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Math Level 2 SAT Subject Test

Richard Ku, Howard P. Dodge

Chapter 1

Diagnostics Test - all with Video Answers

Educators

+ 3 more educators

Chapter Questions

01:24

Problem 1

A linear function, $f$ has a slope of $-2 . f(1)=2$ and $f(2)$ $=q .$ Find $q$
(A) 0
(B) $\frac{3}{2}$
(C) $\frac{5}{2}$
(D) 3
(E) 4

Dilip Paruchuri
Dilip Paruchuri
Numerade Educator
02:12

Problem 2

A function is said to be even if $f(x)=f(-x) .$ Which of the following is not an even function?
(A) $y=|x|$
(B) $y=\sec x$
(C) $y=\log x^{2}$
(D) $y=x^{2}+\sin x$
(E) $y=3 x^{4}-2 x^{2}+17$

Sahil Kumar
Sahil Kumar
Numerade Educator
01:13

Problem 3

What is the radius of a sphere, with center at the origin, that passes through point $(2,3,4) ?$
(A) 3
(B) 3.31
(C) 3.32
(D) 5.38
(E) 5.39

Linh Vu
Linh Vu
Numerade Educator
01:37

Problem 4

If a point $(x, y)$ is in the second quadrant, which of the following must be true?
I. $x<y$
II. $x+y>0$
III. $\frac{x}{y}<0$
(A) only I
(B) only II
(C) only III
(D) only I and II
(E) only I and III

Ronald Prasad
Ronald Prasad
Numerade Educator
01:20

Problem 5

If $f(x)=x^{2}-a x,$ then $f(a)=$
(A) $a$
(B) $a^{2}-a$
(C) 0
(D) 1
(E) $a-1$

Grant Castaneda
Grant Castaneda
Numerade Educator
02:45

Problem 6

The average of your first three test grades is 78 . What grade must you get on your fourth and final test to make your average 80$?$
(A) 80
(B) 82
(C) 84
(D) 86
(E) 88

Jennifer Hudspeth
Jennifer Hudspeth
Numerade Educator
01:18

Problem 7

$\log _{7} 9=$
(A) 0.89
(B) 0.95
(C) 1.13
(D) 1.21
(E) 7.61

Pronoy Sinha
Pronoy Sinha
Numerade Educator
02:38

Problem 8

If $\log _{2} m=x$ and $\log _{2} n=y,$ then $m n=$
(A) $2^{x+y}$
(B) $2^{x y}$
(C) $4^{x y}$
(D) $4^{x+y}$
(E) cannot be determined

Ahmad Reda
Ahmad Reda
Numerade Educator
01:44

Problem 9

How many integers are there in the solution set of $| x-$ $2 | \leq 5 ?$
(A) 0
(B) 7
(C) 9
(D) 11
(E) an infinite number

Dilip Paruchuri
Dilip Paruchuri
Numerade Educator
01:03

Problem 10

If $f(x)=\sqrt{x^{2}},$ then $f(x)$ can also be expressed as
(A) $x$
(B) $-x$
(C) $\pm x$
(D) $|x|$
(E) $f(x)$ cannot be determined because $x$ is unknown.

Sahil Kumar
Sahil Kumar
Numerade Educator
00:35

Problem 11

The graph of $\left(x^{2}-1\right) y=x^{2}-4$ has
(A) one horizontal and one vertical asymptote
(B) two vertical but no horizontal asymptotes
(C) one horizontal and two vertical asymptotes
(D) two horizontal and two vertical asymptotes
(E) neither a horizontal nor a vertical asymptote

Rikhil Makwana
Rikhil Makwana
Numerade Educator
01:06

Problem 12

$\lim _{x \rightarrow \infty}\left(\frac{3 x^{2}+4 x-5}{6 x^{2}+3 x+1}\right)=$
(A) $-5$
(B) $\frac{1}{5}$
(C) $\frac{1}{2}$
(D) 1
(E) This expression is undefined.

