Math Subject Test Missed Questions
f(t) = 24.62sin(0.53t-2.57) + 27.27 The function f above can be used to approximate the average monthly temperature, in degrees fahrenheit, for Nome, Alaska. Integer values of t represent the first day of each month (e.g. t=1 represents January 1, t =2 represents February 1, etc.) Using the calendar year, during what month does the average temperature first reach 32ºF? a. March b. April c. May d. June e. July
c. May graph both the function and line y=32, see where they intersect
If f(x)= ax^2+bx+c, how must a and b be related so that the graph of f(x-3) will be symmetric about the y-axis? a a=b b b=0, a is any real number c b=3a d b=6a e a=1/9(b)
d b=6a barron's test 2#45
For a class test, the mean score was 65, the median score was 71, and the standard deviation of the scores was 7. The teacher decided to add 5 points to each score due to a grading error. Which of the following statements must be true for the new scores? I. the new mean score is 70 II. the new median score is 76 iii. the new standard deviation of the scores is 12 a. none b I only c II only d I and II only e I, II, and II
d I and II only - For this type of question you need to evaluate each statement separately. Statement text I end text is true. If you add 5 to each number in a data set, the mean will also increase by 5. Statement text II end text is also true. The relative position of each score will remain the same. Thus, the new median score will be equal to 5 more than the old median score. Statement text III end text is false. Since each new score is 5 more than the old score, the spread of the scores and the position of the scores relative to the mean remain the same. Thus, the standard deviation of the new scores is the same as the standard deviation of the old scores.
The solution set of 3x+4y<0 lies in which quadrants? a I only b I and II c I, II, and III d II, III, and IV e I, II, III, and IV
d II, III, and IV barron's test 2 #32
If f(x) = ax+b, which of the following make(s) f(x) f^-1 (x)? I. a=-1, b= any real number II. a=1, b=0 III. a = any real number, b=0 a only I b only II c only III d only I and II e only I and III
d only I and II`
Which of the following functions are odd ? I. y=2 II. y=x II. x^2+y^2=1 a only II b only I and II c only I and III d only II and III e I, II, and III
d only II and III
The graph of y=sin2x for x between 10º and 350º crosses the x-axis a zero times b one time c two times d three times e six times
d three times barron's test 2#10
The domain of the function f(x) = 4-√x^2-0 is a x<-3 b x>0 c x>3 d x≤-3 or x≥3 e all real numbers
d x≤-3 or x≥3 barron's test 2#4
If f(x)=√x^2, then f(x) can also be expressed as A. x b. -x c. +/-x d. |x| e. f(x) cannot be determined bc x is unknown
d. |x|
In the equation x^2+kx+54=0, one root is twice the other root. The value(s) of K is(are) a -5.2 b 15.6 c 22.0 d +/- 5.2 e +/- 15.6
e +/- 15.6
Which of the following is equivalent to cos(x)-(1/(cos(x))), where 0≤x<π/2? a. (cos(x)-1/cosX b cos^2(x)-1 c tanX d -tanX e -tanXsinX
e -tanXsinX
If 0≤x≤π/2 and sinx=3cosx, what is the value of x? a 0.322 b 0.333 c 0.34 d 1.231 e 1.249
e 1.249
If 4sinx+3=0 on 0≤x≤2π, then x= a -0.848 b 0.848 c 5.345 d 0.848 or 5.435 e 3.990 or 5.435
e 3.990 or 5.435 barron's test 3
In ∆JKL, sinL=1/3, sinJ=3/5, and JK =√5 inches. The length of KL, in inches, is a 1.7 b 3 c 3.5 d 3.9 e 4
e 4 barron's test 2#27
If x^2+3x+2<0 and f(x) = x^2-3x=2, then a 0<f(x)<6 b f(x)≥3/2 c f(x)>12 d f(x)>0 e 6< f(x)<12
e 6< f(x)<12
The graph of the curve represented by { x=secø y=cosø is a a line b a hyperbola c an ellipse d a line segment e a portion of a hyperbola
e a portion of a hyperbola - just graph in PARAMETRIC barrons test 3
What is the radius of a sphere, with center at the origin, that passes through point(2,3,4)
5.39
