Friday, August 26, 2016

(Sample) LET Specialization Mathematics 1

1.            Which of the following are antiderivatives of $f(x)={{\cos}^{3}}x\sin{x}$?
                A.            $F(x)=\frac{-{cos}^{4}x}{4}$   
                B.            $F(x)=\frac{{sin}^{2}x}{2}-\frac{{sin}^{4}x}{4}$
                C.            $F(x)=\frac{1-{cos}^{4}x}{4}$
                D.            all of these

2.            If you wanted to estimate the true percentage of all voters in Canada who are in favour of abolition of the senate, and if you wanted your maximum error of estimate to be 6% with a confidence level of 95%, what would the required sample size be?
                A.            267 
                B.            1068
                C.            131         
                D.            4272

3.            $\underset{x\to \infty }{\mathop{\lim }}\,\frac{5{{x}^{2}}+7x-3}{2+3x-11{{x}^{2}}}$ = _____.
                A.            -3/2 
                B.            -5/11 
                C.            0               
                D.            It is nonexistent.

4.            What is the horizontal asymptote of this graph?

          A.            x = 0
             B.            y = 0
             C.            x = 2.5
             D.            y =2.5

5.            A building that is 25 m tall casts a shadow of 10 m long. How long is the shadow of a 5-foot girl standing beside the building?
            A.            2 ft
            B.            2.5 ft
            C.            10 ft
            D.            250 ft

6.            Person M bought two radial tires at Php49.95 each and two seat cushions at  Php16.99 each. The sales tax where she lives is 6 percent. What was the total amount of the purchase?
                A.             Php 141.91
                B.             Php 99.00
                C.             Php 33.98
                D.             Php 133.88

7.            Find the general equation of the line which passes through the points (2,-1) and (-3,5).
                A.            6x +5y -7 = 0 
                B.            5x -6y -7 = 0  
                C.            6x +7y -5 = 0 
                D.            6x +6y -5 = 0

8.            In 4 years, Lynley will be twice as old as she was 6 years ago. How old is Lynley?
                A.            14
                B.            15
                C.            16
                D.            18

9.            For the parabola$y={x}^{2}+x-6$, find the equation of the axis of symmetry.
                A.            x = -1/2
                B.            x = -1 
                C.            x = 1/2
                D.            x = 1

10.          He is known as the "Father of Geometry" and had written a book that is considered to be the greatest piece of historical work in mathematics.
                A.            Archimedes
                B.            Euclid       
                C.            Newton
                D.            B. Pascal

11.          Find all real numbers that satisfy the equation,$cos(x)=1$.
                A.            $\left\{ x|x=\frac{\pi }{2}+2k\pi  \right\}$
                B.            $\left\{ x|x={\pi}+2k\pi  \right\}$
                C.            $\left\{ x|x=\frac{3\pi }{2}+2k\pi  \right\}$  
                D.            $\left\{ x|x=0+2k\pi  \right\}$

12.          Find all real numbers that satisfy the equation, $cos(2x)=\frac{\sqrt{3}}{2}$.
                A.            $\left\{ x|x=\frac{\pi }{6}+k\pi{or} x=\frac{5\pi }{6}+k\pi\right\}$
                B.            $\left\{ x|x=\frac{\pi }{12}+k\pi  \right\}$
                C.            $\left\{ x|x=\frac{\pi }{12}+2k\pi{or} x=\frac{11\pi }{12}+2k\pi\right\}$
                D.            $\left\{ x|x=\frac{\pi }{12}+k\pi{or} x=\frac{11\pi }{12}+k\pi\right\}$

13.          9i(5 - 6i) = _____.
                A.            54 + 45i
                B.            45i - 54  
                C.            $45i-54{i}^{2}$
                D.            none of these

14.          If the length of the radius of a circle is doubled, what happens to the circumference?
                A.            halved 
                B.            quadrupled
                C.            doubled
                D.            tripled

15.          What is the midpoint of the line segment joining the points (5, -3) and (-2, -7)?
                A.            (1/2, -10)
                B.            (3, -10)
                C.            (7, 4)
                D.            (3/2, -5)

16.          Solve for a: ${\log}_{4}{(3a-4)}=2$
                A.            a =3
                B.            a = 4
                C.            a = 20/3
                D.            a = 20

17.          "Which statement best describes these two functions?
$f(x)={x}^{2}-x+4$
$g(x)=-3{{x}^{2}}+3x+7$
"              A.            The maximum of f(x) is less than the minimum of g(x).
                B.            The minimum of f(x) is less than the maximum of g(x).
                C.            The maximum of f(x) is greater than the minimum of g(x).
                D.            The minimum of f(x) is greater than the maximum of g(x).

