Free Full-Length Adaptive SAT Practice Test Online with Complete Analysis Module -2 -Test - 1

MATH DIGITAL SAT PRACTICE-MODULE-2 -TEST -1

YOUR TOTAL SCORE IS :
12		YOUR PERCENTAGE IS :
54 

SCORING SUMMARY

TOTAL QUESTIONS :22 
TOTAL TIME TAKEN : 0 
 TOTAL CORRECT QUESTION :12 
  TOTAL INCORRECT QUESTION:10 
  TOTAL QUESTION ATTEMPTED :22

QUESTION AND ANSWER REVIEW 

1. Module -2
The average SAT score of 7 students in a class is 1,320. If a student with an SAT score of 1,460 joins the class, what will be the new average SAT score (rounded off to the nearest IO)’

1,38901,3401,3001,460
**Key Explanation: Choice B is correct. To find the average of a set of data, divide the total sum of the values of the data by the number of items. The average of the SAT scores of the 7 students is 1,320. Therefore, the sum of their scores would be 1,320 x 7 = 9,240. Adding in the SAT score of the 8th student, the new sum of the SAT scores ¾ill be 9,240 + 1,460 = 10,700. The new average l0,700 SAT score will be 10,700/ 8 -=1,337.5 , which is 1,340 rounded to the nearest tens place. 
2. Module -2
A researcher studies bacteria in a pond and models a function that shows how the bacteria populate in the pond. Let t be the number of days since the bacteria began to populate the pond Which of the following is the best interpretation of
\( (3) ^{ \frac{t}{14}} \)  in the equation  \( p(t) = 2,034(3) ^{ \frac{t}{14}}\)


The number of bacteria at the beginning of the studyThe number of bacteria triples every two weeksThe number of bacteria increases by 3 every two weeksThe number of bacteria in the pond after two weeks
*Distractor Explanation; The equation for an
exponential model is y=ab”, where a represents
the initial amount of the data. Choice A is
incorrect because a=2,034 would represent the
amount of bacteria at the beginning of the study
and not the given term. Choic.e C is incorrect
because it assumes that the model is linear,
however, the model is exponential Choice D is
incorrect as this answer gives rp(t) and not the
given term in the equation
3. Module -2
∠X is measured in degrees. If the cosine of ∠X is , what is the sine of (90
− ∠X)?

1/2√2/2√3/22/√3
*(B) ∠X and (90 − ∠X) are complementary angles, since they would add
up to 90 degrees. Recall that the sine of one angle is equal to the cosine
of the angle that is complementary to it; similarly, the cosine of one
angle is equal to the sine of the angle that is complementary to it.
Thus, the sine of (90 − ∠X) will simply be the same as the cosine of  ∠X =√2/2
4. Module -2
The expression \( x^{2} – x – 56 \) is equivalent to which of the following?

(x – 14)(x+4)(x – 7)(x+8)(x – 8)(x+7)(x – 4)(x+14)
The question asks for an equivalent form of an expression. When
given a quadratic in standard form, which is \(ax^{2} + bx + c \) one
approach is to factor it. Find two numbers that multiply to 56 and add
to –1. These are –8 and 7, so the factored form of the quadratic is (x –
8)(x + 7), which is (C). When a quadratic is more difficult to factor
than this one was, another approach is to use a graphing calculator.
Enter the expression given in the question, then enter the expressions
from the answer choices one at a time and stop when one of the
answers produces the same graph. Using either method, the correct
answer is (C).
5. Module -2


The total amount of plastic remaining to be recycled in a facility over x shifts is represented by the graph above. Which of the following represents the y-intercept of the graph?

The total amount of plastic remaining at any given timeThe number of shifts it will take to finish recycling the plasticThe amount of plastic that is recycled per shiftThe initial amount of plastic to be recycled
The question asks about a graph representing a certain situation. In a
linear graph that represents an amount over time, the y-intercept
represents the initial amount. In this case, it represents the amount of
plastic remaining to be recycled when x = 0. After 0 shifts, no plastic
has been recycled yet, so the y-intercept represents the initial amount
of plastic to be recycled. The answer is (D).
6. Module -2
If /(x)=2(x-3)² +8 is transformed to g(x) = 2(x-S)² + 5 , which of the following describes the transformation?