Malika Singh
Malika Singh
Numerade Educator
00:47

Problem 13

A linear function has an $x$ -intercept of $\sqrt{3}$ and a $y-$ intercept of $\sqrt{5}$ . The graph of the function has a slope of
(A) $-1.29$
(B) $-0.77$
(C) 0.77
(D) 1.29
(E) 2.24

Donald Albin
Donald Albin
Numerade Educator
01:12

Problem 14

If $f(x)=2 x-1,$ find the value of $x$ that makes $f(f(x))$ $\quad=9$
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

Bobby Barnes
Bobby Barnes
University of North Texas
02:35

Problem 15

The plane $2 x+3 y-4 z=5$ intersects 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) $\frac{35}{12}$
(C) 5
(D) $\frac{65}{12}$
(E) 9

Jeff Vermeire
Jeff Vermeire
Numerade Educator
03:40

Problem 16

Given the set of data $1,1,2,2,2,3,3,4,$ which one of the following statements is true?
(A) mean $\leq$ median $\leq$ mode
(B) median $\leq$ mean $\leq$ mode
(C) median $\leq$ mode $\leq$ mean
(D) mode $\leq$ mean $\leq$ median
(E) mode $\leq$ mean $\leq$ median the median cannot be calculated.

Vishal Sharma
Vishal Sharma
Numerade Educator
01:14

Problem 17

If $\frac{x-3 y}{x}=7$ , what is the value of $\overline{y} ?$
(A) $^{-\frac{8}{3}}$
(B) $-2$
(C) $^{-\frac{1}{2}}$
(D) $\frac{3}{8}$
(E) 2

Lily An
Lily An
Numerade Educator
05:27

Problem 18

Find all values of $x$ that make $\left(\begin{array}{ccc}{2} & {-1} & {4} \\ {3} & {0} & {5} \\ {4} & {1} & {6}\end{array}\right)=\left(\begin{array}{ll}{x} & {4} \\ {5} & {x}\end{array}\right)$
(A) 0
(B) $\pm 1.43$
(C) $\pm 3$
(D) $\pm 4.47$
(E) 5.34

Oluwaseyitan Balogun
Oluwaseyitan Balogun
Numerade Educator
01:15

Problem 19

Suppose $f(x)=\frac{1}{2} x^{2}-8$ for $-4 \leq x \leq 4,$ then the maximum value of the graph of $|f(x)|$ is
(A) $-8$
(B) 0
(C) 2
(D) 4
(E) 8

Carson Merrill
Carson Merrill
Numerade Educator
01:47

Problem 20

If tan $\quad \theta=\frac{2}{3},$ then $\sin \theta=$
(A) $\pm 0.55$
(B) $\pm 0.4$
(C) 0.55
(D) 0.83
(E) 0.89

Rikhil Makwana
Rikhil Makwana
Numerade Educator
00:31

Problem 21

If $a$ and $b$ are the domain of a function and $f(b) < f(a),$ which of the following must be true?
(A) $a < b$
(B) $b < a$
(C) $a=b$
(D) $a \neq b$
(E) $a=0$ or $b=0$

Lily An
Lily An
Numerade Educator
01:11

Problem 22

Which of the following is perpendicular to the line $y$ $\quad=-3 x+7 ?$
(A) $y=\frac{1}{-3 x+7}$
(B) $y=7 x-3$
(C) $^{y}=\frac{1}{3} x+5$
(D) $^{y}=-\frac{1}{3} x+7$
(E) $y=3 x-7$

Rikhil Makwana
Rikhil Makwana
Numerade Educator
View

Problem 23

The statistics below provide a summary of IQ scores of 100 children.
Mean: 100
Median: 102
Standard Deviation: 10
First Quartile: 84
Third Quartile: 110
About 50 of the children in this sample have IQ scores that are
(A) less than 84
(B) less than 110
(C) between 84 and 110
(D) between 64 and 130
(E) more than 100

Shu Naito
Shu Naito
Numerade Educator
01:28

Problem 24

If $f(x)=\frac{1}{\sec x}$ then
(A) $f(x)=f(-x)$
(B) $f\left(\frac{1}{x}\right)=-f(x)$
(C) $f(-x)=-f(x)$
(D) $f(x)=f\left(\frac{1}{x}\right)$
(E) $f(x)=\frac{1}{f(x)}$

Rikhil Makwana
Rikhil Makwana
Numerade Educator
01:39

Problem 25

The polar coordinates of a point $P$ are $\left(2,240^{\circ}\right) .$ The Cartesian (rectangular) coordinates of $P$ are
(A) $(-1,-\sqrt{3})$
(B) $(-1, \sqrt{3})$
(C) $(-\sqrt{3},-1)$
(D) $(-\sqrt{3}, 1)$
(E) $(1,-\sqrt{3})$

