Practice Test 4 1 hour — 50 Questions Directions For each question, choose the BEST answer from the choices given. If the precise answer is not among the choices, choose the one that best approximates the answer. Notes Reference Information: Use the following formulas as needed. Right circular cone: If r = radius and h = height, then and if c = circumference of the base and ℓ = slant height, then Sphere: If r = radius, then and Surface Area = 4πr 2 . Pyramid: If B = area of the base and h = height, then To answer some of these questions, you will need a calculator. You must use at least a scientific calculator, but programmable and graphing calculators are also allowed. (1) All angle measures on this test are in degrees, so your calculator should be set to degree mode. (2) Figures in this test are drawn as accurately as possible UNLESS it is stated in a specific question that the figure is not drawn to scale. All figures are assumed to lie in a plane unless otherwise specified. (3) The domain of any function f is assumed to be the set of all real numbers x for which f(x) is a real number, unless otherwise indicated. (4) 1. What is a possible form of the quadratic equation, if the sum of the roots is −1 and the product of the roots is −20?
Transcript
Practice Test 4
1 hour — 50 Questions
DirectionsFor each question, choose the BEST answer from the choices given. If the precise answer is not among the choices, choose the one thatbest approximates the answer.
Notes
Reference Information: Use the following formulas as needed.
Right circular cone: If r = radius and h = height, then
and if c = circumference of the base and ℓ = slant height, then
Sphere: If r = radius, then
and Surface Area = 4πr2 .
Pyramid: If B = area of the base and h = height, then
To answer some of these questions, you will need a calculator. You must use at least a scientific calculator, but programmableand graphing calculators are also allowed.
(1)
All angle measures on this test are in degrees, so your calculator should be set to degree mode.(2)
Figures in this test are drawn as accurately as possible UNLESS it is stated in a specific question that the figure is not drawn toscale. All figures are assumed to lie in a plane unless otherwise specified.
(3)
The domain of any function f is assumed to be the set of all real numbers x for which f(x) is a real number, unless otherwiseindicated.
(4)
1. What is a possible form of the quadratic equation, if the sum of the roots is −1 and the product of the roots is −20?
y = 2x2 + 2x − 40(A)y = x2 − x − 20(B)y = x2 + x + 20(C)y = 2x2 − 2x − 20(D)−20y = x − 1(E)
2. A boat sights the top of a 40-foot lighthouse at an angle of elevation of 25 degrees. How far away is the boat from the lighthouse(the horizontal distance), to the nearest tenth of a foot?
Figure 1 shows a square with total area of 121 square units. Based on the figure, what is the value of x?
2(A)4(B)7(C)11(D)49(E)
4. A plumbing company charges $42.50 plus x dollars per hour to make a house call. Which expression below represents the cost ofa 90-minute house call?
7. Solve for x, to the nearest tenth: log12 640 = x.
1.7(A)2.6(B)2.8(C)53.3(D)7,680(E)
8. A triangle with coordinates (2,0), (2,6), and (6,0) is rotated about the line x = 2. What is the volume, in cubic units, of the resultantsolid?
16(A)8π(B)16π(C)32π(D)48π(E)
9. Within a given area code, how many seven-digit numbers are available, given the restrictions that the first three digits cannot be911 or 411 and the first digit cannot be a 1 or a 0?
−3 ≤ x ≤ 10(A)−10 ≤ x ≤ 3(B)x ≤ −10 or x ≥ 3(C)x ≤ −3 or x ≥ 10(D)−11 ≤ x ≤ 4(E)
11. What is the point of intersection of the line that passes through the points (1,5) and (3,9) and the line perpendicular to that linethat passes through the point (0,−2)?
(−2,−1)(A)(−2,2)(B)(2,−2)(C)(−1,−2)(D)(1,2)(E)
12. Solve for x: | 4x − 3 | − 9 < 0.
1.5 ≤ x ≤ 3(A)x < 3(B)x < 1.5 or x > 3(C)x ≤ −3(D)−1.5 < x < 3(E)
13. Given that what is the multiplicative inverse of 5 − i?
5 + i(A)
(B)
(C)
(D)
(E)
14. What is the value of x: logx125 = 3?
5(A)41.7(B)122(C)128(D)375(E)
15. Given f(x) = 7x + 5, what is f−1(x), the inverse function?
f−1(x) = 7x + 5(A)
f−1(x) = 5x + 7(B)
(C)
(D)
(E)
16. Take 6 less than a number n. If you raise this result to the 5th power, it is equal to 32. What is the value of n?
2(A)2.07(B)4 only(C)4 or 8(D)8 only(E)
17. Take a fraction that is equivalent to and add 2 to both the numerator and the denominator. If the result is what was theoriginal fraction?