The polar coordinates of a point P are (2, 240º). The cartesian(rectangular) coordinates of P are A. (-1, √3) b. (-1, √3) c. (-√3, -1) d. (-√3, 1) e. (1, -√3)
A. (-1, √3)
All of the following numbers satisfy the inequality (2x+1)(x-5)<0 EXCEPT A. -1 B. 0 C. 1 D. 2 E. 3
A. -1
The function g is defined by g(x) = 3sin(2x+1)-1 A. -4≤g(x)≤2 b -2≤g(x)≤4 c -1≤g(x)≤3 d -1/2≤g(x)≤0 e 2≤g(x)≤3
A. -4≤g(x)≤2
In a group of 10 people, 60 percent have brown eyes. Two people are to be selected at random from the group. What is the probability that neither person selected will have brown eyes? A. 0.13 B 0.16 C 0.25 D 0.36 E 0.64
A. 0.13 HELP
The number of hours of daylight, d, in Hartsville can be modeled by d= 35/3 + 7/3sin((2π/365)(t)), where t is the number of days after March 21. The day with the greatest number of hours of daylight has how many more daylight hours than May 1? (March and May have 31 days each. April and June have 30 days each.) A. 0.8 hr b 1.5 hr c 2.3 hr d 3 hr e 4.7 hr
A. 0.8 hr HELP
The prime factorization of a positive integer n is p^3. Which of the following is true? I. n cannot be even II. n has only one positive prime factor III. n has exactly three distinct factors
II only
If (x-2) is a factor of x^3+kx^2+12x-8, then k= a -6 b -3 c 2 d 3 e 6
a -6
If the graph of x+2y+3=0 is perpendicular to the graph of ax+3y+2=0, then a equals a -6 b -3/2 c 2/3 d 3/2 e 6
a -6 barron's test 2#5
The plane whose equation is 5x+6y+10z=30 forms a pyramid in the first octant with the coordinate planes. Its volume is a 15 b 21 c 30 d 36 e 45
a 15 barrons test 3
If f(x) =x^3 and g(x) = x^2+1, which of the following is an odd function(are odd functions)? I. f(x)•g(x) II f(g(x)) III g(f(x)) a only I b only II c only III d only II and III e I, II, and III
a only I barron's test 2#23
A committee of 5 people is to be selected from 6 men and 9 women. I the election is made randomly, what is the probability that the committee consists of 3 men and 2 women? a 1/9 b 240/1001 c 1/3 d 1260/3003 e 13/18
b 240/1001 barron's test 2#42
In the x y-plane, what is the area of a triangle whose vertices are (√2, 0), (2, √10), and (5,0)? a 3.59 b 5.67 c 7.91 d 11.18 e 11.34
b 5.67
Which of the following functions are both odd and even? I. x^2+y^2=1 II. x^2-y^2=0 II. x+y=0 a only II b only I and II c only I and III d only II and II e I, II, and III
b only I and II
If the probability that the Giants will win the NFC championship is p and if the probability that the raiders will win the AFC championship is q, what is the probability that only one of these teams will win its respective championship? a pq b p+q-2pq c |p-q| d 1-pq e 2pq-p-q
b p+q-2pq
If sinø=t, then, for all ø in the interval, 0<ø≤ π/2, tanø= a 1/(√1-t^2) b t/(√1-t^2) c 1/(1-t^2) d t/(1-t^2) e 1
b t/(√1-t^2)
The plane 2x+3y-4z=5 interests the x axis at (a,0,0), the y axis at (0,b,0), and the z axis at (0,0,c), the value of a+b+c is a. 1 b. 35/12 c. 5 d. 65/12 e. 9
b. 35/12 ADD
Which value of x in the interval -π/2<x<π/2 satisfies the equation cosx=sec x a-π/3 b-π/4 c 0 d π/4 e π/3
c 0
If tan x=3, the numerical value of √csc x is a 0.32 b 0.97 c 1.03 d 1.78 e 3.16
c 1.03 DON"T MESS UP TRIG VALUES barrons test #3 8
If f is a linear function and f(-2)=11, f(5)=-2, and f(x)=4.3, what is the value of x? a -3.1 b -1.9 c 1.6 d 2.9 e 3.2
c 1.6 c 1.634 barron's test 2#34
What is the measure of one of the larger angles of a parallelogram in the x y plane end text that has vertices with coordinates (2,1)(5,1) (3,5) and (6,5) ? a. 93.4 b 96. 8 c 104 d 108.3 e 119
c 104 - use law of cosines with vertices (2,1)(3,5) and (6,5) - or use right triangle (2,1), (3,5), (3,1)
The norm of vector V= 3i-√2(j) is a 4.24 b 3.61 c 3.32 d 2.45 e 1.59
c 3.32 barrons test 3
What is the value of x if π≤x≤3π/2 and sinx=5cosx? a 3.399 b 3.625 c 4.515 d 4.623 e 4.663