Linda Hand
Linda Hand
Numerade Educator
02:55

Problem 26

The height of a cone is equal to the radius of its base. The radius of a sphere is equal to the radius of the base of the cone. The ratio of the volume of the cone to the volume of the sphere is
(A) $\frac{1}{12}$
(B) $\frac{1}{4}$
(C) $\frac{1}{3}$
(D) $\frac{1}{3}$

Lily An
Lily An
Numerade Educator
03:13

Problem 27

In how many distinguishable ways can the seven letters in the word MINIMUM be arranged, if all the letters are used each time?
(A) 7
(B) 42
(C) 420
(D) 840
(E) 5040

Jennifer Hudspeth
Jennifer Hudspeth
Numerade Educator
01:46

Problem 28

Which of the following lines are asymptotes of the graph of $^{y=\frac{x}{x+1}}$
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

Grant Castaneda
Grant Castaneda
Numerade Educator
01:23

Problem 29

What is the probability of getting at least three heads when flipping four coins?
(A) $\frac{3}{16}$
(B) $\frac{1}{4}$
(C) $\frac{5}{16}$
(D) $\frac{7}{16}$
(E) $\frac{3}{4}$

Matthew Bradley
Matthew Bradley
Numerade Educator
03:43

Problem 30

The positive zero of $y=3 x^{2}-4 x-5$ is, to the nearest tenth, equal to
(A) 0.8
(B) $0.7+1.1 i$
(C) 0.7
(D) 2.1
(E) 2.2

Gregory Higby
Gregory Higby
Numerade Educator
02:32

Problem 31

In the figure above, $S$ is the set of all points in the shaded region. Which of the following represents the set consisting of all points $(2 x, y),$ where $(x, y)$ is a point in $S ?$
Graph cannot copy

Cinsy Krehbiel
Cinsy Krehbiel
Numerade Educator
02:21

Problem 32

If a square prism is inscribed in a right circular cylinder of radius 3 and height $6,$ the volume inside the cylinder but outside the prism is
(A) 2.14
(B) 3.14
(C) 61.6
(D) 115.6
(E) 169.6

Sarah Klein
Sarah Klein
Numerade Educator
03:55

Problem 33

What is the length of the major axis of the ellipse whose equation is $10 x^{2}+20 y^{2}=200 ?$
(A) 3.16
(B) 4.47
(C) 6.32
(D) 8.94
(E) 14.14

AG
Ankit Gupta
Numerade Educator
01:31

Problem 34

The fifth term of an arithmetic sequence is $26,$ and the eighth term is $41 .$ What is the first term?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

Grant Castaneda
Grant Castaneda
Numerade Educator
01:16

Problem 35

What is the measure of one of the larger angles of the parallelogram that has vertices at $(-2,-2),$ $(0,1),(5,1),$ and $(3,-2) ?$
(A) $117.2^{\circ}$
(B) $123.7^{\circ}$
(C) $124.9^{\circ}$
(D) $125.3^{\circ}$
(E) $131.0^{\circ}$

Akshaya Rs
Akshaya Rs
Numerade Educator
01:35

Problem 36

If $f(x)=\frac{k}{x}$ for all nonzero real numbers, for what value of $k$ does $f(f(x))=x ?$
(A) only 1
(B) only 0
(C) all real numbers
(D) all real numbers except 0
(E) no real numbers

Aman Gupta
Aman Gupta
Numerade Educator
03:23

Problem 37

$F(x)=\left\{\begin{array}{c}{\frac{3 x^{2}-3}{x-1}, \text { when } x \neq 1} \\ {k, \text { when } x=1}\end{array}\right.$ For what value(s) of $k$ is $F$ a continuous function?
(A) 1
(B) 2
(C) 3
(D) 6
(E) no value of $k$

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
01:19

Problem 38

If $f(x)=2 x^{2}-4$ and $g(x)=2^{x},$ the value of $g(f(1))$ is
(A) $-4$
(B) 0
(C) $\frac{1}{4}$
(D) 1
(E) 4

James Kiss
James Kiss
Numerade Educator
01:10

Problem 39

If $f(x)=3 \sqrt{5 x},$ what is the value of $f^{-1}(15) ?$
(A) 0.65
(B) 0.90
(C) 5.00
(D) 7.5
(E) 25.98

