students play both hockey and basketball?

    $12$

    $5$

    $8$

    $3$

24. Given $U = \{\text{all quadrilaterals}\} $, $S = \{\text{squares}\} $, $R = \{\text{rectangles}\} $, and $P = \{\text{parallelograms}\} $. Which statement is true: (a) $R \subset S$ or (b) $S \subset R$?

    Neither statement is true.

    Both statements are true.

    (b) $S \subset R$ (All squares are rectangles).

    (a) $R \subset S$ (All rectangles are squares).

25. Let $U = \{x \mid x \text{ is an integer, } 0 < x < 12\}$, $A = \{\text{multiples of } 2\}$, $B = \{\text{multiples of } 3\}$. List the elements of the set $(A \setminus B)$.

    $\{2, 4, 8, 10\}$

    $\{2, 4, 6, 8, 10\}$

    $\{6\}$

    $\{3, 9\}$

26. A line passes through the points $(2, 5)$ and $(-1, -4)$. Does this line also pass through the point $(4, 11)$?

    No, it does not.

    Yes, the line passes through $(4, 11)$.

    It is impossible to tell without plotting the points.

    It only passes through points with positive coordinates.

27. What is the equation of a line that is parallel to $y = 2x + 5$ and passes through the $y$-axis at the same point as the line $3x + 2y = 6$?

    $y = 2x + 6$

    $y = -3/2x + 3$

    $y = 3x + 2$

    $y = 2x + 3$

28. The cost $(C)$ in dollars of a taxi ride is given by the formula $C = 1.5d + 4$, where $d$ is the distance in kilometres. What does the $1.5$ represent?

    The cost per kilometre ($1.50/km$).

    The total cost of the ride.

    The initial fare or flat rate.

    The maximum distance.

29. Find the area of the triangle formed by the x-axis, the y-axis, and the line $y = -2x + 8$.

    $8$ square units

    $32$ square units

    $4$ square units

    $16$ square units

30. Line A is defined by $4x + ky = 8$. If Line A is perpendicular to the line $y = 2x - 1$, what is the value of $k$?

    $1/2$

    $8$

    $2$

    $-8$

31. The ratio of boys to girls in a school is $5:6$. If there are $165$ students in total, how many more girls are there than boys?

    $11$

    $75$

    $90$

    $15$

32. A recipe for a cake requires flour, sugar, and butter in the ratio $5:3:2$. If a baker uses $450g$ of sugar, how much flour is needed?

    $150g$ of flour.

    $300g$ of flour.

    $450g$ of flour.

    $750g$ of flour.

33. Car A travels $240 \text{ km}$ in $3 \text{ hours}$. Car B travels $350 \text{ km}$ in $4 \text{ hours}$. Which car is travelling at a faster average speed?

    Car B.

    They are travelling at the same speed.

    It is impossible to determine.

    Car A.

34. The ratio of Angle A to Angle B is $2:3$. The ratio of Angle B to Angle C is $3:4$. If the three angles are in a triangle, find the size of the smallest angle.

    $60$ degrees

    $40$ degrees

    $80$ degrees

    $20$ degrees

35. It takes $6$ printers $10$ hours to print a batch of magazines. If $2$ printers break down, how much longer will it take the remaining printers to finish the job?

    $15$ hours.

    $10$ hours longer.

    $2.5$ hours longer.

    $5$ hours longer.

36. A rectangular garden has a length that is $4$ metres longer than its width. If the perimeter of the garden is $48$ metres, what is its area?

    $100$ square metres.

    $140$ square metres.

    $120$ square metres.

    $48$ square metres.

37. Alex can paint a room in $6$ hours. Ben can paint the same room in $4$ hours. If they work together, how long will it take them to paint the room?

    $3$ hours

    $5$ hours

    $2.4$ hours

    $10$ hours

38. A mobile phone plan costs $20$ per month plus $0.15$ for every minute of calls made. A second plan costs $35$ per month with unlimited calls. For how many minutes of calls is the cost of the two plans exactly the same?

    $120$ minutes.

    $75$ minutes.

    $50$ minutes.

    $100$ minutes.

39. The value of a car depreciates by $10\%$ each year. If a new car costs $25,000$, what is its value after $3$ years?

    $22,500$

    $18,225$

    $17,500$

    $20,250$

40. The sum of the digits of a two-digit number is $9$. If the digits are reversed, the new number is $45$ less than the original number. What is the original number?

    $72$

    $54$

    $63$

    $27$