18.          If (14x + 2) units is the perimeter of a rectangle and (4x + 2) units is its length, how many units is its width?
                A.            2x + 1
                B.            3x - 1 
                C.            x + 4    
                D.            2x - 2
  
19.          What is the y-intercept of the graph of $y=-4{x}^{2}+2x-3$?
                A.            -3
                B.            3
                C.            -4
                D.            4
20.          Find all real numbers in [0, 2p] that satisfy the equation,$\sin{4x}=\frac{\sqrt{3}}{2}$.
                A.            0, $\frac{\pi}{4}$, $\pi$
                B.            $\frac{\pi}{12}$, $\frac{\pi}{6}$, $\frac{2\pi}{3}$, $\frac{7\pi}{12}$, $\frac{7\pi}{6}$, $\frac{13\pi}{12}$, $\frac{5\pi}{3}$, $\frac{19\pi}{12}$
                C.            $\frac{\pi}{4}$, $\frac{5\pi}{4}$   
                D.            0

21.          If $f(x)=\left\{ \begin{matrix}  {{e}^{x}},x<\ln 2  \\   2,x\ge \ln 2  \\\end{matrix} \right.$, then $\underset{x\to \ln 2}{\mathop{\lim }}\,f(x)$ = _____.
                A.            $\frac{1}{2}$
                B.            $\ln{2}$          
                C.            2        
                D.            ${e}^{2}$

22.          Find the area of the triangle, given that $\gamma={105}^{\circ}$, a = 2, and b = 9. Note that $\alpha$, $\beta$, and $\gamma$ are the opposite angles of the sides: a, b, and c, respectively.
                A.            2.33   
                B.            8.69 
                C.            101.42  
                D.            34.77

23.          Compute for the determinant.
\[\left| \begin{matrix}   1 & 2 & 3 & 4  \\   1 & 4 & 5 & 8  \\   1 & 1 & 2 & 3  \\   1 & 3 & 5 & 8  \\\end{matrix} \right|\]
                A.            -4
                B.            -3  
                C.            -2
                D.            -1

24.          $\frac{5(\cos{{200}^{\circ}} + i\sin{{200}^{\circ}})}{4(\cos{{50}^{\circ}} + i\sin{{50}^{\circ}})}$ = ______.
                A.            $-2+2\sqrt{3}i$
                B.            $-\frac{1}{2}+\frac{\sqrt{3}}{2}i$
                C.            $-10+10\sqrt{3}i$
                D.            $-\frac{5\sqrt{3}}{8}+\frac{5}{8}i$

25.          Which of the following is equal to ${\log}_{3}{(243)}=5$?
                A.            ${5}^{4}=243$
                B.            ${243}^{\frac{5}{3}}$
                C.            ${3}^{5}=243$
                D.            $\sqrt[3]{243}=5$

26.          The earliest known use of the equals symbol ( = ) is by Robert Recorde in what year?
                A.            1409
                B.            1452 
                C.            1508
                D.            1557

27.          If one side of a square is doubled in length and the adjacent side is decreased by two centimeters, the area of the resulting rectangle is 96 square centimeters larger than that of the original square. Find the dimensions of the rectangle.
                A.            17 x 24
                B.            24 x 24
                C.            10 x 24 
                D.            6 x 16



28.          The smallest angle of a triangle is two-thirds the size of the middle angle, and the middle angle is three-sevenths of the largest angle. Find all three angle measures.
                A.            30°, 60°, 90°  
                B.            45°, 45°, 90°   
                C.            35°, 45°, 110° 
                D.            30°, 45°, 105°

29.          What is the area of the largest rectangular garden that can be fenced off with 50m of fencing materials?
                A.            156.25 sq m
                B.            175.5 sq m   
                C.            475.75 sq m
                D.            625 sq m

