Full Practice Exams — Exam 15

Questions in this quiz (45)

1. The function $$g(x) = x^2 + 5$$. If a constant $$m$$ is subtracted from the function, as in $$g(x) - m$$, what is a possible value of $$m$$ that would make it so that the new function has exactly one zero?

   • 0
   • 3
   • 2
   • 5

2. Three angles, $$p$$, $$q$$, and $$r$$, share the same vertex and lie along a straight line. If $$p = \frac{3}{4}q$$ and $$q = \frac{1}{2}r$$, how much is $$r - p$$?

   • 67.5
   • 135
   • 36
   • 60

3. You buy a used laptop for $$1200$$ and its value decreases by $$25\%$$ per year. Approximately, after how many years will the value of the laptop be less than $$600$$?

   • Approximately 3 years.
   • Approximately 4 years.
   • Approximately 2 years.
   • Approximately 5 years.

4. In the parallelogram ABCD shown below, determine the value of $$b$$.

   • 85
   • 15
   • 75
   • 105

5. A positive integer $$a$$ when divided by the smallest odd prime, leaves a remainder $$r$$. Which of the following CANNOT be $$r$$?

   • 1
   • 2
   • 3
   • 0

6. The number $$\frac{2 + \sqrt{5}}{2 - \sqrt{5}}$$ is:

   • An integer
   • A rational number
   • A real number
   • An irrational number

7. Find the value of $$b$$ and $$c$$ if $$a=1$$ and the graphical representation of the polynomial $$ax^2+bx+c$$ passes through the points $$(-2,0)$$ and $$(3,0)$$.

   • $$b=-2$$ and $$c=3$$
   • $$b=0$$ and $$c=0$$
   • $$b=-1$$ and $$c=-6$$
   • $$b=2$$ and $$c=-3$$

8. If $$\alpha$$ and $$\beta$$ are the zeroes of the polynomial $$5x^2 - px + 1$$ and $$\alpha - \beta = 1$$, then find the value of $$p$$.

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

9. I am three times as old as my son's age. Five years later, I shall be two and a half times as old as my son. How old am I and how old is my son?

   • I am 45 years old and my son is 15 years old.
   • I am 50 years old and my son is 20 years old.
   • I am 30 years old and my son is 10 years old.
   • I am 55 years old and my son is 12 years old.

10. In the figure, it is given that: $$\frac{AO}{OC} = \frac{BO}{OD} = \frac{1}{2}$$ and $$AB = 5 \text{ cm}$$Find the value of $$CD$$.

    • 10
    • 11
    • 15
    • 17

11. In the figure, MN is parallel to QR and the ratio of PM to MQ is $$8:5$$. Find the ratio $$\frac{\text{Area of } \triangle QOR}{\text{Area of } \triangle MON}$$.

    • $$\frac{8}{5}$$
    • $$\frac{5}{8}$$
    • $$\frac{25}{64}$$
    • $$\frac{1}{5}$$

12. Simplify:$$(1+\tan^2\theta)(1+\sin\theta)(1-\sin\theta)$$

    • $$-\sin\theta$$
    • $$\sin\theta$$
    • $$\tan^2\theta$$
    • 1

13. Find the median of the following data: $$19, 25, 59, 48, 35, 31, 30, 32, 51$$If 25 is replaced by 52 and 19 by 29, what will be the new median?

    • 31
    • 25
    • 29
    • 35

14. A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/hr less, then it would have taken 3 hours more to cover the same distance. Formulate the quadratic equation in terms of the speed of the train.

    • $$x^2 - 8x - 1280 = 0$$
    • $$x^2 + 3x - 480 = 0$$
    • $$x^2 + 4x - 80 = 0$$
    • $$x^2 - 3x - 480 = 0$$

15. Two cars start together in the same direction from the same place. The first goes with uniform speed of $$10$$ km/h. The second goes at a speed of $$8$$ km/h in the first hour and increases the speed by $$\frac{1}{2}$$ km/h in each succeeding hour. After how many hours will the second car overtake the first car if both cars go non-stop?

    • 20
    • 10
    • 15.5
    • 9

16. A tangent $$TR$$ is drawn at a point $$R$$ on a circle with center $$O$$ and radius $$9\text{ cm}$$. It meets a line through $$O$$ at point $$T$$, such that $$OT = 30\text{ cm}$$. Find the length of $$TR$$.