c 4.515 barron's test 2#47
When a positive integer n is divided by 4, the remainder is 3, which of the following could equal n for some integer t a 4T + 2 b 4t c 4t-1 d 4t-2 e 4t-3
c 4t-1
An insect population is growing in such a way that the number in each generation is approximately 1.5 times that of the previous generation. If there are 100 insect in the first generation, approximately how many insects will there be in the fourth generation? A 338 b 475 c 506 d 813 e 1319
c 506
Which of the following statements is logically equivalent to: "If he studies, he will pass the course"? a He passed the course; therefore, he studied b He did not study; therefore, he will not pass the course c he did not pass the course; therefore he did not study d He will pass the course only if he studies e none of the above
c he did not pass the course; therefore he did not study barron's test 2 #29
If f(x)= cost and g(x) = 2x+1, which of the following are even functions? I. f(x)• g(x) II. f(g(x)) III g(f(x)) a only I b only II c only III d only I and II e only II and III
c only III
For all x and y such that xy≠0, let f(x,y)= xy/x^2+y^2. Then f(x,-x) = a. -x^2 b. -1/x^2 c. -1/2 d. 0 e. 1/2
c. -1/2 CARELESS FORKING MISTAKE
What is the value of f(g(π/4)) if f(x) = x/√1-x^2 for -1<x<1, and g(x)=sin x for all x? a. 0.89 b. 0.95 c. 1 d. 1.27 e. 2.05
c. 1 F(G(π/4)) READ MORE CAREFULLY
A deposit of $1,000 is used to open an account that pays 8 percent annual interest compounded monthly. Assuming that no withdrawals or other deposits are made, how many months after the original deposit will the amount in the account first reach $2,000? A. 109 b. 108 c. 105 d. 11 e. 10
c. 105 BAD FORKING CALCULATIONS
Observers at locations due north and due south of a rocket launchpad sight a rocket at a height of 10 km. Assume that the curvature of earth is negligible and that the rocket's trajectory at that time is perpendicular to the ground. How far apart are the two observers if their angles of elevation to the rocket are 80.5º and 68º? a. 0.85 b. 4.27 c. 5.71 d. 20.92 e. 84.50
c. 5.71 bc 10/(tan80.5) + 10/(tan68) = 5.71
The intersection of a cube with a plane could be which of the following? I. a square II. a parallelogram III. a triangle a I only b II only c III only d I and III only e I, II, and III
college board #3 6 e I, II, and III
The ellipse 4x^2+8y^2=64 and the circle x^2+y^2=9 intersect at points where the y coordinate is a +/-√2 b +/- √5 c +/- √6 d +/-√7 e +/- 10
d +/-√7
Let f(x)=e^x + x + K. If f(x)<0 when x =1.27 and f(x)>0 when x = 1.28, which of the following could be a value of k? a -4.7 b -4.75 c -4.8 d -4.85 e -4.9
d -4.85
A central angle of two concentric circles is 3π/14. The area of the large sector is twice the area of the small sector. What is the ration of the lengths of the radii of the two circles? a 0.25:1 b 0.50:1 c. 0.67:1 d 0.71:1 e 1:1
d 0.71:1 barrons test 3
In a+bi form, the reciprocal of 2+6i is a 1/2 + (1/6)i b -1/16 + (3/16)i c 1/16+(3/16)i d 1/20 - (3/20)i e 1/20+ (3/20)i
d 1/20 - (3/20)i barrons test 3
The pendulum on a clock swings through an angle of 1 radian, and the tip sweeps out an arc of 12 inches. How long is the pendulum? a 3.8 inches b 6 inches c 7.6 inches d 12 inches e 35 inches
d 12 inches barron's test 2#14
If f(x) = |x| +[x], where [x] is the greatest integer less than or equal to x, the value of f(-2.5) + f(1.5) is a -2 b 1 c 1.5 d 2 e 3
d 2
If f(x) = 3x^2 +4x=5, what must the value of k equal so that the graph of f(x-k) will be symmetric to the y-axis? a -4 b -4/3 c -2/3 d 2/3 e 4/3
d 2/3
The points in the rectangle coordinate plane transformed in such a way that each point P(x,y) is moved to the point P'(2x, 2y). If the distance between a point P and the origin is d, then the distance between the point P' and the origin is a 1/d b d/2 c d d 2d e d^2