30.          If tan x = 2/3 and tan y = 3/4, what is the value of tan (x + y)?
                A.            1/6
                B.            4/5   
                C.            1           
                D.            17/6

31.          How many terms are there in a geometric series if the first term is 3, the common ratio is 4, and the sum of the series is 1,023?
                A.            4
                B.            5
                C.            6
                D.            23

32.          Sampling  that subdivides the population into subgroups is called a _____ sampling.
                A.            cluster 
                B.            stratified 
                C.            systematic
                D.            random

33.          A, B, and C are 3 consecutive numbers. If A > B > C, what is the value of (A - B)(A - C)(B - C)?
                A.            -2   
                B.            -1             
                C.            1  
                D.            2

34.          arcsec $\left(\sqrt{2}\right)$ = _____.
                A.            $\frac{7\pi}{4}$ 
                B.            $\frac{3\pi}{4}$  
                C.            $\frac{\pi}{4}{\pm}2{\pi}n$ , $\frac{7\pi}{4}{\pm}2{\pi}n$          
                D.            $\frac{\pi}{4}$

35.          In a Filipino test, eight students obtained the following scores: 10, 15, 12, 18, 16, 24, 12, 14. What is the median score?
                A.            14
                B.            14.5 
                C.            15
                D.            15.5

36.          Two angles of a triangle measure 4 cm and 7 cm. What is the range of values for the possible lengths of the third side?
                A.            4 < x < 7   
                B.            3 < x < 11  
                C.            7 < x < 11    
                D.            11 < x < 15

37.          A wood frame for pouring concrete has an interior perimeter of 14 meters. Its length is one meter greater than its width. The frame is to be braced with twelve-gauge steel cross-wires. Assuming an extra half-meter of wire is used at either end of a cross-wire for anchoring, what length of wire should be cut for each brace?
                A.            6 m      
                B.            7 m         
                C.            8 m        
                D.            12 m

38.          Which of the following statements is true?
                A.            A rectangle is a square.
                B.            A parallelogram is a trapezoid.
                C.            A rhombus is a rectangle.    
                D.            A square is a rhombus.

39.          Which expression represents the result of the following subtraction? $\frac{3x-1}{x+2}- \frac{x-2}{x-1}$
                A.            $\frac{2x+1}{3}$ 
                B.            $\frac{2x+1}{{x}^{2}+x-2}$
                C.            $\frac{3{{x}^{2}}-4x+5}{3}$ 
                D.            $\frac{2{{x}^{2}}-4x+5}{{x}^{2}+x-2}$

40.          Adrian Rice has written in Historia Mathematica about _____.
                A.            the London Mathematical Society 
                B.            the Brazilian Mathematical Society
                C.            the Mathematics of Ancient Egypt   
                D.            the Mathematics of Macedonia

41.          At which of the following points is the graph of $f(x)={x}^{4}-2{x}^{3}-2{x}^{2}-7$ decreasing and concave down?
                A.            (1, -10) 
                B.            (2, -15)      
                C.            (3, 2)     
                D.            (-1, -6)

42.          Rodia can cross-stitch a design for 10 days while Vessy can do the same job in 15 days. How long will they finish the job is they help each other?
                A.            5 days    
                B.            6 days    
                C.            8 days  
                D.            10 days

43.          Evaluate: $\left( {{\log }_{3}}4 \right)\left( {{\log }_{2}}3 \right)$
                A.            2    
                B.            3           
                C.            4  
                D.            5

44.          There are how many inversions in the permutation (1, 5, 3, 2, 4)?
                A.            1      
                B.            2              
                C.            3          
                D.            4

45.          Which of these is a root of $f(x)={x}^{3}-3{{x}^{2}}-4x+12$ ?
                A.            -3         
                B.            3          
                C.            4        
                D.            12

46.          How many unique diagonals can be drawn in a pentagon?           
                A.            5           
                B.            6             
                C.            7             
                D.            10

47.          Find the value of x: ${\log}_{2}{x}=5$
                A.            2.5    
                B.            3.2           
                C.            10    
                D.            32

48.          A German expert known as 'Princeps Mathematicon' meaning the "Prince of Mathematicians".
                A.            Archimedes
                B.            Euclid        
                C.            C. Gauss
                D.            B. Pascal