    • $$29$$
    • $$3\sqrt{3}$$
    • $$3\sqrt{91}$$
    • $$25$$

17. Which of the following is a solution for the equation $$2x^2-7|x|+5=0$$?

    • 2
    • $$\frac{5}{2}$$
    • -1
    • $$-\frac{5}{2}$$

18. Which of the expressions is equivalent to the expression $$\left(2-\frac{a}{3}\right)^2-(-2)^2\left(1+\frac{a^2}{3}\right)$$?

    • $$\frac{a}{3}(\frac{11a}{3}-4)$$
    • $$-a(\frac{11a}{3}-2)$$
    • $$a(\frac{11a}{3}+4)$$
    • $$-\frac{a}{3}(\frac{11a}{3}-2)$$

19. The solution of the equation $$3^x=5^{x-2}$$ is:

    • $$\frac{2\ln5}{\ln(\frac{5}{3})}$$
    • $$\frac{2\ln5}{2\ln(\frac{5}{3})}$$
    • $$\frac{-2\ln5}{2\ln(\frac{5}{3})}$$
    • $$\frac{-\ln5}{\ln(\frac{5}{3})}$$

20. Which of the following statements is true?

    • The amplitude of $$f(t)=-2\sin(2t)+2$$ is 1.
    • The period of $$g(t)=-\frac{1}{2}\cos(2t)$$ is $$\pi$$.
    • The period of $$h(t)=3\tan(2t)$$ is $$\frac{\pi}{4}$$.
    • The amplitude of $$k(t)=-3\tan(t)$$ is $$-3$$.

21. In the $$xy$$-plane, let $$x^2+y^2-2kx+4y-3k^2=0$$ be the equation of a circle of center $$A\left(\frac{1}{2},-2\right)$$ and radius $$r=\sqrt{5}$$. What is the value of the real number $$k$$?

    • $$\frac{1}{3}$$
    • $$2$$
    • $$\frac{1}{4}$$
    • $$\frac{1}{2}$$

22. For a point source, sound intensity is given by $$I=\frac{P}{4\pi D^2}$$, where:I is the sound intensity,P is the power of the sound source,D is the distance from the source to point A.If the power doubles $$P'=2P$$ and the distance doubles $$D'=2D,$$ find $$\frac{I'}{I}$$.

    • $$\frac{1}{2}$$
    • $$2$$
    • $$1$$
    • $$\frac{1}{4}$$

23. The graph above depicts a function $$f(x)$$. How many solutions does the equation $$f(x)=0$$ admit?

    • 1
    • 2
    • 3
    • 4

24. If $$|-2b-3|\le7$$, how many possible integer values of $$b$$ are there?

    • 1
    • 2
    • 3
    • 4

25. If the expression $$\frac{-2i-i^3}{1+3i}$$ is written in the form $$a+bi$$ where $$a$$ and $$b$$ are real numbers and $$i=\sqrt{-1}$$, what is the value of $$b-a$$?

    • $$\frac{1}{2}$$
    • $$\frac{1}{5}$$
    • $$\frac{1}{4}$$
    • $$\frac{3}{4}$$

26. If $$f(x)=-3-2x$$ and $$g(x)=\frac{-x^2}{6}$$, which of the following could not be in the range of $$f(g(x))$$?

    • -4
    • -2
    • 0
    • 2

27. A shop sells two sizes of doughnuts: mini and regular. Mini doughnuts have a diameter of 1.8 inches while regular ones have a diameter of 3 inches. Approximately, by what percentage is a regular normal doughnut larger (in area) than a mini doughnut?

    • $$67\%$$
    • $$33\%$$
    • $$178\%$$
    • $$57\%$$

28. Line (A) passes through the points $$\left(-\frac{5}{3},0\right)$$ and $$(0,-\frac{2}{3})$$. Which of the following lines will never intersect with line (A)?

    • $$y=-\frac{5}{2}x-1$$
    • $$y=\frac{5}{2}x-1$$
    • $$y=-\frac{2}{5}x-1$$
    • $$y=\frac{2}{5}x-1$$

29. A refrigerator costs 200 dollars less than 3 times the cost of a dishwasher. If the refrigerator and the dishwasher cost together 860 dollars, how much more does the refrigerator cost than the dishwasher?

    • $$330$$
    • $$400$$
    • $$280$$
    • $$460$$

30. Based on the graph below, what is the value of $$f(-1)+g(-1)+h(-1)$$?

    • -5
    • -4
    • -2
    • 1

31. Given the system of inequalities:$$y \leq 3x - 2 \\y > \frac{3x}{4} - 3$$In which quadrant(s) the system has no solutions?

