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1
Words in Context
Wrong
Handedness, a preferential use of either the right or left hand, typically is easy to observe in humans. Because this trait is present but less ______ in many other animals, animal-behavior researchers often employ tasks specially designed to reveal individual animals' preferences for a certain hand or paw.
Which choice completes the text with the most logical and precise word or phrase?
recognizable
Correct Answer
B
intriguing
C
significant
D
useful
No explanation
2
Standard English Conventions
Wrong
Paintings by the renowned twentieth-century US ______ were featured in Artist to Artist, an exhibition at the Smithsonian Art Museum that paired the works of artists whose career trajectories intersected in meaningful ways.
Which choice completes the text so that it conforms to the conventions of Standard English?
A
artists: Thomas Hart Benton and Jackson Pollock,
artists Thomas Hart Benton and Jackson Pollock
Correct Answer
C
artists Thomas Hart Benton, and Jackson Pollock,
D
artists, Thomas Hart Benton and Jackson Pollock
No explanation
3
Problem Solving and Data Analysis
Wrong
| Type of store | Average number of employees |
|---|---|
| Warehouse store | 365 |
| Department store | 213 |
| Supermarket | 130 |
A
83
B
152
235
Correct Answer
D
495
No explanation
4
Advanced Math
Wrong
The expression \(90 y^5 - 54 y^4\) is equivalent to \(r y^4 (15 y - 9)\), where \(r\) is a constant. What is the value of \(r\)?
My Answer
(No answer)
Correct Answer
6
No explanation
5
MCQ
Wrong
\(\operatorname*{lim}\limits_{x \rightarrow 0} \dfrac{x^2 - 1}{1 - 2 x^2} =\)
\(-1\)
Correct Answer
B
\(-\dfrac{1}{2}\)
C
\(\dfrac{1}{2}\)
D
\(1\)
E
non-existent
Explanation
Substitute \(x = 0\): \(\dfrac{-1}{1} = -1\).
6
Algebra
Wrong
The point \((8, 2)\) in the \(x y\)-plane is a solution to which of the following systems of inequalities?
\(x > 0\) and \(y > 0\)
Correct Answer
B
\(x > 0\) and \(y < 0\)
C
\(x < 0\) and \(y > 0\)
D
\(x < 0\) and \(y < 0\)
No explanation
7
Algebra
Wrong
\( 2 a + 8 b = 198 \)
\( 2 a + 4 b = 98 \)
The solution to the given system of equations is \((a, b)\). What is the value of \(b\)?
My Answer
(No answer)
Correct Answer
25
No explanation
8
Information and Ideas
Wrong
Many mosquito repellents contain natural components that work by activating multiple odor receptors on mosquitoes' antennae. As the insects develop resistance, new repellents are needed. Ke Dong and her team found that EBF, a molecular component of a chrysanthemum-flower extract, can repel mosquitoes by activating just one odor receptor—and this receptor, Or31, is present in all mosquito species known to carry diseases. Therefore, the researchers suggest that in developing new repellents, it would be most useful to ______
Which choice most logically completes the text?
identify molecular components similar to EBF that target the activation of Or31 receptors.
Correct Answer
B
investigate alternative methods for extracting EBF molecules from chrysanthemums.
C
verify the precise locations of Or31 and other odor receptors on mosquitoes' antennae.
D
determine the maximum number of different odor receptors that can be activated by a single molecule.
No explanation
9
MCQ
Wrong
\(\displaystyle\int_{1}^{2} x^{-3} d x =\)
A
\(-\dfrac{7}{8}\)
B
\(-\dfrac{3}{4}\)
C
\(\dfrac{15}{64}\)
\(\dfrac{3}{8}\)
Correct Answer
E
\(\dfrac{15}{16}\)
Explanation
\([-x^{-2}/2]_1^2 = -\dfrac{1}{8} + \dfrac{1}{2} = \dfrac{3}{8}\).
10
Words in Context
Wrong
Former astronaut Ellen Ochoa says that although she doesn't have a definite idea of when it might happen, she ______ that humans will someday need to be able to live in other environments than those found on Earth. This conjecture informs her interest in future research missions to the moon.
Which choice completes the text with the most logical and precise word or phrase?
A
demands
speculates
Correct Answer
C
doubts
D
establishes
No explanation
11
Problem Solving and Data Analysis
Wrong
For a particular machine that produces beads, 29 out of every 100 beads it produces have a defect. A bead produced by the machine will be selected at random. What is the probability of selecting a bead that has a defect?
A
\(\dfrac{1}{2,900}\)
B
\(\dfrac{1}{29}\)
\(\dfrac{29}{100}\)
Correct Answer
D
\(\dfrac{29}{10}\)
No explanation
12
MCQ
Wrong
Particle velocity \(v(t) = e^t\). Distance from \(t = 0\) to \(t = 2\)?
\(e^2 - 1\)
Correct Answer
B
\(e - 1\)
C
\(2 e\)
D
\(e^2\)
E
\(\dfrac{e^3}{3}\)
Explanation
\(\displaystyle\int_{0}^{2} e^t dt = e^2 - 1\).
13
Algebra
Wrong
Sean rents a tent at a cost of \$11 per day plus a onetime insurance fee of \$10. Which equation represents the total cost \(c\), in dollars, to rent the tent with insurance for \(d\) days?
A
\(c = 11(d + 10)\)
B
\(c = 10(d + 11)\)
\(c = 11 d + 10\)
Correct Answer
D
\(c = 10 d + 11\)
No explanation
14
Advanced Math
Wrong
The area \(A\), in square centimeters, of a rectangular cutting board can be represented by the expression \(w(w + 9)\), where \(w\) is the width, in centimeters, of the cutting board. Which expression represents the length, in centimeters, of the cutting board?