(A)
(B)
(C)
(D)
Cannot be determined.(E)
18. Simplify:
(A)
2x − 4(B)
(C)
−7(D)
−12(E)
19. When 3x3 + 2x2 + 2x + k is divided by x + 2, the remainder is 4. What is the value of k?
4(A)24(B)34(C)54(D)x + 4(E)
20. Simplify:
2x4yz2(A)
(B)
2x8y4z2(C)
(D)
6y4z2(E)
21. What is the solution to this system of equations?
(1,4) and (−2,5)(A)(1,−4) and (2,11)(B)(1,4) and (−2,−5)(C)(−2,7)(D)(0,1)(E)
22. Which of the following graphs is NOT a function?
(A)
(B)
(C)
(D)
(E)
23. What is the solution to this system of equations?
(−5,0) only(A)(0,5) only(B)(0,−5) and (−5,0)(C)(0,5) and (5,0)(D)(0,−5) and (5,0)(E)
24. A bus travels from point A to point B. The bus starts out going slowly and then drives faster. Traffic is then at a total standstill dueto an accident. The bus continues at the faster speed. The bus reaches point B. Which of the following graphs could representthe bus’s distance from point A, as a function of time?
(A)
(B)
(C)
(D)
(E)
25. A parallelogram has angles of measure 45 degrees and 135 degrees. The shorter side of the parallelogram measures 2.83 meters,and the other side is 8.83 meters. What is the area of the parallelogram, to the nearest hundredth?
26. A fitness club offers weights, treadmills, and aerobic classes. Fifty members were asked which services they used, and the resultswere as follows:
How many members use only one of the three services?
18 members use weights and do aerobics.25 members use weights and the treadmill.15 members use the treadmill and do aerobics.10 members use all three activities.
0(A)10(B)12(C)18(D)40(E)
27. Given the equation what is x in terms of y and a?
(A)
(B)
(C)
x = y(a2 + 7a)(D)
x = (y + 7a)(y − a2)(E)
28. Solve for x to the nearest hundredth:
−0.76(A)−0.69(B)−0.67(C)0.69(D)0.76(E)
29. If x = y3 + 4y and what is the approximate value of x when k = 21?
1.37(A)1.44(B)1.67(C)4.04(D)4.11(E)
30. Solve for x:
0.71(A)3.57(B)5.8(C)25(D)45(E)
31. A car travels a steady speed of x miles per hour. How many hours, in terms of x, will it take to drive 540 miles?
540x(A)
540 + x(B)
(C)
(D)
x − 540(E)
32.
Figure 2
In the segment shown in Figure 2, the length of is three more than twice the length of . If the length of is 27 cm,what is the length of ?
8 cm(A)9 cm(B)10 cm(C)12 cm(D)15 cm(E)
33. If f(x) = x2 − 10 and g(x) = 4x + 3, what is f(g(2))?
−24(A)−21(B)12(C)27(D)111(E)
34. Which graph below represents the solution to the following system of inequalities?
(A)
(B)
(C)
(D)
(E)
35.
Figure 3
In the rectangular solid shown in Figure 3, what is the length of diagonal , to the nearest tenth?
7.07(A)8.6(B)10(C)13.60(D)25(E)
36.
Figure 4
In the segment shown in Figure 4, the ratio of the lengths of to is 5:8. If x represents AB, what is the midpoint of in terms of x?
4x(A)
(B)
(C)
(D)
(E)
37. Let be defined as a b = a2 + ba − 16b ÷ a. What is the value of 8 3?
−2.67(A)5(B)34(C)46(D)82(E)
38.
Figure 5
In Figure 5, a circle is inscribed in a square. What is the area of the shaded portion, to the nearest hundredth?
