Full Practice Exam 5 — Module 1

Questions in this quiz (22)

1. If $$a\star b=4a-3(a+b)$$ what is $$3\star5$$?

   • $$-24$$
   • $$-12$$
   • $$24$$
   • $$36$$

2. The function $$h(x)=x^2+4$$. For which value of $$x$$ is $$h(x)=40$$?

   • $$\sqrt{10}$$
   • $$10$$
   • $$-6$$
   • $$5$$

3. A jacket originally costs $$470$$ dollars. It is discounted by $$15\%$$, and then a sales tax of $$8\%$$ is added to the discounted price. What is the final price of the jacket?

   • $$360.20$$
   • $$383.56$$
   • $$399.88$$
   • $$431.46$$

4. Which equation has the same solution as$$7(3x-2)+5=4x+31$$?

   • $$17x=15$$
   • $$17x=40$$
   • $$17x=24$$
   • $$17x=45$$

5. Each face of a fair $$20$$-sided die is labeled with a number from $$1$$ through $$20$$, with a different number appearing on each face. If the die is rolled one time, what is the probability of rolling a $$7$$?

   • $$\frac{1}{20}$$
   • $$\frac{7}{20}$$
   • $$\frac{13}{20}$$
   • $$\frac{19}{20}$$

6. A kayak rental shop charges a $$32$$ equipment fee plus $$14$$ per hour to rent a kayak. A group also buys safety gear that costs $$6$$ per person for each of the $$p$$ people in the group. If the group plans to spend no more than $$200$$ total, and they rent the kayak for $$h$$ hours, which inequality represents this situation?

   • $$14h+6p\le32$$
   • $$32h+14p+6\ge200$$
   • $$32+14h+6p\le200$$
   • $$14h+6p\ge200$$

7. A factory produces bottles at a constant rate. It fills $$135$$ bottles every $$9$$ minutes when running at full speed. At this rate, how many bottles does the factory produce in $$2$$ hours?

   • $$900$$
   • $$1800$$
   • $$3600$$
   • $$7200$$

8. $$2x-3y=7$$$$5x+2y=4$$The solution to the system is $$(x,y)$$.What is the value of $$x$$?

   • $$-\frac{2}{19}$$
   • $$\frac{26}{19}$$
   • $$\frac{2}{19}$$
   • $$\frac{4}{19}$$

9. $$f(x)=3x^2-5x+4$$What is the value of $$f(x)$$ when $$x=-2$$?

   • $$26$$
   • $$-6$$
   • $$6$$
   • $$18$$

10. Right triangles $$\triangle ABC$$ and $$\triangle DEF$$ are similar. Angles $$C$$ and $$F$$ are right angles, and angle $$A$$ corresponds to angle $$D$$. In $$\triangle ABC$$, $$\angle A=2x+5^\circ$$ and $$\angle B=x+25^\circ$$. In $$\triangle DEF$$, $$\angle D=41^\circ$$. What is the measure of angle $$E$$?

    • $$41^\circ$$
    • $$49^\circ$$
    • $$57^\circ$$
    • $$64^\circ$$

11. A school club is selling tickets for a performance. General admission tickets cost $$8$$ dollars each, and VIP tickets cost $$14$$ dollars each. The club must sell at least $$120$$ tickets in total and wants to collect exactly $$1280$$ dollars in revenue. If $$x$$ represents the number of general admission tickets sold and $$y$$ represents the number of VIP tickets sold, which system of equations and inequalities represents this situation?

    • $$8x+14y=120$$ $$x+y=1280$$
    • $$8x+14y=1280$$ $$x+y\ge120$$
    • $$8x+14y\ge1280$$ $$x+y\ge120$$
    • $$8x+14y\le1280$$ $$x+y\ge120$$

12. $$2x^2-7x-30=0$$The equation above has two real solutions. What is the greater solution?