d 2d
If a, b, and c are real numbers and if a^5b^3c^8 = 9a^3c^8/b^-3, then a could equal a 1/9 b 1/3 c 9 d 3 e 9b^6
d 3
If x=y, then x^2=y^2 If x and y are real numbers, which of the following CANNOT be inferred from the statement above? a In order for x^2 to be equal to y^2, it is sufficient that x be equal to y b a necessary condition for x to be equal to y is that x^2 be equal to y^2 c x is equal to y implies that x^2 is equal to y^2 d If x^2 is not equal to y^2, then x is not equal to y e if x^2 is equal to y^2, then x is equal to y
e if x^2 is equal to y^2, then x is equal to y
What is the equation of the horizontal asymptote of the function f(x) = (2x-1)(x+3)/((x+3)^2)? a y=-9 b y=-3 c y=0 d y=1/2 e y=2
e y=2 barron's test 2#40
If the points (2b, 3), (b+3, -2), and (b, 7) lie on the same line, what is the value of b? a. -2 b. -4/3 c. -1/3 d. 3/4 e. 4/3
e. 4/3 ANOTHER CARELESS FORKING MISTAKE
What is the domain of the function f(x) = 4- √3x^3-7 ? a x≥1.33 b x≥1.53 c x≥2.33 d x≤-1.33 or x≥1.33 e x≤-2.33 or x≥2.33
a x≥1.33 barron's test 2#15
If tanx=2/3, then sinX= a. +/-0.55 b. +/-0.4 c. 0.55 d. 0.83 e. 0.89
a. +/-0.55, bc tan can be positive in 1st/3rd quadrant
If f(r, θ)= rcosθ, then f(2,3) = a -3 b -1.98 c 0.1 d 1.25 e 2
b -1.98 barron's test 2#7
A US dollar equals 0.716 European euros, and a Japanese yen equals 0.00776 European euros. How many US dollars equal a Japanese yen? a 0.0056 b 0.011 c 0.71 d 94.2 e 179.98
b 0.011
Twenty-five percent of a group of unrelated students are only children. The students are asked one at a time whether they are only children. What is the probability that the 5th student asked is the first only child? A. 0.00098 b 0.08 c 0.24 d 0.25 e 0.5
b 0.08 bc you have to do (.75)^4(.25)
The area of the region enclosed by the graph of the polar curve r=1/(sinX+cosX) and the x and y axes is a 0.48 b 0.50 c 0.52 d 0.98 e 1
b 0.50 barron's test 2#48
If f(x)= 2 for all real numbers x, then f(x+2) = a 0 b 2 c 4 d x e the value cannot be determined
b 2
If ln(x)=1.58, then ln(2x)= A 1.15 b 2.27 c 2.49 d3.16 e 3.58
b 2.27
A coin is tossed three times. Given that at least one head appears, what is the probability that exactly two heads will appear? a 3/8 b 3/7 c 5/8 d 3/4 e 7/8
b 3/7 barron's test 2#38
A rectangular box has dimensions of length=6, width=4, and height = 5. The measure of the angle formed by a diagonal of the box with the base of the box is a 27º b 35º c 40º d 44º e 55º
b 35º barron's test 2#49
If the region is bounded by the lines y=-(4/3)x+4, x=0, y=0 is rotated about the y-axis, the volume of the figure formed is a 18.8 b 37.7 c 56.5 d 84.8 e 113.1
b 37.7 barrons test 3
In how many ways can a committee of four be selected from nine men so as to always include a particular man? a 48 b 56 c 70 d 84 e 126
b 56 barron's test 2#24
Each term of a sequence, after the first, is inversely proportional to the term preceding it. If the first two terms are 2 and 6, what is the 12th term? a 2 b 6 c 46 d 2 X 3^11 e the twelfth term cannot be determined
b 6
At the end of a meeting all participants shook hands with each other. Twenty-eight handshakes were exchanged. How many people were at the meeting? a 7 b 8 c 14 d 28 e 56
b 8
The length, width, and height of a rectangular solid are 8, 4, and 1, respectively. What is the length of the longest line segment whose end points are two vertices of this solid? a 4√5 b 9 c 3√10 d 10 e 12
b 9
Point P has coordinates (x,y), where x = cos 22.5 and y = sin 22.5. The point p is on the graphs of which of the following? I. x^2y^2 =1 II. x^2+y^2 =1 III. x^2-y^2 =0 A. I only b II only c III only d I and II only e I, II, and III
b II only
