SAT Practice Test 6 Digital

Question 1 of 54 | Algebra · Level 1

$(p + 3) + 8 = 10$
What value of $p$ is the solution to the given equation?

$-1$

$5$

$15$

$21$

Question 2 of 54 | Statistics · Level 1

The scatterplot shows the relationship between two variables, x and y.
Which of the following graphs shows the most appropriate model for the data?

$Question image$

[Graph A: Linear fit] $Choice A$

[Graph B: Exponential fit curving up] $Choice B$

[Graph C: Exponential fit starting low then rising sharply] $Choice C$

[Graph D: Exponential fit curving upward, similar to B] $Choice D$

Question 3 of 54 | Algebra · Level 1

$k^2 - 53 = 91$
What is the positive solution to the given equation?

144

Question 4 of 54 | Algebra · Level 1

During a portion of a flight, a small airplane's cruising speed varied between 150 miles per hour and 170 miles per hour. Which inequality best represents this situation, where $s$ is the cruising speed, in miles per hour, during this portion of the flight?

$s \leq 20$

$s \leq 150$

$s \leq 170$

$150 \leq s \leq 170$

Question 5 of 54 | Advanced Math · Level 2

An object was launched upward from a platform. The graph shown models the height above ground, $y$, in meters, of the object $x$ seconds after it was launched. For which of the following intervals of time was the height of the object increasing for the entire interval?

$Question image$

From $x = 0$ to $x = 2$

From $x = 0$ to $x = 4$

From $x = 2$ to $x = 3$

From $x = 3$ to $x = 4$

Question 6 of 54 | Ratios, Rates and Percentages · Level 2

How many yards are equivalent to 1,116 inches? (1 yard = 36 inches)

Question 7 of 54 | Algebra · Level 2

$f(x) = 14 + 4x$
The function $f$ represents the total cost, in dollars, of attending an arcade when $x$ games are played. How many games can be played for a total cost of \$58?

Question 8 of 54 | Algebra · Level 2

$f(x) = x + b$
For the linear function $f$, $b$ is a constant. When $x = 0$, $f(x) = 30$. What is the value of $b$?

$-30$

$-\dfrac{1}{30}$

$\dfrac{1}{30}$

$30$

Question 9 of 54 | Advanced Math · Level 2

$P(t) = 1,800(1.02)^t$
The function $P$ gives the estimated number of marine mammals in a certain area, where $t$ is the number of years since a study began. What is the best interpretation of $P(0) = 1,800$ in this context?

The estimated number of marine mammals in the area was 102 when the study began.

The estimated number of marine mammals in the area was 1,800 when the study began.

The estimated number of marine mammals in the area increased by 102 each year during the study.

The estimated number of marine mammals in the area increased by 1,800 each year during the study.

Question 10 of 54 | Algebra · Level 3

A manager is responsible for ordering supplies for a shaved ice shop. The shop's inventory starts with 4,500 paper cups, and the manager estimates that 70 of these paper cups are used each day. Based on this estimate, in how many days will the supply of paper cups reach 1,700?

Question 11 of 54 | Algebra · Level 3

$y > 4x + 8$
For which of the following tables are all the values of $x$ and their corresponding values of $y$ solutions to the given inequality?

$2$, $19$
$4$, $30$
$6$, $41$

$2$, $8$
$4$, $16$
$6$, $24$

$2$, $13$
$4$, $18$
$6$, $23$

$2$, $13$
$4$, $21$
$6$, $29$

Question 12 of 54 | Advanced Math · Level 3

Which expression is equivalent to $(x^2 + 11)^2 + (x - 5)(x + 5)$?

$x^4 + 23x^2 - 14$

$x^4 + 23x^2 + 96$

$x^4 + 12x^2 + 121$

$x^4 + x^2 + 146$

Question 13 of 54 | Advanced Math · Level 3

The function $h$ is defined by $h(x) = \dfrac{8}{5x + 6}$. What is the value of $h(2)$?

Question 14 of 54 | Geometry · Level 3

The figure shows the lengths, in inches, of two sides of a right triangle. What is the area of the triangle, in square inches?