49.          "Which quadrants contain the solutions to the following system of inequalities?
            \[\left\{ \begin{align}  & y-2x\le -3 \\ & 3y+x\ge -4 \\\end{align} \right\}\]
                A.            quadrants I and IV
                B.            quadrants II and III
                C.            quadrants III and IV
                D.            quadrants II, III, and IV

50.          (9 - 4i)(2 + 6i) = _____.
                A.            42 - 46i   
                B.            42 + 46i  
                C.            -6 - 62i    
                D.            none of these

51.          Write an equation to represent the following: "Eigtheen is ten less than twice some number, x."
                A.            2x - 10 = 18
                B.            2x - 18 = 10  
                C.            10 - 2x = 18
                D.            18 - 10 = 2x

52.          Solve the triangle, given that a = 8.9, b = 13.2, and c = 16.1. Note that $\alpha$, $\beta$, and $\gamma$ are the opposite angles of the sides: a, b, and c, respectively.
                A.            $\alpha={31.5}^{\circ}$, $\beta={55.0}^{\circ}$, $\gamma={93.4}^{\circ}$
                B.            $\alpha={35.5}^{\circ}$, $\beta={53.0}^{\circ}$, $\gamma={91.4}^{\circ}$
                C.            $\alpha={33.5}^{\circ}$, $\beta={55.0}^{\circ}$, $\gamma={91.4}^{\circ}$  
                D.            no solution

53.          How many liters of water should be added to 8 liters of 70% solution to make it 60% of the acid?
                A.            1 1/3  
                B.            2 1/2
                C.            3       
                D.            3 2/3

54.          It is the set of points in a plane such that the sum of the distances of each point from two fixed points is a constant.
                A.            parabola  
                B.            circle    
                C.            ellipse   
                D.            hyperbola

55.          Which expression is equivalent to  $\sqrt{-6}(\sqrt{-4}-\sqrt{3})$ ?
                A.            $2\sqrt{6}+3\sqrt{2}$
                B.            $-24-6i\sqrt{3}$
                C.            $2\sqrt{6}-3i\sqrt{2}$ 
                D.            $-2\sqrt{6}-3i\sqrt{2}$

56.          Simplify: $5\sqrt{12}-3\sqrt{27}+7\sqrt{48}$
                A.            $2\sqrt{5}$   
                B.            $9\sqrt{6}$
                C.            $29\sqrt{3}$   
                D.            $3\sqrt{7}$

57.          Given the following scores of 70, 95, 60, 80, and 100, what is the mean absolute deviation?
                A.            11.7  
                B.            13.2 
                C.            14.6   
                D.            15.9

58.          Which expression is equivalent to ${(4i)}^{3}$ ?
                A.            -12i 
                B.            12i      
                C.            -64i    
                D.            64i

59.          Which of the following exhibits an odd permutation?
                A.            5, 2, 4, 1, 7, 9
                B.            1, 4, 3, 2, 6, 5 
                C.            c, a, g, b, d
                D.            6, 1, 4, 3, 5, 2

60.          ${\csc}^{-1}\left({2}\right)$ = _____.
                A.            ${{60}^{\circ }}$        
                B.            $-{{30}^{\circ }}$             
                C.            ${{420}^{\circ }}$                 
                D.            ${{30}^{\circ }}$

61.          _____ is 20% more than 50.
                A.            110        
                B.            55            
                C.            60       
                D.            72

62.          What is the sum of the measures of the interior angles of an icosagon?
                A.            3100      
                B.            3140        
                C.            3240      
                D.            2850

63.          $-15+20i$ = _____.
                A.            25(cos 126.9° + i sin 126.9°)
                B.            25(cos 306.9° + i sin 306.9°)
                C.            25(cos 53.1° + i sin 53.1°)
                D.            25(cos 233.1° + i sin 233.1°)

64.          What is the measure of an interior angle of a regular dodecagon?
                A.            120 degrees       B.            130 degrees 
                C.            140 degrees       D.            150 degrees



65.          Find all solutions to the following systems of linear equations.
\[\left( \begin{align} & x+y+3z=3 \\ & -x+y+z=-1 \\ & 2x+3y+8z=4 \\ \end{align} \right)\]
                A.            x =1; y = 2; z = 4
                B.            x =1; y = 2; z = 6
                C.            x =1; y = 2; z = 8  
                D.            there are no solutions

