DIGITAL SAT FREE MATH PRACTICE TEST 1

DIGITAL SAT MATH PRACTICE -TEST 1

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.

If an equation of a parabola in the xy-plane is $f(x)=-(x+2)^{2}-1$, what
are the coordinates of the vertex of the parabola defined by g(x) = f(x − 2)?

(0, −1)

(−2, 1)

(−2, −3)

(4, −1)

None

After its initial offering, the price of a stock increased by 20% in the first year, decreased by 25% in the second year, then increased by 10% in the third year. What was the net change in the stock price over the entire three-year period?

It increased by 1%.

It increased by 5%.

It decreased by 1%.

It decreased by 5%

None

If 10 cubic centimeters of blood contains 1.2 grams of hemoglobin,
how many grams of hemoglobin are contained in 35 cubic centimeters
of the same blood?
Write your answer in decimal

Natalie is planning a school celebration and wants to have live music
and food for everyone who attends. She has found a band that will
charge her \$750 and a caterer who will provide snacks and drinks for
\$2.25 per person. If her goal is to keep the average cost per person
between \$2.75 and \$3.25, how many people, p, must attend?

750 < p < 1,500

500 < p < 1,000

225 < p < 325

325 < p < 750

None

The Eye Surgery Institute just purchased a new laser machine for
\$500,000 to use during eye surgery. The Institute must pay the inventor
\$550 each time the machine is used. If the Institute charges \$2,000 for
each laser surgery, what is the minimum number of surgeries that must
be performed in order for the Institute to make a profit?
Write your answer

Which of the following statements is true about the parabola whose
equation in the xy-plane is y = (2x − 6)(x + 1)?
I. The line x = 2 is a vertical line of symmetry.
II. The minimum value of y is −8.
III. The y-intercept is −6

II and III only

I and III only

I, II, and III

I and II only

None

If function g is defined by g(x) = x − 1 and 2g(c) = 10, what is the
value of g(3c)?
Write your answer

On a test that has a normal distribution of scores, a score of 59 falls
two standard deviations below the mean, and a score of 74 is one
standard deviation above the mean. If x is an integer score that lies
between 2.5 and 3.0 standard deviations above the mean, what is a
possible value of x?
Write your answer

C(n) = 110n + 900
The cost of airing a commercial on television, C, is modeled by the
function above where n is the number of times the commercial is aired.
Based on this model, which statement is true?€

The commercial costs \$110 to produce and can air an unlimited number of times.

The commercial costs \$110 to produce and \$900 each time it is aired.

The commercial costs \$0 to produce and \$110 per airing up to $900.

The commercial costs \$900 to produce and \$110 each time it is aired.

None

10.

If one pound of grain can feed either 5 chickens or 2 pigs, then ten pounds of grain can feed 20 chickens and how many pigs?

None

11.

The figure above shows part of the graph of function f. If f(x + 6) = f(x)
for all values of x, what is the value of f(23)?

None

12.

The table above shows the annual salaries for the 24 members of a
professional sports team in terms of millions of dollars. If the team
signs an additional player to a contract worth 7.3 million dollars per
year, which statement about the median and mean is true?

The median will increase by a greater amount.

The mean will increase by a greater amount

The median and mean will increase by the same amount.

Neither will change

None

13.

Function f is defined for 0 ≤ x ≤ 5, as shown in the accompanying figure.
If (r, s) is a point inside the shaded region bounded by the x-axis, the line
x = 5, and y = f(x), which statement must be true?

I. r + s ≤ 5
II. s ≤ f(r)
III. r ≠ s

I and III only

I only

II only

III only

None

14.

If i= √−1, which of the following is NOT equal to i³ + i ?
2i²-2

(2i)²+4

2-2i³

i²-1

2i²-2

None

15.

If $\frac{-3}{x}+4\leq -11\, and\, x> 0$, what is the greatest possible value for x?

1/8

-3/4

-1/5

1/5

None

16.