$Question image$

Question 15 of 54 | Algebra · Level 3

The graph models the number of active projects a company was working on $x$ months after the end of November 2012, where $0 \leq x \leq 6$. According to the model, what is the predicted number of active projects the company was working on at the end of November 2012?

$Question image$

Question 16 of 54 | Algebra · Level 3

The relationship between two variables, $x$ and $y$, is linear. For every increase in the value of $x$ by 1, the value of $y$ increases by 8. When the value of $x$ is 2, the value of $y$ is 18. Which equation represents this relationship?

$y = 2x + 18$

$y = 2x + 8$

$y = 8x + 2$

$y = 3x + 26$

Question 17 of 54 | Algebra · Level 3

$P = N(19 - C)$
The given equation relates the positive numbers $P$, $N$, and $C$. Which equation correctly expresses $C$ in terms of $P$ and $N$?

$C = \dfrac{19 + P}{N}$

$C = \dfrac{19 - P}{N}$

$C = 19 + \dfrac{P}{N}$

$C = 19 - \dfrac{P}{N}$

Question 18 of 54 | Advanced Math · Level 3

$w^2 + 12w - 40 = 0$
Which of the following is a solution to the given equation?

$6 - 2 \sqrt{19}$

$2 \sqrt{19}$

$\sqrt{19}$

$-6 + 2 \sqrt{19}$

Question 19 of 54 | Statistics · Level 4

The table shown summarizes the number of employees at each of the 17 restaurants in a town.

Number of employees	Number of restaurants
2 to 7	2
8 to 13	4
14 to 19	2
20 to 25	7
26 to 31	2

Which of the following could be the median number of employees for the restaurants in this town?

$2$

$9$

$15$

$21$

Question 20 of 54 | Algebra · Level 4

What is the $y$-coordinate of the $y$-intercept of the graph of $\dfrac{3x}{7} = -\dfrac{5y}{9} + 21$ in the $xy$-plane?

Question 21 of 54 | Advanced Math · Level 4

The graph of $y = 2x^2 + bx + c$ is shown, where $b$ and $c$ are constants. What is the value of $bc$?

$Question image$

Question 22 of 54 | Ratios, Rates and Percentages · Level 4

In 2008, Zinah earned 14% more than in 2007, and in 2009 Zinah earned 4% more than in 2008. If Zinah earned $y$ times as much in 2009 as in 2007, what is the value of $y$?

$0.5600$

$1.0056$

$1.1800$

$1.1856$

Question 23 of 54 | Geometry · Level 4

Circle A (shown) is defined by the equation $(x + 2)^2 + y^2 = 9$. Circle B (not shown) is the result of shifting circle A down 6 units and increasing the radius so that the radius of circle B is 2 times the radius of circle A. Which equation defines circle B?

$Question image$

$(x + 2)^2 + (y + 6)^2 = (4)(9)$

$2(x + 2)^2 + 2(y + 6)^2 = 9$

$(x + 2)^2 + (y - 6)^2 = (4)(9)$

$2(x + 2)^2 + 2(y - 6)^2 = 9$

Question 24 of 54 | Trigonometry · Level 5

Right triangle ABC is shown. What is the value of $\tan A$?

$Question image$

$\dfrac{\sqrt{3}}{54}$

$\dfrac{1}{\sqrt{3}}$

$\sqrt{3}$

$27\sqrt{3}$

Question 25 of 54 | Advanced Math · Level 5

At the time that an article was first featured on the home page of a news website, there were 40 comments on the article. An exponential model estimates that at the end of each hour after the article was first featured on the home page, the number of comments on the article had increased by 190% of the number of comments on the article at the end of the previous hour. Which of the following equations best represents this model, where $C$ is the estimated number of comments on the article $t$ hours after the article was first featured on the home page and $t \leq 4$?

$C = 40(1.19)^t$

$C = 40(1.9)^t$

$C = 40(19)^t$

$C = 40(2.9)^t$

Question 26 of 54 | Advanced Math · Level 5

$x$	$g(x)$
-27	3
-9	0
21	5

The table shows three values of $x$ and their corresponding values of $g(x)$, where $g(x) = \dfrac{f(x)}{x + 3}$ and $f$ is a linear function. What is the $y$-intercept of the graph of $y = f(x)$ in the $xy$-plane?