66.          $\sqrt{-25}$ = _____.
                A.            5i            
                B.            -5i      
                C.            $-i\sqrt{5}$             
                D.            $\pm5$

67.          At a large university, the probability that a student takes calculus and statistics in the same semester is 0.0125. The probability that a student takes statistics is 0.125. Find the probability that a student is taking calculus, given that he or she is taking statistics.
                A.            0.1                 
                B.            0.1125    
                C.            0.0016     
                D.            0.1375

68.          If $f(x)={x}^{2}-1$ and $g(x)=x-1$ , what is the value of $(\frac{f}{g})(x)$ ?
                A.            x - 1        
                B.            x + 1          
                C.            $\frac{1}{x-1}$      
                D.            $\frac{1}{x+1}$

69.          Given the matrix, \[A=\left( \begin{matrix}   1 & 1 & 1  \\   1 & 2 & t  \\   1 & 4 & {{t}^{2}}  \\\end{matrix} \right)\],  for what values of t is matrix A invertible?
                A.            A is invertable for $t\ne{3}$, $t\ne{0}$.      
                B.            A is invertable for$t\ne{2}$, $t\ne{1}$.
                C.            A is invertable for$t\ne{-2}$, $t\ne{-1}$.     
                D.            A is not invertable at all values of t.

70.          if the sum of the interior angles of a regular polygon is 1980 degrees, how many sides does it have?
                A.            11        
                B.            12      
                C.            13      
                D.            14

71.          If$f(x)=(1+6x)(1-6x)$, what are the zeros of the function f?
                A.            0, -1/6     
                B.            1/6. 1/6  
                C.            -1/6, 1/6   
                D.            6, -6

72.          Find the magnitude and direction angle of the vector, <$\sqrt
{21}$. -1>. Give the measure of the direction angle as an angle in [0°, 360°).
                A.            22; 347.7° 
                B.            22; 102.3°   
                C.            $\sqrt{22}$; 347.7°
                D.            $\sqrt{22}$; 282.3°

73.          A boat sails 40 miles north, 60 miles west, and 40 miles north again. How many miles is it from the starting point?
                A.            100  
                B.            120         
                C.            140   
                D.            150

74.          Which among the measures of central tendency is not influenced by outliers?
                A.            mean   
                B.            weighted mean      
                C.            median  
                D.            mode

75.          3(cos 30° + i sin 30°) · 2(cos 90° + i sin 90°)
                A.            $2\sqrt{6}-\sqrt{2}i$ 
                B.            $-3+3\sqrt{3}i$
                C.            $-6-6\sqrt{3}i$
                D.            $3-12\sqrt{3}i$

76.          The mass of a radioactive sample is given by $M(t)={{M}_{0}}{{10}^{-kt}}$ , where t is the time in years, ${M}_{0}$ is the initial mass, and k is a constant. If 400 grams of this material decays to 40 grams in 10 years, what is the value of k?
                A.            1      
                B.            -1      
                C.            0.1      
                D.            -0.1

77.          What measure of central tendency can best describe the size of t-shirts commonly used by teenagers?     
               A.            mean     
               B.            median    
               C.            mode             
               D.            both a and c

78.          The price of a magazine rises from Php5.00 to Php15.00. What is the percent increase in price?
                A.            100%    
                B.            150%  
                C.            180%    
                D.            200%

79.          In a senior class of 100 students, 60 are taking Spanish as a foreign language, while 70 are taking Japanese. If 40 are taking both Spanish and Japanese, and if these are the only foreign languages courses offered in the school, how many are not taking any foreign language courses?
                A.            5         
                B.            8     
                C.            10        
                D.            30

80.          Solve the triangle, given that $\gamma={65.7}^{\circ}$, a = 4.42, and b = 17.5. Note that $\alpha$, $\beta$, and $\gamma$ are the opposite angles of the sides: a, b, and c, respectively.
                A.            c = 18.5, $\alpha={16.4}^{\circ}$, $\beta={40.1}^{\circ}$
                B.            c = 12.7, $\alpha={18.4}^{\circ}$, $\beta={38.1}^{\circ}$
                C.            c = 15.6, $\alpha={20.4}^{\circ}$, $\beta={36.1}^{\circ}$
                D.            no solution