The x coordinate moves to the right 2 units and the y coordinate moves 3 units down.The x coordinate moves to the left 2 units and they coordinate moves 3 units down.The x coordinate moves to the right 2 units and the y coordinate moves 3 units up.The x coordinate moves to the left 2 units and they coordinate moves 3 units up.
*Key Explanation: Choke A is correct. The vertex
form of the equation of a parabola is y = (x – Ii)’ +
k , where (Ii , k) is the vertex of the parabola. Thus,
the vertex of the j(x) equation is (3, 8) and the
vertex of the g(x) equation is (5 , 5). Therefore, the
x coordinate moves to the right 2 units from j(x)
to g(x). and they coordinate moves dovm 3 units. 
7. Module -2
The table below shows the condition and subject type for 200 textbooks at a bookstore.

CategoryBiologyChemistryPhysicsAnatomyTotal
Used1025301580
New30251055120
Total40504070200
What is the probability that a textbook chosen at random will be a
new textbook? (Express your answer as a decimal or fraction, not as a
percent.)

12/ 2012/3010/200.5
The question asks for a probability based on data in a table.
Probability is defined as .
(#of outcomes that fit requriements )/ total # of outcomes

Read the table carefully to find the numbers to make the probability. There are 200 total textbooks, so that is the total # of outcomes. Of these 200
textbooks, 120 are new textbooks, so that is the # of outcomes that fit
requirements. Therefore, the probability that a textbook chosen at
random is a new textbook is 120/200. This cannot be entered into the fillin box, which only accepts 5 characters when the answer is positive.
All equivalent answers that fit will be accepted, so reduce the fraction
or convert it to a decimal. The correct answer is ,12/20 or  0.6, or another
equivalent form.
8. Module -2
The mean height of seven teenage boys is 67 inches. If one of the boys has a
height of 74 inches, what is the mean height of the remaining boys to the
nearest tenth of an inch? 

65.865.26565.1
*(65.8) Calculate the total height of the seven boys by using the mean
formula and solving for the sum: 

subtract the height of 74 from the total:
469-74=395
Finally, find the mean of the six boys using 395 as the sum:
395/6 =65.8
9. Module -2
There are 10 cards, each distinctly numbered from 1 to 10. After a card is
selected from the randomly shuffled set, it is returned to the set. If someone
first picks a 3 and then picks a 2, what is the probability that on the third
selection the person will pick a 9?

1/201/101/91/6
(B) Since the cards are returned to the set after each selection, the total
number of choices will remain at 10. So, the probability that someone
would pick a 9 on this selection would simply be . 1/10
10. Module -2
\( x^3 + x^2 – 20x \)

Which of the following is NOT a factor of the above expression? 

x − 4x − 7x +5x
*(B) Factor the expression to determine what would be factors:


\( x^3 + x^2 – 20x \)
\( x(x^2 + x – 20x \)
x(x-4)(x-5)
So, choices (A), (C), and (D) would all be factors. Choice (B), x − 7,
would not be, so choice (B) is correct.


11. Module -2
The height of a certain triangle is twice the width of its base. If the area of
the triangle is 25 square units, what is the height of the triangle?
__________

10
*(10) Let h represent the height of the triangle and let b represent the
width of the base of the triangle. Express the idea that the height of the
triangle is twice its width with this equation:
h=2b
The formula to calculate the area of a triangle is . Substitute 25
for the area and h/2 =bfrom manipulating the above equation, then solve
for the height:
h=10
12. Module -2



In the function with values given above, in which C is a constant, if f (2) = 8,
what is the value of f (3)?

16276481
*(B) Use the fact that f(2) = 8 to find what the constant C is. According
to the table, f(2) = 2C. So, solve for C

Now that we know that C = 3, we can solve for f(3):
13. Module -2
In the equation 3x − 6 = 3(x − a), the constant a is greater than 2. Which of
the following statements must be true?