Dilip Paruchuri
Dilip Paruchuri
Numerade Educator
01:06

Problem 40

Which of the following could be the equation of one cycle of the graph in the figure above?
I. $y=\sin 4 x$
II. $y=\cos \left(4 x-\frac{\pi}{2}\right)$
III. $y=-\sin (4 x+\pi)$
(A) only I
(B) only I and II
(C) only II and III
(D) only II
(E) I, II, and III

Carson Merrill
Carson Merrill
Numerade Educator
02:11

Problem 41

If $2 \sin ^{2} x-3=3 \cos x$ and $90^{\circ} < x < 270^{\circ},$ the number of values that satisfy the equation is
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

Aman Gupta
Aman Gupta
Numerade Educator
01:07

Problem 42

If $A=\tan ^{-1}$ $\left(-\frac{3}{4}\right)$ and $A+B=315^{\circ},$ then $B=$
(A) $278.13^{\circ}$
(B) $351.87^{\circ}$
(C) $-8.13^{\circ}$
(D) $171.87^{\circ}$
(E) $233.13^{\circ}$

Aman Gupta
Aman Gupta
Numerade Educator
03:11

Problem 43

Observers at locations due north and due south of a rocket launchpad sight a rocket at a height of 10 kilometers. 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 $80.5^{\circ}$ and $68.0^{\circ} ?$
(A) 0.85 $\mathrm{km}$
(B) 4.27 $\mathrm{km}$
(C) 5.71 $\mathrm{km}$
(D) 20.92 $\mathrm{km}$
(E) 84.50 $\mathrm{km}$

Linda Hand
Linda Hand
Numerade Educator
02:37

Problem 44

The vertex angle of an isosceles triangle is $35^{\circ} .$ The length of the base is 10 centimeters. How many centimeters are in the perimeter?
(A) 16.6
(B) 17.4
(C) 20.2
(D) 43.3
(E) 44.9

Martha Richards
Martha Richards
Numerade Educator
01:54

Problem 45

If the graph below represents the function $f(x),$ which of the following could represent the equation of the inverse of $f ?$
(A) $x=y^{2}-8 y-1$
(B) $x=y^{2}+11$
(C) $x=(y-4)^{2}-3$
(D) $x=(y+4)^{2}-3$
(E) $x=(y+4)^{2}+3$

Alexander Cheng
Alexander Cheng
Numerade Educator
06:09

Problem 46

If $k > 4$ is a constant, how would you translate the graph of $y=x^{2}$ to get the graph of $y=x^{2}+4 x+k ?$
(A) left 2 units and up $k$ units
(B) right 2 units and up $(k-4)$ units
(C) left 2 units and up $(k-4)$ units
(D) right 2 units and down $(k-4)$ units
(E) left 2 units and down $(k-4)$ units

Rahul Kumar
Rahul Kumar
Numerade Educator
00:52

Problem 47

If $f(x)=\log _{b} x$ and $f(2)=0.231,$ the value of $b$ is
(A) 0.3
(B) 1.3
(C) 13.2
(D) 20.1
(E) 32.5

Rikhil Makwana
Rikhil Makwana
Numerade Educator
03:36

Problem 48

If $f_{n+1}=f_{n-1}+2 f_{n}$ for $n=2,3,4, \ldots,$ and $f_{1}=1$ and $f_{2}=1, \text { then } f_{5}=$
(A) 7
(B) 11
(C) 17
(D) 21
(E) 41

Rahul Mittal
Rahul Mittal
Numerade Educator
02:01

Problem 49

Suppose cos $\theta=u$ in $^{0<\theta<\frac{\pi}{2}}$ . Then tan $\theta=$
(A) 1
(B) $\frac{1}{\sqrt{1-u^{2}}}$
(C) $\sqrt{1-u^{2}}$
(D) $\sqrt{1-u^{2}}$
(E) $\frac{\sqrt{1-u^{2}}}{u}$

Rikhil Makwana
Rikhil Makwana
Numerade Educator
02:02

Problem 50

A certain component of an electronic device has a probability of 0.1 of failing. If there are 6 such components in a circuit, what is the probability that at least one fails?
(A) 0.60
(B) 0.47
(C) 0.167
(D) 0.000006
(E) 0.000001

Aman Gupta
Aman Gupta
Numerade Educator