Matrix X has r rows and c columns, and matrix Y has c rows and d columns, where r,c, and d are different. Which of the following statements must be true? I. The product YX exists II The product of XY exists and has r rows and d columns III The product XY exists and has c rows and c columns A I only b II only c III only d I and II e I and III
b II only barron's test 2#28
A taxicab company anted to determine the fuel cost of its fleet. A sample of 30 vehicles was selected, and the fuel cost for the last month was tabulated for each vehicle. Later it was discovered that the highest amount was mistakenly recorded with an extra zero, so it was 10 times the actual amount. When the corrections as mad,e this was still the highest amount. Which of the following must have remained the same after the correction was made? a mean b median c mode d range e standard deviation
b median barron's test 2 #35
George invests $1000 into an account he hopes will earn 12% interest annually. How many years(rounded to the nearest year) will it take his investment to double in value? A. 4 b. 6 c. 7 d. 8 e. 12
b. 6 bc ROUNDED TO THE NEAREST YEAR
If (x-4)^2 +4(y-3)^2=16 is graphed, the same of the distances from any fixed point on the curve to the two foci is a. 4 b. 8 c. 12 d. 16 e. 32
b. 8
For what values of k does the graph of (x-2k)^2/1 - (y-3k)^2/3 = 1 pass through the origin? a only 0 b only 1 c +/-1 d +/-√5 e no value
c +/-1
If f(x)= {x when 0≤x≤1, f(x-1) when x≥1, what is the value of f(4.7)? a 4.7 b 3.7 c 0.7 d 0.3 e -0.3
c 0.7
The domain of f(x) = log(sinx) contains which of the following intervals? a 0<x<π b -π/2<x<π/2 c 0<x<π d -π/2<x<π/2 e π/2<x<3π/2
c 0<x<π barron's 3 #5
If (secX)(tanX)<0, which of the following must be true? I tanX<0 II cscXcotX<0 III x is in the third or fourth quadrant a I only b II only c III only d II and III e I and II
c III only barron's test 1 #37
The set of points (x, y, z) such that x=5 is a a point b a line c a plane d a circle e a cube
c a plane barron's #3
The value of 453!/450!3! is a greater than 10^100 b between 10^10 and 10^100 c between 10^5 and 10^10 d between to and 10^5 e less than 10
c between 10^5 and 10^10
If f(x)=3-2x+x^2, then (f(x+t)-f(x))/t= a t^2+2xt-2t b x^2t^2-2xt+3 c t+2x-2 d 2x-2 e none of the above
c t+2x-2 barron's test 2#22
Which of the following is the equation to the circle that has its center at the origin and is tangent to the line with equation 3x-4y=10? a x^2+y^2-2 b x^2+y^2=3 c x^2+y^2=4 d x^2+y^2=5 e x^2+y^2=10
c x^2+y^2=4 barron's test 2#21
The only prime factors of a number n are 2, 5, 7 and 17. Which of the following could NOT be a factor of n? a 10 b 20 c 25 d 30 e 34
d 30
Suppose the graph of f(x)=-x^3+2 is translated 2 units right and 3 units down. If the result is the graph of y=g(x), what is the value of g(-1.2)? a -33/77 b -1.51 c -0.49 d 31.77 e 37.77
d 31.77 barrons test 3
What is the difference between the min and max values of the function f defined by f(x)= 2x^2+3x-8 on the interval [-2, 5] a 7 b 57.75 c 63 d 66.13 e 71.25
d 66.13
What is the total surface area of a right circular cylindrical solid if the diameter of its base is 2r and its height is 2r a 2πr+2r b πr^2 + 2r c 8πr^2 d 6πr^2 e 2πr^2
d 6πr^2
If a and b are in the domain of a function f and f(a)<f(b), which of the following must be true? a a=0 or b=0 b a<b c a>b d a≠b e a=b
d a≠b
If 5 and -1 are both zeros of the polynomial P(x), then a factor of P(x) is a x^2-5 b x^2-4x=5 c x^2+4x-5 d x^2+5 e x^2-4x-5
e x^2-4x-5 barron's test 2#8
Suppose f(x)= 1/2(x^2)-8 for -4≤x≤4. Then the maximum value of the graph of |f(x)| is a -8 b 0 c 2 d 4 e 8
e. 8 bc ABSOLUTE VALUE
Which of the following lines are asymptotes of the graph of y = x/(x+1) ? I. x=1 II. x=-1 III y=1 a. I only b. II only c. III only d. I and II e. II and III
e. II and III bc DO OUT III, CHECK TO MAKE SURE ALL OF THEM WORK
In right triangle ABC, the measure of <A=90º, AB=3, BC=X, if sinC=k, then in terms of k, AC=
√(3/k)^2-9