    • Quadrants I and III
    • Quadrants I and IV
    • Quadrants II and IV
    • Quadrants II and III

32. In a right triangle, if $$\tan\theta = \frac{15}{8}$$, what is the value of $$\cos\theta$$?

    • $$\frac{5}{8}$$
    • $$\frac{8}{17}$$
    • $$\frac{9}{17}$$
    • $$\frac{3}{8}$$

33. The mean of $$a$$, $$b$$, $$c$$ and $$d$$ is 14.2. The mean of $$a$$, $$b$$, $$c$$, $$d$$ and $$e$$ is 15. What is the value of $$e$$?

    • 18.2
    • 15
    • 17.5
    • 16.8

34. The bar graph above represents the percentage of money spent by a company on different sectors last year. If 200000 dollars were spent on the transport sector, what was the budget used for salaries?

    • $$350,000$$
    • $$320,000$$
    • $$360,000$$
    • $$380,000$$

35. Triangle $$ABC$$ has area of $$16$$. Three lines parallel to side $$BC$$ divide side $$AC$$ into four equal segments. As a result, three non-overlapping trapezoids are produced. Find the area of the middle trapezoid.

    • 5
    • 9
    • 12
    • 7

36. Knowing that $$x$$ < $$5$$, use the figure below to find the set of real numbers $$x$$ if twice the area of triangle $$BME$$ added to 2 times the area of triangle $$MEA$$ is less than or equal to triple the area of rectangle $$ABCD$$.

    • $$x\in[0,4)$$
    • $$x\in[4,10)$$
    • $$x\in[0,4]$$
    • $$x\in(1,4)$$

37. The table below shows some values for the function $$f$$. If $$f$$ is a linear function, what is the value of $$m+n$$?

    • 10
    • 8
    • 16
    • 12

38. Jack has $$k$$ dollars. He spends $$\frac34$$ of his money on a T-shirt and $$\frac13$$ of what was left on a sandwich. If this left him with $$t$$ dollars, which of the following is the value of $$k$$ in terms of $$t$$?

    • 9t
    • 12t
    • 24t
    • 6t

39. The circular diagram below shows the results of a survey made on the number of books read by 200 pupils in a certain school. What is the number of pupils who read less than 3 books?

    • 76
    • 136
    • 100
    • 40

40. In the figure below, the circles are tangent to each other. The radius of circle (1) is $$R$$ and the radius of circle (2) is $$2R$$.

    • $$\sqrt{5}$$
    • $$6\sqrt{5}$$
    • $$2\sqrt{5}$$
    • $$12\sqrt{5}$$

41. The graph below shows the test grades over 20 of 40 students. Based on the bar graph above, what is the average grade on the test?

    • 12.8
    • 10.4
    • 14.6
    • 12.8

42. In the figure above, $$AE = \frac{1}{3}AB$$ and $$AD = \frac{1}{3}AC$$. The area of triangle $$ABC$$ is how many times the area of trapezoid $$EDCB$$?

    • $$\frac{4}{3}$$
    • $$\frac{8}{9}$$
    • $$\frac{9}{8}$$
    • $$\frac{3}{4}$$

43. The table below summarizes students' work placement after graduation, based on the major. Given a person who works outside his field of study, which of the following is closest to the probability that he majored in business?

    • 0.16
    • 0.35
    • 0.06
    • 0.5

44. What happens to the graph of $$y=|x|$$ when the equation changes to $$y=|x-2|$$?

    • The graph shifts right 2 units.
    • The graph shifts left 2 units.
    • The graph shifts up 2 units.
    • The graph shifts down 2 units.

45. In which matrix is the value of $$a_{23}$$ double the value of $$a_{31}$$?

    • $$\begin{pmatrix} 2 & 1 & -2 \\ 3 & 0 & 1 \\ 4 & 8 & 3 \end{pmatrix}$$
    • $$\begin{pmatrix} -1 & 1 & -2 \\ 2 & 3 & 4 \\ 2 & 9 & 3 \end{pmatrix}$$
    • $$\begin{pmatrix} 0 & 0 & 5 \\ 6 & 0 & 5 \\ 2 & 10 & -3 \end{pmatrix}$$
    • $$\begin{pmatrix} 6 & 0 & 2 \\ 6 & 5 & 4 \\ 8 & 7 & -3 \end{pmatrix}$$