81.          If tan x = 2/3 and tan y = 3/4, what is the value of tan (x + y)?
                A.            1/6  
                B.            4/5       
                C.            1      
                D.            17/6

82.          How many sides does a regular polygon have if the exterior angle is ${15}^{\circ}$?
                A.            15          
                B.            24       
                C.            30          
                D.            48

83.          Find the banker's interest to the nearest cent. Principal: Php 2500.00; rate: 9%; time: 180 days
                A.            Php 104.32
                B.            Php 109.75    
                C.            Php 112.50
                D.            Php 110.96

84.          Which of the following is true for all acute angles?
                                 I. ${\cos}^{2}\theta=1-{\sin}^{2}\theta$              
                                 II. $\cos\theta\tan\theta=\sin\theta$
                                 III. ${\sec}^{2}{\cot\theta}=\csc\theta$      
                A.            I only    
                B.            II only   
                C.            I and II  
                D.            I, II, and III

85.          Find all real numbers that satisfy the equation, $cos(x)=1$.
                A.            $\left\{ x|x=\frac{\pi }{2}+2k\pi  \right\}$  
                B.            $\left\{ x|x={\pi}+2k\pi  \right\}$
                C.            $\left\{ x|x=\frac{3\pi }{2}+2k\pi  \right\}$
                D.            $\left\{ x|x=0+2k\pi  \right\}$

86.          3(cos 30° + i sin 30°) · 2(cos 90° + i sin 90°)
                A.            $2\sqrt{6}-\sqrt{2}i$ 
                B.            $-3+3\sqrt{3}i$
                C.            $-6-6\sqrt{3}i$
                D.            $3-12\sqrt{3}i$

87.          Find all solutions to the following systems of linear equations.
\[\left( \begin{align} & x-2y+2z=5 \\ & x-y=-1 \\ & -x+y+z=5 \\ \end{align} \right)\]
                A.            x =1; y = 2; z = 4
                B.            x =1; y = 2; z = 5
                C.            x =1; y = 2; z =3   
                D.            there are no solutions

88.          If x and y are real numbers, what is the simplified radical form of ${{\left( {{x}^{2}}{{y}^{5}} \right)}^{\frac{1}{5}}}$  ?
                A.            $y\sqrt[5]{{{x}^{2}}}$ 
                B.            $y\sqrt{{{x}^{5}}}$   
                C.            $\left| y \right|\sqrt[5]{{{x}^{2}}}$    
                D.            $\left| y \right|\sqrt{{{x}^{5}}}$

89.          Which of the following equations is  a graph of a point?
                A.            ${x}^{2}+{y}^{2}-4x+10y+29=0$      
                B.            ${x}^{2}+{y}^{2}+8x-6y+30=0$
                C.            ${x}^{2}+{y}^{2}-6x-8y+9=0$
                D.            $4{x}^{2}+4{y}^{2}-81=0$

90.          Mr. L worked at three jobs in 3 days. In the first day, he earned Php 310.00. In the next day, he was paid Php 334.00. In the third day, he was paid Php 307. What average per day did Mr. L earn for these 3 days?
                A.            Php 951.00
                B.            Php 317.00
                C.            Php 978.00
                D.            Php 326.00

91.          Let f be a function such that, $\underset{h\to 0}{\mathop{\lim }}\,\frac{f(5+h)-f(5)}{h}=3$. Which of the following must be true?
                A.            f(5) = 3       
                B.            f'(5) = 3
                C.            f is continuous and differentiable at x = 5.
                D.            both B and C

92.          What is the set of approximate y-values of the relative minimum and maximum of this graphed function?

                A.            {2} 
                B.            {-1, 2}    
                C.            {-1, 3}
                D.            {-2, 1, 3}
                                                                               
93.          What is the maximum number of books, each 1.4 cm thick that can be put vertically in a shelf which is 64 cm long?
                A.            44
                B.            45  
                C.            46    
                D.            64



