Full Practice Exams — Exam 18

Questions in this quiz (45)

1. Find the area of the figure shown.

   • $$65 + 3.125\pi$$
   • $$25 + 5\pi$$
   • $$44 + 6.25\pi$$
   • $$25 + 4\pi$$

2. Triangle ACD is a right triangle at C. AC=6, CD=3, BC=2. E is the orthogonal projection of B on AD. Find the measure of BE.

   • $$\frac{2\sqrt{5}}{5}$$
   • $$\frac{8\sqrt{5}}{5}$$
   • $$\frac{4\sqrt{5}}{5}$$
   • $$\frac{\sqrt{5}}{5}$$

3. What is the slope of the line perpendicular to the line represented by $$3y-6x=3$$?

   • $$-6$$
   • $$3$$
   • $$-\frac{1}{2}$$
   • $$\frac{1}{2}$$

4. Determine the sum of the series:$$7 - 2 + \frac{4}{7} - \frac{8}{49} + \dots$$

   • $$\frac{16}{49}$$
   • $$\frac{101}{49}$$
   • $$\frac{49}{9}$$
   • $$\frac{50}{7}$$

5. What is the value of $$x \cdot y$$?$$(\sqrt{7})^{8x} = 2401^{3y}$$

   • $$3y^2$$
   • $$3y$$
   • $$\frac{3}{2} y^2$$
   • $$\frac{3}{2} y$$

6. Determine the product of the median and mean of the first 7 prime numbers.

   • $$30$$
   • $$28$$
   • $$58$$
   • $$41$$

7. A hill makes an angle of 30 degrees with the horizontal AB. A wire AC runs from the base of the hill to the point C located in a vertical pole. Using the figure shown below, determine the length of AC.CD = 30'AD = 100'

   • $$50\sqrt{3}$$
   • $$\frac{50\sqrt{3}}{3}$$
   • $$10\sqrt{139}$$
   • $$50$$

8. Given $$f(z)=\left(\frac{1}{3}\right)^z$$ and $$h(z)=\frac{z+4}{z+1}$$. Find $$h(f(0))$$.

   • 0
   • 1
   • 4
   • $$2.5$$

9. A circle in the $$xy$$-plane has its center at $$(2,-3)$$ and has a radius of $$7$$. An equation of this circle is $$x^2+y^2+ax+by+c=0$$ where $$a$$, $$b$$, and $$c$$ are constants. What is the value of $$c$$?

   • -4
   • 6
   • -36
   • 4

10. What is the 245th digit after the decimal point in the repeating decimal $$0.\overline{1497}$$?

    • 1
    • 4
    • 7
    • 9

11. In a ball pit $$75\%$$ of the balls are yellow in color. If you randomly pick a ball from the ball pit, what is the probability that the ball picked is not one of the yellow balls?

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

12. If PQRS is a parallelogram, then which of the following must be equal to $$x$$?

    • $$180-b$$
    • $$180-c$$
    • $$a + b$$
    • $$b + c$$

13. Let $$a$$ and $$b$$ be numbers such that $$a^3 = b^2$$. Which of the following is equivalent to $$b\sqrt{a}$$?

    • $$b^{3/2}$$
    • $$b^{2/3}$$
    • $$b^{1/3}$$
    • $$b^{4/3}$$

14. An arch is built so that it has the shape of a parabola with the equation $$y = -3x^2 + 24x$$ where $$y$$ represents the height of the arch in meters. How many times greater is the maximum height of the arch than the width of the arch at its base?

    • 6
    • 8
    • 16
    • 12

15. The graph of $$y = (x - 1)(x + 1)(x + 2)$$ contains the point $$(a,b)$$. If $$-1 \leq a \leq 1$$ which of the following is NOT a possible value of $$b$$?

    • -2
    • -1
    • 0
    • 1

16. If $$\frac{2}{5}x-\frac{1}{3}y=7$$ and $$-\frac{m}{10}x+\frac{5}{6}y=3$$ is a system of linear equations that admits no solutions, and $$m$$ is an integer, what is the value of $$m$$?