An economist purchases a kitchen appliance at the beginning of 2014
for $3,000. The salesperson advises him that the only changes in price
for the appliance since the beginning of 2012 have been due to
inflation. Assuming that is the case, what would have been the
purchase price for the appliance at the beginning of 2012 correct to the
nearest dollar?

1,236

3,897

5,638

2,895

None

17.

A soccer team has played 25 games and has won 60% of the games it
has played. What is the minimum number of additional games the team
must win in order to finish the season winning 80% of the games it has
played?

None

18.

Using the conversion relationships above, what is the maximum
number of 2-teaspoon doses of cough medicine that can be dispensed
from a bottle that contains 225 milliliters of cough medicine?
Write your answer

19.

In the figure above, triangle ABC has an area of 19.
What is the value of tan θ ?

4/13

8/13

1/13

7/13

None

20.

If x and y are real numbers, and $2\sqrt{x-4}-2 =1$, and
|y– 5| < 2, what is the smallest possible integer value of x+ y?

None

21.

The table above shows the average diameter, in millimeters, of a pupil
in a person’s eye as she or he grows older from age 20 to age 80.
Which equation expresses the relationship between pupil diameter, p,
and age, a?

p = −0.04a + 34.3

p = −0.04a + 5.5

p = 0.235a

p = 0.04a + 3.9

None

22.

The graph above shows how the size of a country’s population has
changed over time. Which of the following are the most likely
underlying reasons for the type of graph shown?

A liberal immigration policy and a thriving economy with increased job opportunities.

A large increase in annual birthrates and increased life expectancy rates.

The spread of a highly contagious fatal disease and a history of political strife and unrest

A moderate increase in annual birthrates and a liberal immigration policy.

None

23.

Which of the following statements includes a function divisible by 2x +1?
I. f(x) = 8x² − 2
II. g(x) = 2x² − 9x + 4
III. h(x) = 4x³ + 2x² − 6x − 3

I only

I and III only

I, II, and III

I and II only

None

24.

How many solutions to the equation 4 cos x = 1 lie between x = 0 and x = 3p

Two

Four

Three

Six

None

25.

Which of the following expressions is equivalent to
$\frac{1}{2}x^{3}(x^{2}-4)$

$$\frac{1}{2}x^{5}-4x^{2}$$

$$\frac{1}{2}x^{6}-2$$

$$\frac{1}{2}x^{6}-2x^{2}$$

$$\frac{1}{2}x^{5}-2x^{3}$$

None

26.

Which function could represent the graph above?

f(x) = (x − 3)(x² + x − 2)

f(x) = (x − 6)(x² − 4x + 3)

f(x) = (x + 2)(x² − 4x − 12)

f(x) = (x − 1)(x² − 5x − 6)

None

27.

Impedance measures the opposition of an electrical circuit to the flow
of electricity. The total impedance in a particular circuit is given by the
formula $Z_{r}=\frac{z_{1}\times z_{2}}{z_{1} + z_{2}}$ . What is the total impedance of a circuit,
$$Z_{T}, if Z_{1}= 1+2i \, and\, Z_{2}=1-2i? [Note\,i=\sqrt{-1}]$$

$$2i$$

1/2

-3/2

5/2

None

28.

In the physics lab, a student determined the kinetic energy, KE, of an
object at various velocities, V, and found a strong positive association
between KE and V. Which of the above scatterplots show this
relationship?

Graph (3)

Graph (2)

Graph (1)

Graph (4)

None

29.

When a ball is thrown straight up at an initial velocity of 54 feet per
second. The height of the ball t seconds after it is thrown is given by
the function h(t) = 54t − 12t². How many seconds after the ball is
thrown will it return to the ground?

4.5

9.2

None

30.

If the function f is defined by the equation f(x) = k(x + 6)(x − 1), where k > 5, then which of the following is equivalent to f(7)

f(-78)

f(-12)

f(78)

f(-2)

None

31.

