Full Practice Exams — Exam 4

Questions in this quiz (45)

1. What is the value of $$\frac{3}{4}x^2 + 1$$, if $$(x+1)(2x-2) = 2x^2 + x - 2$$?

   • $$1$$
   • $$3$$
   • $$4$$
   • $$2$$

2. What is the product of the solutions of the equation $$3x^2+3x-36=0$$?

   • $$-36$$
   • $$36$$
   • $$3$$
   • $$-12$$

3. If the subtraction of a positive number and eight times its reciprocal is 7, determine the value of three times the number.

   • $$24$$
   • $$7$$
   • $$8$$
   • $$-8$$

4. If $$5x+4y=0$$ and $$3x-2y=22$$, determine the value of $$22x$$.

   • $$22$$
   • $$44$$
   • $$11$$
   • $$88$$

5. What is the equivalent expression of: $$(\frac{y^2 \cdot z^3}{x^4})^{-1} \cdot (\frac{y^4 \cdot z^6}{x^8})^{\frac{1}{2}}$$

   • $$4$$
   • $$3$$
   • $$1$$
   • $$2$$

6. What is the solution set if: $$|x-5|\geq 5$$

   • $$(-\infty,0]\cup[10,\infty)$$
   • $$(-\infty,10]$$
   • $$(-\infty,-10)$$
   • $$(0,\infty)$$

7. What is the equation of the circle with a radius of 9 and a center at $$(0,1)$$?

   • $$x^2+(y+1)^2=9$$
   • $$(x+1)^2+(y-1)^2=9$$
   • $$x^2+(y-1)^2=81$$
   • $$(x-1)^2+y^2=81$$

8. What is the equivalent expression of: $$1+\tan^2x+\csc^2x$$?

   • $$\sec^2x+\sin^2x$$
   • $$\cos^2x-\sin^2x$$
   • $$\cos^2x+\csc^2x$$
   • $$\sec^2x+\csc^2x $$

9. The price of a cotton white shirt is 20 dollars and has a 20% discount. Determine the final price of the shirt after applying a 7.5% sales tax.

   • $$17.2\,\text{dollars}$$
   • $$16.0\,\text{dollars}$$
   • $$11.5\,\text{dollars}$$
   • $$15.6\,\text{dollars}$$

10. Determine the equation of the line passing through $$(0,2)$$ and $$(1,1)$$.

    • $$y=x-2$$
    • $$y=x+2$$
    • $$y=-x-2$$
    • $$y=-x+2$$

11. A red car is traveling at a speed of $$60$$ mph from point $$A$$ to point $$B$$ while a blue one is traveling at a speed of $$45$$ mph from $$B$$ to $$A$$. If the distance between $$A$$ and $$B$$ is $$5$$ miles and the two cars started driving at the same time, determine how much time (in minutes) is needed until they intersect with each other.

    • $$51.22$$
    • $$35.45$$
    • $$31.43$$
    • $$45.15$$

12. Let's consider two functions $$f$$ and $$g$$ such that: $$f(x)=\sqrt{x+1}$$ and $$g(x)=\frac{1}{x+3}$$. What is the value of $$g(f(2))$$?

    • $$g(f(2))=\frac{1}{\sqrt{3}+3}$$
    • $$g(f(2))=\frac{1}{\sqrt{3}+3}$$
    • $$g(f(2))=\frac{1}{\sqrt{3}+3}$$
    • $$g(f(2))=\frac{1}{\sqrt{3}+3}$$

13. Determine the least common multiple (LCM) of $$25, 35, 49$$.

    • 1225
    • 42875
    • 1715
    • 875

14. Alex has $$72$$ average in his Algebra class before taking the final exam. If the final counts for $$30\%$$ of the final grade, what grade should Alex score in the final exam to get an $$80$$ in the class?

    • $$80.00$$
    • $$98.67$$
    • $$29.60$$
    • $$50.40$$

15. If $$f(x)=x^2-1$$, find the midpoint between $$(f(1),f(-1))$$ and $$(f(3),f(-2))$$.

    • $$\left(4,3\right)$$
    • $$\left(8,3\right)$$
    • $$\left(4,\frac{3}{2}\right)$$
    • $$\left(3,2\right)$$

16. If the area of a rhombus is 100 and the length of one diagonal is double the other, determine the perimeter of the rhombus.