94.          Which expression represents the quotient of the following? $\frac{4{{x}^{2}}y}{8x{{y}^{2}}}\div \frac{12x{{y}^{2}} }{8{{x}^{6}}{{y}^{3}}}$
                A.            $\frac{{{x}^{5}}}{3}$     
                B.            $\frac{3}{{{x}^{5}}}$       
                C.            $\frac{{{x}^{6}}}{3}$   
                D.            $\frac{3}{{{x}^{6}}}$

95.          The earth revolves ${360}^{\circ}$ of longitude in one day. How many minutes does it take to revolve through ${15}^{\circ}$?
                A.            30   
                B.            60        
                C.            90  
                D.            120

96.          How many vertical asymptotes does the graph of $y=\frac{x-2}{{x}^{2}+4}$ have?
                A.            0        
                B.            1           
                C.            2        
                D.            4

97.          If ${x}^{2}$ is proportional to ${y}^{3}$, and if x = 1 when y = 4, find x when y = 3.
                A.            $\frac{3\sqrt{3}}{8}$     
                B.            $\frac{4\sqrt{2}}{5}$          
                C.            $\frac{6\sqrt{3}}{7}$       
                D.            12

98.          If $f(x)=x-\frac{1}{2}$ and $g(x)=-2$ , which graph corresponds to the function $(fg)(x)$ ?

                A.            line R
                B.            line S     
                C.            line T
                D.            line U        
                                                                                        
99.          What is the value of x in this rational equation, $\frac{2}{x-1}=\frac{3}{x+1}$ ?
                A.            2
                B.            3
                C.            4      
                D.            5

100.        What is the converse of the statement, "If a, then b"?
                A.            If not a, then b.
                B.            If b, then a. 
                C.            If not b, then a.
                D.            If not a, then not b.

101.        Evaluate: $\frac{{{a}^{2}}}{ab}* \frac{3{{b}^{2}}}{2a}$
                A.            3/2a   
                B.            b/a            
                C.            3b/2 
                D.            b/2

102.        In a photograph, Bianca is 9 cm tall and her brother Tristan is 10 cm tall. Bianca's actual height is 153 cm. What is Tristan's actual height?
                A.            148 cm
                B.            156 cm     
                C.            168 cm
                D.            170 cm

103.        Which of the following must be always positive?
                A.            The product of three negative numbers.
                B.            The sum of two negative numbers.
                C.            The sum of a positive and a negative number.
                D.            The product of two negative numbers.

104.        $10+\sqrt{-81}$ = _____.
                A.            1      
                B.            10 - 9i      
                C.            10 + 9i
                D.            10 + i

105.        Which of the following must be true if points L, M, N, and O are coplanar points and a line segment drawn from L to M passes through N while a line segment drawn from N to M passes through O?
                A.            LN + NO = LM                  
                B.            LO + NO = LN
                C.            Point N is the midpoint of segment NO.   
                D.            Points L, M, N, and O are collinear.

106.        If the height of a triangle is five inches less than the length of its base, and if the area of the triangle is 52 square inches, find the base(b) and the height (h).
                A.            b=13, h=8
                B.            b=12, h=9  
                C.            b=11, h=7
                D.            b=13, h=4

107.        A triangle has a perimeter of 50. If 2 of its sides are equal and the third side is 5 more than the equal sides, what is the length of the third side?
                A.            5
                B.            10
                C.            15
                D.            20

108.        Find the magnitude and direction angle of the vector, <0, -18>. Give the measure of the direction angle as an angle in [0°, 360°).
                A.            324; 270°
                B.            18; 90°  
                C.            18; 180°
                D.            18; 270°

109.        Find the component form for the vector v with the given magnitude and direction angle θ. |v| = 153.8, θ = 121.6°
                A.            <131.0, 80.6>
                B.            <80.6, 131.0>  
                C.            <-80.6, 131.0>
                D.            <131.0, -80.6>

110.        Find the area of the figure below.


                 A. 25.02 sq ft
                 B. 6.26 sq ft
                 C. 12.51 sq ft
                 D. 14.69 sq ft


 111.       What is the solution set of this system of equations?
      \[\left\{ \begin{align}  & {{x}^{2}}+y-1=0 \\ & x-y+1=0 \\\end{align} \right\}\]
                A.            {(-1,-1), (-1,0)}
                B.            {(-1,0), (-1,1)}
                C.            {(-1,0), (0,1)}
                D.            {(1,0), (1,1)}