    • -6
    • -2
    • 6
    • 10

17. If $$\sqrt{2^m}=8$$ what is the value of $$\sqrt{3^m}$$?

    • 8
    • 27
    • 8
    • 81

18. In triangle $$RST$$ above, point $$W$$ lies on $$\overline{RT}$$. What is the value of $$\cos(\angle RSW)-\sin(\angle WST)$$?

    • $$\frac{-7}{13}$$
    • $$\frac{5}{13}$$
    • $$\frac{7}{13}$$
    • $$0$$

19. Given the function $$f(x) = (x-2)(x-5)(x+9)$$The function $$f(x)$$ is the result of translating another function $$g(x)$$ up 5 units.Find the y-intercept of $$g(x)$$.

    • $$85$$
    • $$5$$
    • $$13$$
    • $$9$$

20. A rectangular stained-glass panel is designed with seven triangles. The two unshaded triangles ABC and DEC are congruent. In triangle ABC, angle CAB is 65 degrees and angle ACB is 50 degrees. In triangle DEC, angle DCE is 50 degrees. What is the measure of angle CED?

    • $$50^\circ$$
    • $$65^\circ$$
    • $$75^\circ$$
    • $$55^\circ$$

21. The 3 statements are true about positive integers p,q,r.• p is the smallest odd prime number.• q is an even integer such that 12<q<20.• r is a perfect cube such that 5<r<30.How many ordered triples (p,q,r) satisfy the 3 statements?

    • $$2$$
    • $$3$$
    • $$4$$
    • $$6$$

22. The graph of f(x) has horizontal asymptotes at y=-2 and y=2. Which interval is the domain of the inverse function $$f^{-1}(x)$$?

    • $$(-\infty,\infty)$$
    • $$(-2,2)$$
    • $$(-\infty,-2]$$ and $$[2,\infty)$$
    • $$[-2,2]$$

23. If $$x$$ and $$y$$ are real numbers such that $$x$$ > $$1$$ and $$y$$< $$-1$$, which of the following inequalities must be true?

    • $$\frac{x}{y}$$ > $$1$$
    • $$\frac{x}{3}-5$$ > $$\frac{y}{3}-5$$
    • $$x^{-2}$$ > $$y^{-2}$$
    • $$|x|^2$$ > $$|y|$$

24. Which of the following number line graphs represents all values in the domain of the function $$y=\log_{10}(x^2-4x+3)$$?

25. A warehouse stores small toy cubes in large storage bins. Each bin has inside dimensions measuring 18 inches long, 12 inches wide, and 6 inches tall. Each toy cube has an edge length of 3 inches. What is the maximum number of toy cubes that can fit in one storage bin?

    • $$35$$
    • $$48$$
    • $$40$$
    • $$42$$

26. In the standard coordinate plane, consider the vectors PQ and RS. Point P is at (-4,1) and point Q is at (2,5). Point R is at (2,-2) and point S is at (5,4). What is the vector notation of PQ+RS?

    • $$\langle1,5\rangle$$
    • $$\langle-2,6\rangle$$
    • $$\langle7,-2\rangle$$
    • $$\langle9,10\rangle$$

27. Which point is an endpoint of the major axis of the ellipse $$\frac{(x-1)^2}{4}+\frac{(y+2)^2}{36}=1$$?

    • $$(4,8)$$
    • $$(1,-4)$$
    • $$(4,-8)$$
    • $$(1,-8)$$

28. Four matrices are given:Which of the following matrix products is undefined: AB, BC, CD, or DB?

    • AB
    • BC
    • CD
    • DB

29. A community center planned a bus trip. If 20 or fewer people signed up, the cost per person would be 14.00 dollars. If more than 20 people signed up, the cost per person would be 12.50 dollars. In the end, 24 people signed up, but each person had already prepaid 14.00 dollars. The extra money collected will be used to buy snacks. How much total money will be spent on snacks?

    • $$24$$
    • $$28$$
    • $$36$$
    • $$30$$

30. Evaluate the complex expression $$(5+2i-6i^2)-(7+3i^2-4i)$$ where $$i^2=-1$$

    • $$7+6i$$
    • $$5-2i$$
    • $$15+7i$$
    • $$15-7i$$

31. The number of radians in a 660-degree angle can be written as $$n\pi$$ , where n is a constant. What is the value of n?

