Full Practice Exam 1 — Module 2

Questions in this quiz (22)

1. If $$hx-3k+x=5-(k+x)$$, what is the value of $$k$$ in terms of $$h$$ and $$x$$?

   • $$\frac{h-1}{5+2x}$$
   • $$\frac{3h-x}{h}$$
   • $$\frac{h+1}{5-2x}$$
   • $$\frac{(h+2)x-5}{2}$$

2. If 8 is the average (arithmetic mean) of 6 and $$p$$, and 12 is the average of 10 and $$q$$, then what is the average of $$p$$ and $$q$$?

   • $$8$$
   • $$10$$
   • $$12$$
   • $$14$$

3. Maria purchased annual memberships to four museums that cost $$14.50$$, $$19.25$$, $$22.75$$, and $$25.50$$ per year, respectively. She paid one third of the total yearly cost upfront, and paid the remaining balance in three equal monthly payments. How much was each monthly payment?

   • $$12.75$$
   • $$13.50$$
   • $$18.22$$
   • $$22.25$$

4. If $$\frac{3x}{x^2+4}=\frac{3}{x+2},$$ what is the value of $$x$$?

   • $$\frac{1}{2}$$
   • $$2$$
   • $$\frac{3}{2}$$
   • $$0$$

5. A survey of Town Y found an average arithmetic mean of $$2.5$$ persons per household and a mean of $$1.6$$ computers per household. If $$35000$$ people live in Town Y, how many computers are in Town Y?

   • $$14,000$$
   • $$16,000$$
   • $$22.400$$
   • $$56,000$$

6. If I do not have an umbrella, I am not able to walk in the rain.If the statement above is true, which of the following statements must also be true?

   • If I did not walk in the rain, I must have had an umbrella.
   • If I walked in the rain, I must have had an umbrella.
   • If I have an umbrella, I must not be able to walk in the rain.
   • If I was able to walk in the rain, I must not have had an umbrella.

7. Let the function g be defined such that:$$g(x)=3x^2-k$$where $$k$$ is a constant. If $$g(1)=8$$, what is the value of $$k$$?

   • $$-5$$
   • $$-2$$
   • $$2$$
   • $$11$$

8. If $$8k=128$$, then evaluate $$\sqrt{k}\times\sqrt[3]{2k}$$.

   • $$4$$
   • $$8\sqrt[3]{4}$$
   • $$4\sqrt[4]{3}$$
   • $$16$$

9. What is the diameter of a circle with a circumference of $$12$$?

   • $$\frac{6}{\pi}$$
   • $$6$$
   • $$\frac{12}{\pi}$$
   • $$12\pi$$

10. If the product of $$(2+3)$$( $$(4+1)$$, and $$(5+2)$$ is equal to one-half the sum of $$30$$ and $$y$$, what is the value of $$y$$?

    • $$70$$
    • $$84$$
    • $$140$$
    • $$320$$

11. According to the table above, what is $$x+y$$?

    • $$20,000$$
    • $$25,000$$
    • $$30,000$$
    • $$40,000$$

12. If $$\sqrt{y}=3^2$$, then what is $$y$$?

    • $$3$$
    • $$6$$
    • $$9$$
    • $$81$$

13. If $$g(x)=||x+2|-4|$$, what is the value of $$g(-1)$$?

    • $$-1$$
    • $$1$$
    • $$3$$
    • $$5$$

14. If AE>FG, which of the following must be true?I. AE>EFII. AF>EGIII. AF>FG

    • I only
    • II only
    • I and III
    • II and III

15. A scientist is studying a colony of algae that triples in size every $$2$$ hours. If the colony begins with $$5$$ algae, how many algae will there be after $$6$$ hours?

    • $$45$$
    • $$90$$
    • $$135$$
    • $$405$$

16. How many numbers from $$1$$ to $$500$$ inclusive are equal to the square of an integer?

    • $$10$$ numbers
    • $$12$$ numbers
    • $$22$$ numbers
    • $$25$$ numbers

17. A rectangle has side lengths $$a$$ and $$b$$. The perimeter of the rectangle is $$k$$, and $$a=\frac{3}{4}b$$. What is the value of $$b$$ in terms of $$k$$?

    • $$\frac{k}{7}$$
    • $$\frac{2k}{7}$$
    • $$\frac{3k}{7}$$
    • $$\frac{4k}{7}$$

18. If $$g(x)=x^2+4$$, which of the following could be a value of $$g(x)$$?

    • $$-2$$
    • $$0$$
    • $$3$$
    • $$4$$

19. A soccer team had a ratio of wins to losses of $$4:1$$. After the team won $$8$$ games in a row, its ratio of wins to losses became $$6:1$$. How many games had the team won before winning the $$8$$ games in a row?

    • $$12$$
    • $$16$$
    • $$20$$
    • $$24$$

20. Square $$ABCD$$ has vertices at $$A(1,2)$$, $$B(3,6)$$, $$C(7,4)$$, and $$D(5,0)$$ in the $$xy$$-plane. What is the area of square $$ABCD$$?

    • $$12$$
    • $$16$$
    • $$20$$
    • $$24$$

21. In terms of $$a$$, what is the value of $$b+c$$?

    • $$b+c=90-a$$
    • $$b+c=90+a$$
    • $$b+c=180-a$$
    • $$b+c=180+a$$

22. A circle is inscribed inside a square whose side length is $$s$$. What is the probability that a randomly selected point inside the square will NOT lie inside the circle?

    • $$\frac{\pi-2}{\pi}$$
    • $$\frac{4+\pi}{\pi}$$
    • $$1-\frac{\pi}{4}$$
    • $$\frac{2-\pi}{4}$$