DIGITAL SAT FREE MATH PRACTICE TEST 2

DIGITAL SAT MATH PRACTICE -TEST 2

Tackle a series of math questions designed to assess your quantitative skills.
Navigate through a 70-minute timed challenge, testing your ability to solve math problems efficiently.
Answer 44 questions divided into two modules (22 each).
Receive immediate feedback with the display of your raw total math score right after completing the test.
Your converted full math score will be promptly emailed to you for comprehensive review.

For i = √-1, which of the following complex numbers is
equivalent to (10i − 4i²) - (7 − 3i)?

-11 + 7i

3 − 13i

−3 + 13i

11 − 7i

None

The number of donation pledges, p, made to a charity d days after the
charity began a campaign for donations can be approximated by the
equation p = 117 + 32d. What is the best interpretation of the number
32 in this equation?

The total number of donation pledges received during the campaign.

The number of donation pledges received before the campaign for donations started.

The number of donation pledges received each day of the campaign.

The number of donation pledges made on the last day of the campaign

None

3y + 6 = 2x
2y − 3x = 6
The system of equations above can best be described as having

no solution.

one solution with the graphs not intersecting at right angles in the xy-plane.

one solution with the graphs intersecting at right angles in the xy plane.

infinitely many solutions.

None

A teacher from the United States wishes to purchase textbooks for her
classroom when she goes on a trip to Canada, where they are on sale
for 45 Canadian dollars each. At the time of purchase one Canadian
dollar can be exchanged for 0.76 U.S. dollars. Assuming she is able to
exchange her U.S. dollars for Canadian dollars at no cost, what is the
exact cost, in U.S. dollars, to purchase 30 books?

1350 USD

849 USD

1776 USD

1026 USD

None

A city planner estimates that due to lower birth rates and changing
demographics, enrollment in city’s public schools will decrease at the
rate of 16% per year for the next 5 years. If the city planner uses the
equation P=P_{o}(r)^{n} to estimate the school enrollment, P, after n years,
what value should be used for the value of r?

0.16

0.84

0.80

1.16

None

If a and b are the coordinates of two points on the number line, then which of the following is equivalent to the statement that the absolute distance from a to b is greater than the absolute distance from -2 to 6 ?

|a| > -2 and |b| > 6

|a + 2| > |b - 6|

|a - b| > -8

|a - b| > 8

None

The scatterplot above summarizes the wrist and neck circumference
measurements, in centimeters, for 12 people. The line of best fit is
drawn. What proportion of the 12 measurements satisfy the inequality
|o − p| ≤ d where o is the observed measurement, p is corresponding
measurement predicted by the line of best fit, and d is 0.5 cm?

1/3

1/4

1/2

1/6

None

An archer shoots an arrow into the air such that its height at any time,
t, is given by the function h(t) = −16t²+ kt + 3. If the maximum height
of the arrow occurs at 4 seconds after it is launched, what is the value
of k?

128

None

2x − 5y = 3
x + 2y = 6
If (a, b) is the solution to the system of equations above, what is the
value of a?

None

10.

A small, open-top packing box, similar to a shoebox without a lid, is
three times as long as it is wide, and half as high as it is long. Each
square inch of the bottom of the box costs \$0.08 to produce, while each
square inch of any side costs \$0.03 to produce. If x represents the
number of inches in the width of the box, which of the following
functions represent the cost, C, of producing the box? C(x) = 0.96x²

C(x) = 0.60x²

C(x) = 0.42x²

C(x) = 0.72x²

C(x) = 0.96x²

None

11.

An opinion poll survey was conducted in which 120 sports fans and 75
non-sports fans participated. If the sample size was increased by 65
non-sports fans, how many sports fans should be added so that 3/5 of
those polled are sports fans?

Write your answer

12.

A metal belt buckle is being designed so that it has the shape of a
regular hexagon in the center and squares at opposite ends as shown in
the figure above where ABCDEF is a regular hexagon and figures I and
II are squares. The hexagon will be gold plated and the two squares
silver plated. The length of a side of each square is 6 centimeters.
Which of the following is closest to the percent of the total surface area
of the buckle that will be silver plated?
Write your answer

13.

The bird department of a pet store has 12 canaries,
30 finches, and 18 parrots. If the pet store
purchased n more finches, then 80% of its birds
would be finches. Which of the following equations
must be true?

$$\frac{30+n}{60+n}=\frac{4}{5}$$

$$\frac{30+n}{60}=\frac{4}{5}$$

$$\frac{n}{60+n}=\frac{4}{5}$$

$$\frac{1}{2}+n=\frac{4}{5}$$

None

14.

If $x^{-2}=64$what is the value of $x^{\frac{1}{3}}$?