$(0, 36)$

$(0, 12)$

$(0, 4)$

$(0, -9)$

Question 27 of 54 | Geometry · Level 5

In right triangle ABC, angle C is the right angle and $BC = 162$. Point D on side AB is connected by a line segment with point E on side AC such that line segment DE is parallel to side BC and $CE = 2AE$. What is the length of line segment DE?

Question 28 of 54 | Algebra · Level 1

The function $f$ is defined by $f(x) = 8x$. For what value of $x$ does $f(x) = 72$?

Question 29 of 54 | Geometry · Level 1

In the figure, two lines intersect at a point. Angle 1 and angle 2 are vertical angles. The measure of angle 1 is 72°. What is the measure of angle 2?

$Question image$

72°

108°

144°

288°

Question 30 of 54 | Probability · Level 1

On a street with 7 houses, 2 houses are blue. If a house from this street is selected at random, what is the probability of selecting a house that is blue?

$\dfrac{1}{7}$

$\dfrac{2}{7}$

$\dfrac{5}{7}$

$\dfrac{7}{7}$

Question 31 of 54 | Advanced Math · Level 1

The graph of function $f$ is shown, where $y = f(x)$.
Which of the following describes function $f$?

$Question image$

Increasing linear

Decreasing linear

Increasing exponential

Decreasing exponential

Question 32 of 54 | Algebra · Level 2

The graph of the function $f$ is shown, where $y = f(x)$. What is the $y$-intercept of the graph?

$Question image$

$(0, -1)$

$(0, -4)$

$(0, 1)$

$(0, 4)$

Question 33 of 54 | Algebra · Level 2

$x = 8$, $x + 3y = 26$
The solution to the given system of equations is $(x, y)$. What is the value of $y$?

Question 34 of 54 | Ratios, Rates and Percentages · Level 2

The amount of Hanna's bill for a food order was \$50. Hanna gave a tip of 20% of the amount of the bill. What is the amount, in dollars, of the tip Hanna gave?

Question 35 of 54 | Advanced Math · Level 2

Which expression is equivalent to $5x^5 - 6x^4 + 8x^3$?

$x^4(5x - 6)$

$x^3(5x^2 - 6x + 8)$

$8x^3(5x^2 - 6x + 1)$

$6x^5(-6x^4 + 8x^3 + 1)$

Question 36 of 54 | Ratios, Rates and Percentages · Level 2

The ratio of the length of line segment XY to the length of line segment ZV is 6 to 1. If the length of line segment XY is 102 inches, what is the length, in inches, of line segment ZV?

102

612

Question 37 of 54 | Algebra · Level 3

$7(2x - 3) = 63$
Which equation has the same solution as the given equation?

$2x - 3 = 9$

$2x - 3 = 56$

$2x - 21 = 63$

$2x - 21 = 70$

Question 38 of 54 | Algebra · Level 3

The function $f$ defined by $f(t) = 14t + 9$ gives the estimated length, in inches, of a vine plant $t$ months after Tavon purchased it. Which of the following is the best interpretation of 9 in this context?

Tavon will keep the vine plant for 9 months.

The vine plant is expected to grow 9 inches each month.

The vine plant is expected to grow to a maximum length of 9 inches.

The estimated length of the vine plant was 9 inches when Tavon purchased it.

Question 39 of 54 | Advanced Math · Level 3

$(x + 2)(x - 5)(x + 9) = 0$
What is a positive solution to the given equation?

$3$

$4$

$5$

$18$

Question 40 of 54 | Ratios, Rates and Percentages · Level 3

Brian saves $\dfrac{2}{5}$\$215 he earns each week from his job. If Brian continues to save at this rate, how much money, in dollars, will Brian save in 9 weeks?$

Question 41 of 54 | Advanced Math · Level 3

A rectangle has an area of 155 square inches. The length of the rectangle is 4 inches less than 7 times the width of the rectangle. What is the width of the rectangle, in inches?