    • $$20\sqrt{5}$$
    • $$5$$
    • $$20$$
    • $$125$$

17. Determine the area of the trapezoid below:

    • $$1162.5$$
    • $$3000.52$$
    • $$1155.63$$
    • $$2065.72$$

18. If the area bounded by the x-axis, y-axis, and the line $$y=-x+3$$ is rotated around the y-axis, find the volume of the 3D model generated.

    • $$6\pi$$
    • $$3\pi$$
    • $$9\pi$$
    • $$4\pi$$

19. If the sum of 3 angles of an octagon is 350 degrees, find the average of the rest of its angles.

    • $$270$$
    • $$180$$
    • $$360$$
    • $$146$$

20. Find the value of the angle $$x$$ if the lines $$(A)$$ and $$(B)$$ are parallel.

    • $$65^\circ$$
    • $$35^\circ$$
    • $$25^\circ$$
    • $$75^\circ$$

21. If the vertex of a parabola is $$(0.5, 1.25)$$ and its $$y$$-intercept is $$(0, -1)$$, determine the equation of this parabola.

    • $$y=-9(x-0.5)^2+1.25$$
    • $$y=-9(x-0.5)^2+1.25$$
    • $$y=-9(x-0.5)^2+1.25$$
    • $$y=-9(x-0.5)^2+1.25$$

22. Find the domain of the function: $$f(x)=\sqrt{\frac{x^2+2x+1}{x-3}}$$

    • $$(-\infty, \infty)$$
    • $$(-\infty,-1]\cup(3,\infty)$$
    • $$(-3,\infty)$$
    • $$(-\infty, 3]$$

23. What is $$0.20\%$$ of $$20$$?

    • $$0.02$$
    • $$4$$
    • $$2$$
    • $$0.04$$

24. Find the correct interval of $$x$$ if $$7^x=88$$.

    • $$2$$ < $$x$$ < $$3$$
    • $$7$$ < $$x$$ < $$8$$
    • $$9$$ < $$x$$ < $$10$$
    • $$5$$ < $$x$$ < $$6$$

25. A clothing store has a profit of $$400s-s^2$$ dollars from selling shirts. How many shirts need to be sold in order to maximize the store profit? Note that $$s$$ is the number of shirts sold.

    • $$800$$
    • $$400$$
    • $$600$$
    • $$200$$

26. In a parallelogram ABCD, is it always true that the measures of opposite angles:

    • add up to $$45$$ degrees
    • are supplementary
    • are equal
    • are complementary

27. In the figure shown below, determine the length of the segment $$ED$$. Consider the triangle $$ACD$$ as equilateral and the segments $$BE$$ and $$CD$$ are parallel.Given:

    • $$7$$
    • $$8$$
    • $$5$$
    • $$6$$

28. What is the slope of the line perpendicular to the line $$3x+3y=21$$?

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

29. A cone has a volume of $$7$$ cubic feet and a base diameter of $$24$$ inches. Find the height of the cone in feet.

    • $$21$$
    • $$12$$
    • $$15.45$$
    • $$6.69$$

30. Alex is riding his small boat from a lake's beach to a nearby island. If the island is located $$3$$ miles west and $$4$$ miles south of the departure point, find the shortest distance that Alex needs to travel to reach his destination.

    • $$25$$
    • $$5$$
    • $$16$$
    • $$4$$

31. The points $$E,F,G,H$$ are collinear such that $$F$$ is between $$E$$ and $$G$$, and $$G$$ is between $$F$$ and $$H$$. The distance between $$F$$ and $$G$$ is twice the distance between $$E$$ and $$F$$, and the distance between $$G$$ and $$H$$ is $$3$$ times the distance between $$E$$ and $$F$$. If the distance between $$E$$ and $$H$$ is $$12$$ centimeters, determine the distance between $$F$$ and $$H$$ in centimeters.