A
\(w(w + 9)\)
B
\(w\)
C
\(9\)
\((w + 9)\)
Correct Answer
No explanation
15
Systems of Linear Equations
Wrong
Solve each system by using elementary row operations on the equations or on the augmented matrix.
\(2 x_1 + 4 x_2 = -4\)
\(5 x_1 + 7 x_2 = 11\)
My Answer
(No answer)
Correct Answer
Solve by elimination
No explanation
16
Geometry and Trigonometry
Wrong
Note: Figure not drawn to scale.
For the right triangle shown, \(a = 4\) and \(b = 5\). Which expression represents the value of \(c\)?
A
\(4 + 5\)
B
\(\sqrt{(4)(5)}\)
C
\(\sqrt{4 + 5}\)
\(\sqrt{4^2 + 5^2}\)
Correct Answer
No explanation
17
MCQ
Wrong
\(\displaystyle\int_{0}^{\dfrac{\pi}{2}} \cos x d x =\)
A
\(-\pi\)
B
\(-1\)
C
\(0\)
\(1\)
Correct Answer
E
\(\pi\)
No explanation
18
MCQ
Wrong
Let \(f(x) = 1 - 3 x^2\). Which of the following is equal to \(f'(1)\)?
\(-6\)
Correct Answer
B
\(-5\)
C
\(5\)
D
\(6\)
E
Does not exist
Explanation
\(f'(x) = -6 x\). At \(x = 1\): \(-6\).
19
Solution Sets of Linear Systems
Wrong
Determine if the system has a nontrivial solution. Try to use as few row operations as possible.
\(-5 x_1 + 7 x_2 + 9 x_3 = 0\)
\(x_1 - 2 x_2 + 6 x_3 = 0\)
My Answer
(No answer)
Correct Answer
Yes, nontrivial solution exists. More unknowns than equations (3 unknowns, 2 equations), so at least one free variable.
No explanation
20
Series - Concepts
Wrong
Explain what it means to say that \(\displaystyle\sum_{n=1}^{\infty} a_n = 5\).
My Answer
(No answer)
Correct Answer
No explanation
21
Algebra
Wrong
What is \(10! - 7! \cdot 6!\)?
A
\(-120\)
\(0\)
Correct Answer
C
\(120\)
D
\(600\)
E
\(720\)
No explanation
22
Algebra
Wrong
\(x + y = 18\)
\(5y = x\)
What is the solution \((x, y)\) to the given system of equations?
(15, 3)
Correct Answer
B
(16, 2)
C
(17, 1)
D
(18, 0)
No explanation
23
Linear Functions - Graph
Wrong
What is the \(y\)-intercept of the line graphed?
A
\((0, -3)\)
B
\((0, -1)\)
C
\((0, 1)\)
D
\((0, 3)\)
No explanation
24
Words in Context
Wrong
The general store was essential to daily life in the rural United States during the 1800s because it provided the supplies that the people living in nearby communities needed. Also, the store was a ______ of information. People socializing at the general store would share news and help spread it throughout their communities.
Which choice completes the text with the most logical and precise word or phrase?
source
Correct Answer
B
rival
C
condition
D
waste
No explanation
25
Row Reduction and Echelon Forms
Wrong
Determine which matrices are in reduced echelon form and which others are only in echelon form.
a. \(\begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 \end{pmatrix}\)
b. \(\begin{pmatrix} 1 & 0 & 1 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix}\)
c. \(\begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{pmatrix}\)
d. \(\begin{pmatrix} 1 & 1 & 0 & 1 & 1 \\ 0 & 2 & 0 & 2 & 2 \\ 0 & 0 & 0 & 3 & 3 \\ 0 & 0 & 0 & 0 & 4 \end{pmatrix}\)
My Answer
(No answer)
Correct Answer
Identify reduced echelon form vs echelon form for each matrix
No explanation
26
Geometry and Trigonometry
Wrong
Note: Figure not drawn to scale.
In the figure, line \(m\) is parallel to line \(n\), and line \(t\) intersects both lines. What is the value of \(x\)?
A
33
B
57
C
123
147
Correct Answer
No explanation
27
Algebra
Wrong
What is the y-intercept of the line graphed?
A
\((-5, 0)\)
B
\((0, 0)\)
\((0, 5)\)
Correct Answer
D
\((0, 9)\)
No explanation
28
Words in Context
Wrong
Researchers and conservationists stress that biodiversity loss due to invasive species is ______. For example, people can take simple steps such as washing their footwear after travel to avoid introducing potentially invasive organisms into new environments.
Which choice completes the text with the most logical and precise word or phrase?
preventable
Correct Answer
B
undeniable
C
common
D
concerning
No explanation
29
Information and Ideas
Wrong
Video Game Availability by Initial Release Years
In a recent study, researchers found that relatively few video games released over the decades remain available today. For example, only 14.22 percent of games are still available that were initially released in ______
Which choice most effectively uses data from the table to complete the statement?
| Initial release years | Percentage of games still available |
|---|---|
| 1975-1979 | 0.89 |
| 1980-1984 | 3.65 |
| 1985-1989 | 15.38 |
| 1990-1994 | 19.33 |
| 1995-1999 | 14.22 |
A
2000-2004.
1995-1999.
Correct Answer
C
1970-1974.
D
1985-1989.
No explanation
30
Trig Derivatives - Basic
Wrong
Differentiate.
\(y = x^2 + \cot x\)
My Answer
(No answer)
Correct Answer
\(y' = 2x - \csc^2 x\)
No explanation