112.        What are the vertical and horizontal asymptotes of  $f(x)=\frac{{x}^{2}-9}{16-{x}^{2}}$ ?
                A.            x = $\pm4$, and y = -1
                B.            y = $\pm4$, and x = -1
                C.            x = $\pm4$, and y = 1
                D.            y = $\pm4$, and x = 1

113.        Find the inverse of the matrix,   \[B=\left[ \begin{matrix}   1 & 0 & 4  \\   -1 & 1 & -1  \\   -1 & 0 & -3  \\\end{matrix} \right]\]
                A.            1  
                B.            \[{{B}^{-1}}=\left[ \begin{matrix}  - 4 & 2 & 1  \\   -1& 5 & -1  \\   -6 & 8 & -1  \\\end{matrix} \right]\]
                C.            \[{{B}^{-1}}=\left[ \begin{matrix}   -3 & 0 & 4  \\   -2 & 1 & -3  \\   1 & 0 & 1  \\\end{matrix} \right]\]  
                D.                the matrix is not invertible

114.        If the smallest and largest numbers is set Q are removed, what is the median of set Q? Q = {10, 9, 2, 6, 3, 4, 1, 7, 5, 2}
                A.            4    
                B.            4.5      
                C.            5     
                D.            5.5

115.        The Vitamin C content of a particular brand of vitamin supplement pills is normally distributed with mean 490 mg and standard deviation 12 mg. What is the probability that a randomly selected pill contains at least 500 mg of Vitamin C?
                A.            0.0525
                B.            0.1123        
                C.            0.2033
                D.            0.7967

116.        Which set of three numbers can be the measures of the sides of right triangle?
                A.            5, 12, 13
                B.            4, 8, 12   
                C.            7, 13, 15
                D.            6, 7, 8

117.        Which of these observations is a model of population growth?
                A.            The population started out large, decreased in size, then became large again.
                B.            The population is observed to increase at a faster rate as time passes.
                C.            The population is observed to increase steadily over time.
                D.            The population grew very quickly but then declined.

 118.        Simplify: $\frac{1}{2}\left({a-2b}\right)+\frac{1}{4}\left({2a+4b}\right)$
                A.            a       
                B.            a + b      
                C.            2a      
                D.            a + 2b

119.        How many ways can a committee of 4 people be selected from a group of 7 people?
                A.            35          
                B.            70          
                C.            140   
                D.            210

120.        What are the coordinates at the minimum point of $f(x)={{x}^{2}}-4x+3$ ?
                A.            (-1,2)    
                B.            (-1,2)   
                C.            (2, -1)   
                D.            (2, 1)

Answer Key

1.            D
2.            A
3.            B
4.            B
5.            A
6.            A
7.            A
8.            C
9.            A
10.          B
11.          D
12.          D
13.          A
14.          C
15.          D
16.          C
17.          B
18.          B
19.          A
20.          B
21.          C
22.          B
23.          C
24.          D
25.          C
26.          D
27.          C
28.          D
29.          A
30.          D
31.          B
32.          B
33.          D
34.          D
35.          B
36.          B
37.          A
38.          D
39.          D
40.          A
41.          A
42.          B
43.          A
44.          D
45.          B
46.          A
47.          D
48.          C
49.          A
50.          B
51.          A
52.          C
53.          A
54.          C
55.          D
56.          C
57.          B
58.          C
59.          A
60.          D
61.          C
62.          C
63.          A
64.          D
65.          B
66.          A
67.          A
68.          B
69.          B
70.          C
71.          C
72.          C
73.          A
74.          C
75.          B
76.          C
77.          C
78.          D
79.          C
80.          B
81.          D
82.          B
83.          D
84.          C
85.          D
86.          B
87.          A
88.          A
89.          A
90.          B
91.          D
92.          C
93.          B
94.          C
95.          B
96.          A
97.          A
98.          D
99.          D
100.        B
101.        C
102.        D
103.        D
104.        C
105.        D
106.        A
107.        D
108.        D
109.        C
110.        C
111.        C
112.        A
113.        C
114.        B
115.        C
116.        A
117.        B
118.        A
119.        A
120.        C

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