Full Practice Exam 17 — Module 1

Questions in this quiz (22)

1. A container holds $$45$$ kg of a sugar solution. If the concentration of sugar in the solution is $$60\%$$, what is the amount of pure sugar dissolved in the solution?

   • $$24\text{ kg}$$
   • $$27\text{ kg}$$
   • $$30\text{ kg}$$
   • $$36\text{ kg}$$

2. Which of the following expressions is equivalent to $$\left(\frac{1}{a-b}+\frac{1}{a+b}\right)\div\frac{2a}{a^2-b^2}$$?

   • $$\frac{1}{b}$$
   • $$\frac{2}{a}$$
   • $$\frac{2}{b}$$
   • $$1$$

3. The quadratic function is given by $$y=3(x-2)(x+1)$$. Which of the following tables gives the selected values of the function?

4. In a laboratory experiment, a scientist measures the growth rate of bacteria at different temperatures. The data are shown below.If the relation between temperature and growth rate can be expressed by a linear model, which equation best describes the relationship?

   • $$G=0.1T+1$$
   • $$G=0.2T+1$$
   • $$G=0.5T+1$$
   • $$G=T+1$$

5. $$mx+\frac{1}{2}ny=3$$$$2mx+ny=6$$If $$x=4,\ y=-1$$ is the solution set of the system, what are the values of $$m$$ and $$n$$?

   • $$m=1,\ n=2$$
   • $$m=1,\ n=-2$$
   • $$m=2,\ n=1$$
   • $$m=-1,\ n=2$$

6. A square is inscribed in a circle. If the area of the circle is $$K$$, which of the following is the area of the square?

   • $$\frac{K}{\pi}$$
   • $$\frac{2K}{\pi}$$
   • $$\frac{K}{2\pi}$$
   • $$\frac{\pi K}{2}$$

7. The lengths of two sides of a triangle are $$7$$ and $$15$$ units. Which of the following could be the length of the third side?

   • $$5$$
   • $$8$$
   • $$10$$
   • $$23$$

8. In the rational equation $$\frac{(x-4)(x-7)(x-a)}{x+2}=0$$, where $$a\ne-2$$, the sum of the roots of the equation is $$8$$. What is the value of $$a$$?

   • $$1$$
   • $$5$$
   • $$7$$
   • $$-3$$

9. Given the equation $$6x+a=bx+2$$, if the equation has infinitely many solutions, what is the value of $$a+b$$?

   • $$8$$
   • $$6$$
   • $$4$$
   • $$2$$

10. A company studies the relationship between speed and fuel consumption of a vehicle. The data are shown below.If the relation can be modeled by a quadratic function, which of the following equations best fits the data?

    • $$y=\frac{1}{100}x^2+\frac{1}{10}x$$
    • $$y=\frac{1}{100}x^2+\frac{1}{5}x$$
    • $$y=\frac{1}{50}x^2$$
    • $$y=\frac{1}{80}x^2+\frac{1}{20}x$$

11. $$y=x^2-2x-3$$$$y=x+3$$How many distinct solutions does the system have?

    • $$0$$
    • $$1$$
    • $$2$$
    • $$3$$

12. The positive solution of the equation $$x^2-5x-24=0$$ is $$1$$ less than the positive solution of the equation $$x^2-10x+c=0$$. What is the value of $$c$$?

    • 9

13. A company conducted a survey to understand the relationship between employee training and job performance. The results are summarized below.Based on the data, what is the probability that an employee has high performance given that the employee did not attend the training?

    • $$\frac{7}{25}$$
    • $$\frac{12}{25}$$
    • $$\frac{18}{25}$$
    • $$\frac{3}{5}$$

14. In the United Kingdom, area is commonly measured in square feet. A room has an area of $$2500$$ ft$$^2$$. Express this area in square meters if $$1$$ meter $$=3.28$$ feet. Round to the nearest tenth.

    • 232.4

15. If $$x+3$$ is a factor of the polynomial $$P(x)=x^4-5x^3-2x^2+7x+b$$, what is the value of $$b$$?

    • $$-177$$
    • $$24$$
    • $$36$$
    • $$48$$

16. The function $$f$$ is defined by $$f(x)=a(1+r)^{x/n}$$, where $$a,\ r,$$ and $$n$$ are constants. If $$f(3)=16$$ and $$f(6)=128$$, what is the value of $$f(9)$$?

    • 1024

17. In the equation $$(4x-k)^2=(4x+a)(4x-k)$$, where $$a$$ and $$k$$ are nonzero constants and $$4k+a$$ > $$0$$. If the sum of the solutions is equal to $$\frac{k}{2}+5$$, what is the value of $$a$$?

    • 20

18. Which of the following could be the equation of the line shown in the $$xy$$-plane above?

    • $$y=-2x+3$$
    • $$y=\frac{1}{2}x+3$$
    • $$y=-\frac{1}{2}x+3$$
    • $$y=2x-3$$

19. When $$3x^2+4$$ is divided by $$x-1,$$ the result is $$A+\frac{7}{x-1}.$$ What is $$A$$ in terms of $$x$$?

    • $$3x-1$$
    • $$2x+1$$
    • $$2x-1$$
    • $$3x+3$$

20. If $$\tan x=m,$$ what is $$\sin x$$ in terms of $$m$$?

    • $$\frac{1}{\sqrt{m^2+1}}$$
    • $$\sqrt{1-m^2}$$
    • $$\frac{m}{\sqrt{m^2+1}}$$
    • $$\frac{m}{\sqrt{1-m^2}}$$

21. The scatterplot above shows the amount of nitrogen fertilizer applied to $$8$$ oat fields and their yields. The line of best fit is also shown. Which of the following is closest to the amount of nitrogen applied, in pounds per acre, to the oat field whose yield is best predicted by the line of best fit?

    • $$200$$
    • $$350$$
    • $$400$$
    • $$450$$

22. In the figure above, what is the value of $$x$$?

    • $$45^\circ$$
    • $$85^\circ$$
    • $$90^\circ$$
    • $$100^\circ$$