The accompanying diagram shows a revolving door with three panels,
each of which is 4 feet long. What is the number of feet in the width, w,
of the opening between points x and y?

$$4\sqrt{3}$$

$$8\sqrt{2}$$

$$8\sqrt{3}$$

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

None

32.

$$(2-\sqrt{-25})(-7+\sqrt{-4})=x+yi$$
In the equation above, what is the value of y?
write your answer in numbers only

33.

x	1	2	3	4	5
f(x)	3	4	5	6	7

x	3	4	5	6	8
g(x)	4	6	8	10	7

The tables above give the values of functions f and g for several values
of x. If g(f(b)) = 8, what is the value of b?
Write your answer

34.

Mikala exercises in her gym by jogging on the treadmill at an average
rate of 4 miles per hour and then pedaling on a stationary bicycle at an
average rate of 8 miles per hour. In her workout, she jogs the
equivalent of x miles and bicycles the equivalent of y miles. If Mikala
works out for at least 45 minutes, which of the following is true?

$$\frac{4}{x}+\frac{8}{y}\geq 45$$

$$\frac{x}{4}+\frac{y}{8}\geq \frac{3}{4}$$

$$4x+8y\geq 45$$

$$x+\frac{y}{2}\geq \frac{3}{4}$$

None

35.

A square is drawn by joining the mid points of the given square a third square in the same way and this process continues indefinitely. If a side of the first square is 16 cm , then the sum of the area of all of the squares

256 sq. cm

1024 sq. cm

128 sq. cm

512 sq. cm

None

36.

$A=\frac{v^{2}}{R}$
The acceleration of an object moving in a circle is determined by the
equation above, in which v is the velocity of the object, A is its
acceleration, and R is the radius of the circle. What is the value of the
radius in terms of the other variables?

$$R=\frac{v^{2}}{A}$$

$$R=\frac{2v}{A}$$

$$R=\frac{1}{Av^{2}}$$

$$R=A v^{2}$$

None

37.

The price of gas increased by 12% per gallon sometime during the first
fiscal quarter and then decreased by 25% per gallon by the end of the
second fiscal quarter. The final price of gas per gallon at the end of the
second quarter decreased by what percent compared to the starting
price at the beginning of the first fiscal quarter?

18.5%

20%

13%

16%

None

38.

What is one possible solution to the equation
$$\frac{6}{x+1}-\frac{3}{x-1}=\frac{1}{4}$$

-3 or -7

3 or 7

5 or 7

-5 or -7

None

39.

An arch is built so that it has the shape of a parabola with the equation
y = −3x² + 24x where y represents the height of the arch in meters. How
many times greater is the maximum height of the arch than the width of
the arch at its base?

None

40.

In the xy-plane, the graph of the equation y = 3x2 - kx - 35 intersects the x-axis at (5, 0). What is the value of k ?

None

41.

$-\frac{3}{5} <-2t+1<\frac{3}{7}$, what is one possible value of 6t ?

4.29 ≤ x ≤ 4.79

5.29 ≤ x ≤ 6.79

4.80 > 6t > 4.2857

2.29 ≤ x ≤ 4.79

None

42.

If P(−0.6, −0.8) is a point on the unit circle in the figure above, what is
the exact value of tan θ + sin θ?

8/15

1/15

3/17

9/15

None

43.

If cos (x - p) = 0.4, what is the value of sin² x ?

0.54

0.64

0.74

0.84

None

44.

Let function f(x) be defined by the equation f(x) =x² - 1. If b is a positive real number, then $$f\left ( \frac{1}{b} \right )$$

$$\frac{(b-1)(b+1)}{b^{2}}$$

$$\frac{b^{2}-1}{b}$$

$$\frac{b-1}{b^{2}}$$

$$\frac{(1-b)(1+b)}{b^{2}}$$

None

1 out of 44

DIGITAL SAT MATH PRACTICE -TEST 1

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