    • $$\frac{3}{2}$$
    • $$\frac{5}{3}$$
    • $$\frac{11}{3}$$
    • $$\frac{4}{3}$$

32. An investment portfolio is allocated as shown in the figure below. If 10000 dollars is invested in commodities, how much more money is invested in U.S. stocks than in foreign stocks?

    • 30,000
    • 60,000
    • 90,000
    • 200,000

33. The tokens in a game are distributed among five locations in the ratio 5:3:2:4:1. To win, a player must collect at least 1/8 of the tokens in each of three or more of the five locations. What is the minimum percent of the total tokens that must be collected?

    • $$3\%$$
    • $$4\%$$
    • $$5\%$$
    • $$6\%$$

34. What is n if 12 is the greatest common divisor of n and 84, and 756 is the least common multiple of n and 84?

    • $$108$$
    • 168
    • 325
    • 378

35. Which of the following numbers is rational?

    • $$-\sqrt{120}$$
    • $$\sqrt{\frac{1}{2}}$$
    • $$\sqrt{0.49}$$
    • $$\sqrt{40}$$

36. Triangle ABC is similar to triangle DEF. Triangle ABC has sides 4, 6, and 8. Which could NOT be the corresponding sides of triangle DEF?

    • 1, 1.5, and 2
    • 1.5, 2.25, and 3
    • 6, 9, and 12
    • 10, 16, and 20

37. If x is an integer such that $$|x+1|$$ < $$2$$, which of the following is a possible value of $$2x^2-5x+3$$?

    • 0
    • 1
    • 21
    • 36

38. According to the table below, what is the average (arithmetic mean) annual salary of the 10 officers of the Acme Tool Corporation?

    • 34,820
    • 35,000
    • 47,500
    • 52,000

39. The time it took car A to travel 400 miles was 2 hours less than the time it took car B to travel the same distance. If car A's average speed was 10 miles per hour greater than that of car B, what was car B's average speed, in miles per hour?

    • 20
    • 30
    • 40
    • 50

40. In the circle shown, C is the center, radius BC has length 2, and angle ACB measures 45 degrees. What is the area, in square inches, of the shaded region bounded by chord AB and the minor arc AB?

    • $$\frac{\pi}{2}-\sqrt{2}$$
    • $$\pi-\sqrt{2}$$
    • $$\frac{\pi}{2}+\sqrt{2}$$
    • $$\pi+\sqrt{2}$$

41. Find the shortest distance from the line of symmetry of $$y=2x^2-16x+29$$ to the line $$x=-3$$.

    • 7 units
    • 3 units
    • 4units
    • 5 units

42. A square is cut by a horizontal line into two equal halves. It is known that A and B together form one half of the square, and C and D form the other half. The areas satisfy $$A=\frac{1}{2}B$$ and $$C=\frac{2}{5}D$$. What fraction of the whole square is region C?

    • $$\frac{1}{2}$$
    • $$\frac{2}{5}$$
    • $$\frac{1}{7}$$
    • $$\frac{4}{9}$$

43. A community center is preparing gift bags for a fundraiser. Each bag requires 2/5 yard of ribbon and 3/10 yard of fabric. The center originally planned to make 150 bags, but materials are sold only in whole spools: ribbon in 12 yard spools and fabric in 15 yard spools. If they purchase enough full spools of each material to make at least 150 bags, how many extra bags can they make beyond 150?

    • 5
    • 10
    • 15
    • 0

44. The table shows the distribution of ages of 30 students.Which gives the correct order of the mean, median, and mode?

    • Median < Mode < Mean
    • mean < median < mode
    • median < mean < mode
    • mode < median < mean

45. Christian buys, sells, and trades electronic synthesizers. The graph tracks the number of synthesizers in his collection versus time in months. On what interval did the number of synthesizers increase the fastest?

    • Between 0 and 1 month.
    • Between 1 and 2 months.
    • Between 2 and 3 months.
    • Between 5 and 6 months.