    • $$-3$$
    • $$\frac{5}{2}$$
    • $$10$$
    • $$6$$

13. A scientist observes a bacterial culture that initially contains $$120000$$ cells per milliliter. The number of cells per milliliter triples every $$4$$ hours. At the same time, a chemical is added to the medium that removes $$40000$$ cells per milliliter every $$8$$ hours, beginning $$8$$ hours after the initial observation. How many cells per milliliter are in the culture $$16$$ hours after the initial observation?

    • $$2,920,000$$
    • $$3,080,000$$
    • $$9,640,000$$
    • $$9,320,000$$

14. Amira bought party hats, cupcakes, and balloons for a school event. Each package of party hats costs $$4$$ dollars, each cupcake costs $$2$$ dollars, and each balloon costs $$1$$ dollar. Amira spent $$120$$ dollars in total and bought $$3$$ times as many cupcakes as packages of party hats. If she bought $$9$$ packages of party hats, how many balloons did she buy?

    • $$15$$
    • $$18$$
    • $$24$$
    • $$30$$

15. Which expression is equivalent to $$8x^7y^3+12x^3y^3$$?

    • $$8x^3y^3(2x^4)$$
    • $$4x^3y^3(2x^4+3)$$
    • $$8x^3y^3(x^4+2)$$
    • $$4x^3y^3(2x^4+6)$$

16. A circle in the $$xy$$-plane has a diameter with endpoints $$(5,-3)$$ and $$(5,9).$$An equation of this circle is$$(x-5)^2+(y-3)^2=r^2,$$ where $$r$$ is a positive constant. What is the value of $$r$$?

    • $$3$$
    • $$6$$
    • $$12$$
    • $$24$$

17. A line $\ell$ is parallel to the line with equation $$3x-4y=20$$, and passes through the point $(2,-5)$. A second line $m$ is perpendicular to line $\ell$ and passes through the point $(2,-5)$ as well. Which of the following is the equation of line $m$?

    • $$y=-\frac{4}{3}x-\frac{7}{3}$$
    • $$y=\frac{4}{3}x-\frac{34}{3}$$
    • $$y=\frac{3}{4}x-\frac{31}{4}$$
    • $$y=-\frac{3}{4}x-\frac{2}{3}$$

18. Triangle $$ABC$$ is similar to triangle $$DEF$$, where angle $$A$$ corresponds to angle $$D$$, and angles $$B$$ and $$E$$ are right angles. If $$\sin(A)=\frac{40}{41}$$, what is the value of $$\sin(D)$$?

    • $$\frac{1}{41}$$
    • $$\frac{\sqrt{41}}{41}$$
    • $$\frac{40}{41}$$
    • $$\frac{9}{41}$$

19. $$y\ge3x-5$$$$y\le-x+11$$Which point $$(x,y)$$ is a solution to the given system of inequalities in the $$xy$$-plane?

    • $$(-4,0)$$
    • $$(4,0)$$
    • $$(2,7)$$
    • $$(4,10)$$

20. The scatterplot shows the relationship between two variables, $$x$$ and $$y$$. Which of the following statements best describes the relationship between $$x$$ and $$y$$?

    • There is a strong positive linear relationship between $$x$$ and $$y$$.
    • There is a strong negative linear relationship between $$x$$ and $$y$$.
    • There is a weak positive linear relationship between $$x$$ and $$y$$.
    • There is no relationship between $$x$$ and $$y$$.

21. The graph above shows the function $$f(x)$$. Which of the following statements is true about the function $$f$$?

    • $$f(x)$$ is always increasing for all real values of $$x$$.
    • $$f(x)$$ has a local minimum between $$x=0$$ and $$x=2$$.
    • $$f(x)$$ has a local maximum between $$x=1$$ and $$x=3$$.
    • $$f(x)$$ is symmetric about the $$y$$-axis.

22. Four students Ean, Laura, Lily, and Michael each collected pencils for a donation drive. The bar graph shows the number of pencils each student collected. A teacher wants to divide the total number of collected pencils equally among several classrooms. Exactly $$15$$ pencils are damaged and must be thrown away. The remaining pencils are divided equally among $$k$$ classrooms. Each classroom receives exactly $$1$$ pencil more than the number Ean collected. What is the value of $$k$$?

    • 5