Full Practice Exam 11 — Module 2

Questions in this quiz (22)

1. $$(x-5)^2=49$$What is the positive solution to the equation?

   • $$-2$$
   • $$5$$
   • $$7$$
   • $$12$$

2. Which expression is equivalent to $$\frac{x^2-6x+9}{x-3}+\frac{x^2-16}{x+4}$$ for all values of $$x$$ for which the expression is defined?

   • $$2x-1$$
   • $$2x+1$$
   • $$x^2-2x-1$$
   • $$2x-7$$

3. The function $$f$$ is defined by $$f(x)=4x^2-5x+6$$. What is the value of $$f(3)+f(5)$$?

   • $$82$$
   • $$96$$
   • $$108$$
   • $$124$$

4. The function $$f$$ is defined by $$f(x)=-2(x+4)^2+18$$ What is the maximum value of $$f$$?

   • $$-4$$
   • $$2$$
   • $$18$$
   • $$26$$

5. The equation $$y=3x^2-12$$ is given. If $$y=36$$, what are the possible values of $$x$$?

   • $$x=4$$
   • $$x=\pm4$$
   • $$x=\pm12$$
   • $$x=16$$

6. An electrician charges a flat fee of $$85$$ dollars plus $$60$$ dollars per hour. If $$C$$ represents the total cost, in dollars, for a service call lasting $$h$$ hours, which equation best models the total cost?

   • $$C=85h+60$$
   • $$C=60h+85$$
   • $$C=85-60h$$
   • $$C=145h$$

7. A car's fuel tank initially contains $$18$$ gallons of gasoline. The function $$F(d)=18-0.04d$$ models the amount of fuel remaining after the car has traveled $$d$$ miles. What is the best interpretation of $$0.04$$ in this context?

   • The car uses $$0.04$$ gallons per mile.
   • The car can travel $$0.04$$ miles per gallon.
   • The car starts with $$0.04$$ gallons.
   • The car loses $$18$$ gallons every $$0.04$$ miles.

8. The function $$f$$ is defined by $$f(x)=2x^2-3x+7$$. What is the value of $$f(5)-f(2)$$?

   • $$30$$
   • $$33$$
   • $$42$$
   • $$48$$

9. The graphs of the equations below intersect at points $$(x,y)$$ in the $$xy$$-plane.$$x^2=25$$$$y=2x-3$$Which of the following is a possible value of $$y$$?

   • $$-14$$
   • $$-5$$
   • $$7$$
   • $$25$$

10. A rideshare company charges a booking fee of $$4.75$$ dollars plus $$3.20$$ dollars per mile. If a customer's total fare was $$39.95$$ dollars, what was the distance, in miles, of the ride?

    • $$9.5$$
    • $$10$$
    • $$11$$
    • $$12.5$$

11. A researcher randomly selects $$200$$ students from a large high school. Of the students surveyed, $$68\%$$ say they would support extending the school day by $$30$$ minutes if extracurricular activities were also expanded. Which conclusion is most appropriate?

    • Exactly $$68\%$$ of all students at the school support extending the school day.
    • Most students at the school may support extending the school day with expanded extracurricular activities.
    • All students who participate in extracurricular activities support extending the school day.
    • The school should immediately extend the school day.

12. In a circle, points $$A$$, $$B$$, and $$C$$ lie on the circumference. The measure of arc $$AB$$ is $$140^\circ$$, and the measure of arc $$BC$$ is $$100^\circ$$. What is the measure, in degrees, of $$\angle ABC$$?

    • $$40$$
    • $$50$$
    • $$60$$
    • $$120$$

13. $$2x+3y=19$$$$4x-y=13$$What is the value of $$3x+y$$?

    • $$11$$
    • $$14$$
    • $$16$$
    • $$19$$

14. The height, in feet, of a projectile launched from the ground is modeled by $$h(t)=-16t^2+96t+20$$ where $$t$$ is the time, in seconds, after launch. What is the maximum height, in feet, reached by the projectile?

    • $$144$$
    • $$148$$
    • $$164$$
    • $$176$$

15. Point $$P$$ is outside a circle with center $$O$$. A tangent segment is drawn from point $$P$$ to the circle, touching the circle at point $$A$$. If $$PA=24$$ units and the radius of the circle is $$7$$ units, what is the distance from $$P$$ to the center $$O$$?

    • $$25$$
    • $$26$$
    • $$27$$
    • $$31$$

16. A medical researcher randomly selects $$150$$ healthy adults from members of several fitness centers in a city. The participants are randomly assigned to one of two groups. One group follows a new nutrition plan for $$4$$ months, while the other group maintains their usual diet. At the end of the study, the first group shows significantly lower average cholesterol levels. To which population can the results most appropriately be generalized?

    • All adults in the city.
    • All healthy adults.
    • Healthy adults who are members of fitness centers similar to those sampled.
    • All adults who follow nutrition plans.

17. The price of a laptop was increased by $$25\%$$. Two weeks later, the new price was discounted by $$20\%$$ during a sale. What is the final price as a percentage of the original price?

    • $$95\%$$
    • $$100\%$$
    • $$105\%$$
    • $$120\%$$

18. Given the system of equations:$$y=x^2-4$$$$y=2x$$Which ordered pair $$(x,y)$$ is a solution to the system?

    • $$(4,8)$$
    • $$(1+\sqrt{5},2+2\sqrt{5})$$
    • $$(0,0)$$
    • $$(-2,-4)$$

19. A linear function $$f$$ is defined by $$f(x)=ax+b$$, where $$a$$ and $$b$$ are constants. If $$f(x+4)-f(x-1)=20$$ for all real numbers $$x$$, and $$f(2)=11$$, what is the value of $$f(7)$$?

    • $$26$$
    • $$31$$
    • $$36$$
    • $$41$$

20. In the right triangle $$\triangle ABC$$ shown, the length of side $$AB$$ is $$5$$. What is the length of side $$AC$$?

    • $$5$$
    • $$5\sqrt{2}$$
    • $$5\sqrt{3}$$
    • $$10$$

21. In the figure, lines $$m$$ and $$n$$ are parallel. A transversal line $$T$$ intersects line $$m$$ at point $$A$$ and line $$n$$ at point $$B$$. Point $$C$$ is on line $$n$$ such that $$\triangle ABC$$ is an isosceles triangle with $$AB=BC$$. The measure of $$\angle ABC$$ is $$80^\circ$$. What is the measure, in degrees, of the angle formed by line $$T$$ and line $$m$$ that is alternate interior to $$\angle ABC$$?

    • $$40$$
    • $$50$$
    • $$60$$
    • $$80$$

22. The graph of the quadratic function $$f$$ is shown in the $$xy$$-plane. The function $$f$$ is defined by $$f(x)=a(x-h)^2+k$$ where $$a$$, $$h$$, and $$k$$ are constants. For how many distinct values of $$x$$ does $$f(x)=3$$?

    • Zero
    • One
    • Two
    • Three