1/8

1/2

1/4

None

15.

The figure above shows the graph of the linear function y = f(x). If the
slope of the line is −2 and f(3) = 4, what is the value of b?

None

16.

A group of p people plan to contribute equally to the purchase of a gift
that costs d dollars. If n of the p people decide not to contribute, by
what amount in dollars does the contribution needed from each of the
remaining people increase?

$$\frac{pd}{n(p-n)}$$

$$\frac{nd}{p(p-n)}$$

$$\frac{d}{p-n}$$

$$\frac{pd}{p-n}$$

None

17.

At 9:00 A.M. Allan began jogging and Bill began walking at constant
rates around the same circular 1/4 mile track. The figure above compares
their times in minutes and corresponding distances in miles. Which
statement or statements must be true?
I. Bill’s average rate of walking was 2 miles per hour.
II. At 9:10 A.M., Allan had jogged 3/5 mile more than Bill had walked.
III. At 9:30 A.M., Allan had completed 8 more laps around the track
than Bill.

I and II only

I only

I and III only

II only

None

18.

For the line l, y = ax + n, where a and n are distinct nonzero constants.
Which of these lines must be perpendicular to line l?

$$y = −ax + n$$

$$ y=-\frac{1}{a}x-n $$

$$y = nx + a$$

$$y = ax − n$$

None

19.

A model rocket is launched vertically into the air such that its height at
any time, t, is given by the function h(t) = −16t²+ 80t + 10. What is
the maximum height attained by the model rocket?

110

140

None

20.

x-3y=-2
$y=\frac{5}{x}$
The values of x that satisfy the system of equations
above also satisfy which of the following
equations?

(x - 5)(x + 3) = 0

(x - 3)(x + 5) = 0

(x + 2)(x + 5) = 0

(x - 2)(x - 5) = 0

None

21.

If 4 + √b = 72 , what is the value of 4− √b ?

4/5

1/2

1/5

4/7

None

22.

If y = x², where x ≠ 0, and $w=y^{6}$, which of the following expresses the value of w/y³ in terms of x

$$x^{4}$$

$$x^{6}$$

$$x^{5}$$

$$x^{2}$$

None

23.

A person spent a total of \$720 for dress shirts and sport shirts, each
priced at \$35 and \$20, respectively. If the person purchased two \$35
dress shirts for each \$20 sport shirt, what is the total number of shirts
purchased?
Write your answer

24.

At the beginning of 2015, a retired person is shopping for a retirement annuity, which is an investment policy that will give him fixed monthly payments for the rest of his life. He would like the amount of his
annuity payments to more than keep up with the rate of inflation. He
decides that he will choose a policy that issues payments that increase
annually at a rate that is at least 1.5% greater than the average yearly
compounded rate of inflation calculated from the period that extends
from the second half of 2005 through the first half of 2008. What
should be the minimum annual rate of increase in his monthly annuity
payments, correct to the nearest tenth?

None

25.

A political strategist wants to conduct a survey to determine how the
likely voters in a given state of 10,000,000 people feel about a
politician’s stand on an infrastructure spending plan. The strategist has
a budget to make phone calls to 1,000 people. What would be the most
effective approach for him to minimize the margin of error in his
survey results?

Place calls to rural residents of the state who have demonstrated political activism.

Place calls to randomly selected phone numbers of residents within the state.

Place calls to residents of the state’s largest city who have indicated they are members of a political party.

Place calls to places of business so that people can more likely be reached during the work day

None

26.

A long-distance telephone call costs $1.80 for the first 3 minutes and
$0.40 for each additional minute. If the charge for an x-minute long
distance call at this rate was $4.20, then x =

None

27.

In a survey of 80 students, 55 students stated that
they play a varsity sport, and 35 stated that they are
taking at least one AP level course. Which of the
following statements must be true?

At least one student who takes an AP level course does NOT play a varsity sport.

The number of students who do not play a varsity sport is greater than the number of students who do not take at least one AP level course.

Less than half of the students who play a varsity sport are also taking at least one AP level course.

At least 10 of these students are both playing a varsity sport and taking at least one AP level course.

None

28.

If a + 2b = 13 and 8a + b = 20, what is value of 3a + b?

Write your answer

29.

NASA’s New Horizons interplanetary probe has been making its way to
Pluto since January 2006. In July 2015, it reached Pluto and sent a
radio transmission signal at a speed of 1.86 × 105 miles per second. If
the signal traveled a distance back to Earth of approximately 3.06 × 109
miles, how many minutes did it take for the signal to reach Earth,
correct to the nearest 5 minutes?

400

275

300

105

None

30.