Question 42 of 54 | Statistics · Level 3

4, 10, 18, 4, 4, 5, 6, 5
What is the median of the data set shown?

$4$

$5$

$7$

$14$

Question 43 of 54 | Geometry · Level 3

A right circular cylinder has a volume of 432 cubic centimeters. The area of the base of the cylinder is 24 square centimeters. What is the height, in centimeters, of the cylinder?

216

10,368

Question 44 of 54 | Advanced Math · Level 3

$x^2 = -841$
How many distinct real solutions does the given equation have?

Exactly one

Exactly two

Infinitely many

Zero

Question 45 of 54 | Algebra · Level 3

Line $k$ is defined by $y = 7x + \dfrac{1}{8}$. Line $j$ is perpendicular to line $k$ in the $xy$-plane. What is the slope of line $j$?

$-8$

$-\dfrac{1}{7}$

$\dfrac{1}{8}$

$7$

Question 46 of 54 | Algebra · Level 4

Number of cars	Maximum number of passengers and crew
3	174
5	284
10	559

The table shows the linear relationship between the number of cars, $c$, on a commuter train and the maximum number of passengers and crew, $p$, that the train can carry. Which equation represents the linear relationship between $c$ and $p$?

$55c - p = -9$

$55c - p = 9$

$55p - c = -9$

$55p - c = 9$

Question 47 of 54 | Advanced Math · Level 4

If $4^{8c} = \sqrt[3]{4^7}$, what is the value of $c$?

Question 48 of 54 | Algebra · Level 4

$(x - 2) - 4(y + 7) = 117$, $(x - 2) + 4(y + 7) = 442$
The solution to the given system of equations is $(x, y)$. What is the value of $6(x - 2)$?

Question 49 of 54 | Geometry · Level 4

In triangle ABC, angle B is a right angle. The length of side AB is $10\sqrt{37}$ and the length of side BC is $24\sqrt{37}$. What is the length of side AC?

$14\sqrt{37}$

$26\sqrt{37}$

$34\sqrt{37}$

$\sqrt{34 \cdot 37}$

Question 50 of 54 | Advanced Math · Level 4

$f(x) = (1.84)^{\frac{x}{4}}$
The function $f$ is defined by the given equation. The equation can be rewritten as $f(x) = \left(1 + \dfrac{p}{100}\right)^x$, where $p$ is a constant. Which of the following is closest to the value of $p$?

$16$

$21$

$46$

$96$

Question 51 of 54 | Advanced Math · Level 5

The function $f$ is defined by $f(x) = a \sqrt{x + b}$, where $a$ and $b$ are constants. In the $xy$-plane, the graph of $y = f(x)$ passes through the point $(-24, 0)$, and $f(24) < 0$. Which of the following must be true?

$f(0) = 24$

$f(0) = -24$

$a > b$

$a < b$

Question 52 of 54 | Geometry · Level 5

In the $xy$-plane, a circle has center C with coordinates $(h, k)$. Points A and B lie on the circle. Point A has coordinates $(h + 1, k + \sqrt{102})$, and $\angle ACB$ is a right angle. What is the length of $\overline{AB}$?

$\sqrt{206}$

$2\sqrt{102}$

$103\sqrt{2}$

$103\sqrt{3}$

Question 53 of 54 | Statistics · Level 5

The scatterplot shows the relationship between two variables, $x$ and $y$, for data set E. A line of best fit is shown. Data set F is created by multiplying the $y$-coordinate of each data point from data set E by 3.9. Which of the following could be an equation of a line of best fit for data set F?

$Question image$

$y = 46.8 + 5.9x$

$y = 46.8 + 1.5x$

$y = 12 + 5.9x$

$y = 12 + 1.5x$

Question 54 of 54 | Algebra · Level 5

$48x - 64y = 48y + 24$, $ry = \dfrac{1}{8} - 12x$
In the given system of equations, $r$ is a constant. If the system has no solution, what is the value of $r$?

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\(x\)	\(g(x)\)
-27	3
-9	0
21	5

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