    • $$10$$
    • $$15$$
    • $$12$$
    • $$18$$

32. A chemical product is mainly composed of three ingredients $$X, Y, Z.$$ The volume ratio of the ingredients is respectively $$3:5:2.$$ Determine how many liters of ingredient $$Z$$ are in $$50$$ liters of the chemical product.

    • $$20$$
    • $$50$$
    • $$30$$
    • $$10$$

33. The figure below shows two squares and two semicircles. Find the area of the shaded region in square inches.

    • $$(14+\pi)x$$
    • $$(\pi)x^2$$
    • $$(16)x^2$$
    • $$(14-\pi)x^2$$

34. Solve for $$x$$:$$27^{x+1}+2\cdot3^{3x+3}=9^x.$$

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

35. Determine the equivalent expression of$$\frac{3+i}{1+\frac{2i}{5+3i}},\quad i=\sqrt{-1}.$$

    • $$\frac{12-i}{2}$$
    • $$\frac{12+4i}{4}$$
    • $$\frac{13+i}{5}$$
    • $$\frac{12i}{5}$$

36. Which of the following expressions has an odd numerical value?

    • $$4xy+4y$$
    • $$2xy+6$$
    • $$3x+3$$
    • $$2xy+1$$

37. Find the equation of an ellipse if its center is at $$(0,2)$$, its vertices are at $$(0,-5)$$ and $$(0,5)$$, and its covertices are at $$(-2,2)$$ and $$(2,2).$$

    • $$\frac{x^2}{4}+\frac{(y-2)^2}{25}=1$$
    • $$\frac{x^2}{4}+\frac{(y+2)^2}{5}=1$$
    • $$\frac{x^2}{2}+\frac{(y+2)^2}{5}=1$$
    • $$\frac{x^2}{2}+\frac{(y+2)^2}{25}=1$$

38. If $$f(x)=\sqrt[3]{2x+1}$$, find $$f^{-1}(x)$$.

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

39. Kevin invested 3000 dollars at 5% interest compounded quarterly for 7 years. What would be the absolute value of the difference earned if the interest was compounded annually?

    • $$407.10$$
    • $$35.63$$
    • $$421.30$$
    • $$418.36$$

40. What are the new coordinates of the point $$(1,1)$$ after rotating it $$90$$ degrees counterclockwise about the origin?

    • $$(1,1)$$
    • $$(-1,-1)$$
    • $$(1,-1)$$
    • $$(-1,1)$$

41. Let's consider 3 vectors $$u,v,w$$ such that: $$2u+5v-4w=0$$ where $$u=(1,-1)$$ and $$v=(1,-1)$$. Find the components of the vector $$w$$.

    • $$(-\frac{7}{4},\frac{7}{4})$$
    • $$(4,7)$$
    • $$(-7,4)$$
    • $$(-4,7)$$

42. $$a$$ and $$b$$ are two positive integers such that: $$a$$ > $$b$$ Which of the following must be true?

    • $$0$$ < $$\sqrt{ab}$$ < $$a$$
    • $$b$$ < $$\sqrt{ab}$$ < $$a$$
    • $$b^2$$ < $$\sqrt{ab}$$ < $$a$$
    • $$\sqrt{ab}$$ > $$a^2$$

43. For the triangle shown below, find the value of $$\cot A$$:

    • $$\frac{y}{x}$$
    • $$\frac{z}{x}$$
    • $$\frac{x}{z}$$
    • $$\frac{x}{y}$$

44. The salary of a high school teacher is 45000 dollars per year. One year of work is equivalent to 230 days. In case of absence, the district pays a substitute teacher 120 dollars per day. What would be the difference in salary if the substitute teacher replaces the main one for a whole year?

    • $$42000$$
    • $$27600$$
    • $$17400$$
    • $$31500$$

45. A bag contains 3 red balls, 5 green balls, and 7 white balls. What is the probability of drawing one red ball and two white balls at the same time?

    • $$\frac{9}{65}$$
    • $$\frac{1}{3}$$
    • $$\frac{2}{7}$$
    • $$\frac{2}{21}$$