The weights of 5 boxes of screws vary from 2.85 pounds to 3.45
pounds. If w represents the weight, in pounds, of one of these boxes,
which of the following must be true?

|w − 5| ≤ 0.3

|w − 3.15| ≤ 0.3

|w − 0.3| ≤ 3.15

|w − 2.85| ≤ 0.3

None

31.

Based on the data in the table above, which of the following statements
must be true?
I. For every 3 men who applied to a same state college, 2 women
applied to a same state college.
II. If a female student is selected at random, the probability that she
did not apply to a 2-year college is greater than 75%.
III. Of the students who applied to a same state college, 40% were
females.

II and III only

I, II, and III

I and III only

I and II only

None

32.

A survey is conducted in which 60% of the individuals who responded
indicated that they do not support issuing a bond to help raise money to
fund the construction of a new sports arena in their city. A statistician
calculates the confidence level to be 95% for an interval of 5% below
and above the 60% mark. What conclusion is best supported by this
information?

95% of the people surveyed do not support the issuing of the bond.

The probability that a person selected at random from the sample supports the issuing of the bond is 0.4

If the survey were to be repeated 100 times, 95% of the time the number of people who would not support the issuing of the bond would range from 55% to 65% of those surveyed

The probability that a person selected at random from the sample does not support the issuing of the bond ranges from 0.57 to 0.63.

None

33.

$$m=\frac{M}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$$
The equation above describes, according to Einstein’s theory of
relativity, how the mass of an object increases with velocity where m is
the mass of a moving object, M is the mass the object when it is not
moving, v is the velocity of the object relative to a stationary observer,
and c is the speed of light. Which of the following expresses v in terms
of m, M, and c?

$$c\sqrt{1-\left ( \frac{M}{m} \right )^{2}}$$

$$\sqrt{c^{2}+\left ( \frac{M}{m} \right )^{2}}$$

$$\sqrt{\left ( c+\frac{M}{m} \right )^{2}-1}$$

$$c\sqrt{1+\left ( \frac{M}{m} \right )^{2}}$$

None

34.

If there were 20 students each in Class A and Class C, and 30 students each in Class B and Class D, how many students participated in the May fund-raiser?

None

35.

If p(x) is a polynomial function with p(3) = 0, which statement must be
true?

The highest power of x in p(x) is 3

p(x) is divisible by 3.

x − 3 is a factor of p(x).

p(x) is divisible by x + 3

None

36.

The average (arithmetic mean) of a, b, c, and d is 3 times the median. If
0 < a < b < c < d, what is a in terms of b, c, and d?

5(b + c) + d

3(b + c) − d

5(b + c) − d

3(b + c) + d

None

37.

If f (x) = 3x + n, where n is a constant, and f(2) = 0, then f(n) =

-12

-24

-18

None

38.

Everyone in Niko’s class has a different birth date. If Niko is both the 8th oldest person and the 12th youngest person in his class, how many students are in Niko’s class?
Write your answer

39.

If $3x-1 =x -\frac{7}{9}$ , what is the value of 2x + 1?

$$\frac{10}{3}$$

$$\frac{4}{3}$$

$$\frac{11}{9}$$

$$\frac{25}{9}$$

None

40.

Hours Worked in a Week	Total Payment
8	$108.00
23	$310.50
17	$229.50

Andrew keeps track of his paychecks over the past several weeks,
recording the number of hours he worked and his total payments as
indicated in the table above. He wants to model the relationship
between h hours worked and total payments p, in dollars, using an
equation of the form p = kh where k is a constant. Based on the data in
the table, what value of k should he use?
Write your answer in decimal

41.

The equation of a circle in the xy-plane is $x^{2}+4x+y^{2}-10y=20$If
the line x = k intersects the circle in exactly one point, what is a
possible value of k?
Write your answer

42.

When Sophie was born her parents invested a sum of \$20,000 in her
college fund. They invested it at a nominal annual rate of 5% with
interest compounded quarterly. Which equation could be used to find
the number of dollars, y, in the account, after 18 years assuming no
other deposits or withdrawals are made?

$$y=20,000(1.0125)^{\frac{18}{4}}$$

$$y=20,000(0.21)^{18\times 4}$$

$$y=20,000(1.05)^{18}$$

$$y=20,000(1.0125)^{18\times 4}$$

None

43.

A population, T(x), of wild turkeys, in a certain rural area is
represented by the function $T(x) = 17(1.15)^{2x}$, where x is the number of
years since 2010. According to this model, how many more turkeys are
in the population for the year 2015 than were available for 2010?

None

44.

The value of y varies with x according to the equation y = kx2, where k > 0. When the value of x increases from 3 to 12, which of the following best
describes the behavior of y ?

It increases by 81

It is multiplied by 4

It is multiplied by 16

It increases by 135

None

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