The equation has exactly one solution.The equation has exactly two solutions.The equation has infinitely many solutions.The equation has no solution.
(D) Simplify the equation to visualize what is happening:
3x-6=3x-3a
If the constant a is greater than 2, then 3a would be greater than 6. This
would result in an absurd situation since the equation would no longer
express an equivalence. For example, if a were 3 (a value greater than
2), look at what happens to the equation:
-6 ≠ -9
14. Module -2
What is the value of p, if the equation below has no solutions? 
5(x+3)-3(2-x)= px+7

__________

11(1) 8
*Key Explanation: The first step is to use the
distributive property to expand out the terms on
the left side of the equation as follows:
S(x +3) – 3(2 – x)
Sx+ 15 – 6+3x
Combining like terms on the left side of the
equation yields 8x + 9
Therefore, for the equation below to have no
solutions. the lines represented by both sides of
the equation need to be parallel, and thus have
the san,e slope and different y -i11tercepts. Since the equations are in slope- intercept form y = mx +
b, with different y-i11tercepls, the slope of the line
represented by &x + 9 is 8 and thus p = 8
15. Module -2
In the year 1990, approximately 2 million U.S. residents were Internet users.
In the year 2000, approximately 115 million U.S. residents were Internet
users. Assuming the growth of Internet users was at a steady geometric rate,
which function could be used to model the number of Internet users, I, in
millions of people, T years after 1990?

\( I(T) = 2 \times (1.5)^T \)\( I(T) = 2 \times (0.5)^T \)\( I(T) = 2 \times (1.5)^-T \)\( I(T) = 2 \times (2.5)^-T \)
*(A) Look at the differences among the answer choices to save yourself
time. We need a function that will show an exponential increase over
time. In the function I(T) = 2 × (1.5)T
, as T increases, I(T) would also
increase at an exponential rate. With all of the other options, however,
as T increases, the value of I(T) would consistently decrease. Choice
(B) would involve multiplying by an ever-smaller fraction, and choices
(C) and (D) would involve dividing by ever-larger numbers. So, the
only logical option is choice (A). 
16. Module -2


Based on the information in the table, what is the mass of a solid steel wall
that has a volume of 300 cubic meters?

26 kilograms8,150 kilograms432,000 kilograms2,355,000 kilograms
* Take the 300 cubic meters and multiply it by the density for steel,
7,850 kilograms per cubic meter, to get the total mass of the wall: 
300 x 7,850 = 2,355,000kg
17. Module -2
A carpenter hammers 10 nails per minute and installs 7 screws per
minute during a project. Which of the following equations represents
the scenario if the carpenter hammers nails for x minutes, installs
screws for y minutes, and uses a combined total of 200 nails and
screws?

\(\frac{1}{10}x + \frac{1}{7}y = 200\)\(\frac{1}{10}x + \frac{1}{7}y = 3,420\)10x + 7y = 20010x + 7y = 3,420
The question asks for an equation that represents a specific situation.
Translate the information in bite-sized pieces and eliminate after each
piece. One piece of information says that the carpenter hammers 10
nails per minute, and another piece says that the carpenter hammers
nails for x minutes. Multiplying the rate of 10 nails per minute by the
number of minutes gives the number of nails:
(10 nails /1 minute) (x minutes) =10x nails .
Eliminate (A) and (B) because they multiply the number of minutes by 1/10 instead of by 10. Compare the remaining answer choices. The difference between (C) and (D) is the number on the right side of the equation. Since the carpenter uses a combined total of 200 nails and screws, the equation must equal200. Eliminate (D) because it equals 3,420. The correct answer is (C).
18. Module -2
Which of the following equation best represents the graph below’ 


\( (y= 5 (0.7)^{x} \)\( (y= 5 (1.3)^{x} \)\( (y= 3 (0.7)^{x} \)\( (y= 3 (1.3)^{x} \)
*Key Explanation: Choice D is correct. The graph
depicts an exponential growth equation, which
has its standard equation y=ab\ where if in
an exponential growth equation b> I , then the
equation represents exponential growth. The
value of a in the equation represents the initial
value of the equation when x= 0. Using the
process of elimination, choices A and C can be
ruled out as their b values are less than 1 and
thus represent exponential decay. not growth.
Choice A can also be ruled out as it gives an initial
value of 5 whereas the graph shows a smaller
initial value. Choice D is correct as it is the only
equation that shows that the graph is increasing
exponentially and has a y-infercept of less than 5. 
19. Module -2
If triangle PQR (not shown) is similar to triangle DEF shown below and DE= 2PQ, what is the value of sin R? 

5/1313/51/51/3
*Key Explanation: Since triangle DEF and triangle
PQR are similar, angles F and Rare congruent.
Therefore, sin R = sin F. Therefore using
SOHCAHTOA the sin of an angle is equal to the
length of the opposite side to the angle divided by
the length of the hypotenuse of the triangle. Thus,
the Sin of Fis
20. Module -2
What is the measure of angle F in the triangle DEF, where angle D is 73° and angle E is 35°?

38°72°108°126°
The question asks for the value of the measure of an angle on a figure.
Use the Geometry Basic Approach. Start by drawing a triangle on the
scratch paper. Then label the figure with the given information. Label
angle D as 73°, angle E as 35°, and angle F without a number. Since
the measures of the angles in a triangle have a sum of 180°, set up the
equation 73° + 35° + F = 180°, which becomes 108° + F = 180°.
Subtract 108° from both sides of the equation to get F = 72°. The
correct answer is (B).
21. Module -2
A random sample of 5,000 students out of 60,000 undergraduate students at a university were surveyed about a potential change to the registration system. According to the survey results, 75% of the respondents did not support the existing registration system, with a 4% margin of error. Which of the following represents a reasonable total number of students who did not support the existing registration system?

1,2503,75013,80043,800
D
The question asks for a reasonable number based on survey results and a margin of error. Work in bite-sized pieces and eliminate after each piece. A margin of error expresses the amount of random sampling error in a survey’s results. Start by applying the percent of respondents who did not support the existing registration system to the entire population of undergraduate students. Take 75% of the entire undergraduate student population to get (75/100) (60,000) = 45,000 students. Eliminate (A) and (B) because they are not close to this value and do not represent a reasonable number of students who did not support the existing registration system. The margin of error is 4%, meaning that results within a range of 4% above and 4% below the estimate are reasonable. A 4% margin of error will not change the result by very much, and (D) is the only answer choice close to 45,000. To check, calculate the lower limit of the range based on the margin of error, since 43,800 is less than 45,000. To find the lower limit, subtract 4% from 75% to get 71%, then find 71% of the total population to get a lower limit of  71/ 100 (60,000) = 42,600. The value in (C) is  less than the lower limit, so it is not a reasonable number. Choice (D) contains a value between 42,600 and 45,000, so it is reasonable. The correct answer is (D).
22. Module -2
A data set containing only the values 2, 2, 9, 9, 9, 16, 16, 16, 16, 26,
26, and 26 is represented by a frequency table. Which of the following
is the correct representation of this data set?


NumberFrequency
24
927
1664
2678

NumberFrequency
22
93
164
263

NumberFrequency
22
39
416
326

NumberFrequency
42
279
6416
7826

The question asks for the frequency table that correctly represents a
list of numbers. A frequency table has two columns: the left-hand
column contains the values, and the right-hand column contains the
number of times each value occurs, or its frequency. Work in bitesized pieces and eliminate answer choices that do not match the data.
The number 2 occurs twice in the list, so its frequency is 2. Eliminate
(A) because it shows a frequency of 4 for the number 2. Eliminate (D)
because it does not include the number 2 at all. Next, the number 9
occurs three times in the list, so its frequency is 3. Eliminate (C)
because it shows the number 3 occurring 9 times instead of the
number 9 occurring 3 times. Choice (B) shows the correct frequency
for each value. The correct answer is (B).

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