SAT Practice Test 29 Digital

Question 1 of 44 | Algebra · Level 2

If \(2b - 1 = 5\), what is the value of \(2b^2 - 1\)?

Question 2 of 44 | Geometry · Level 3

In the figure, points P, Q, R, S, and T lie on the same line, and R is the center of the large circle. If the three smaller circles are congruent and the radius of the large circle is 6, what is the radius of one of the smaller circles?

Question 3 of 44 | Problem Solving · Level 2

In a writer's workshop, there are half as many men as women. If there are 24 total men and women in the writer's workshop, how many men are there?

Question 4 of 44 | Problem Solving · Level 2

Jeri has edited \(\dfrac{1}{5}\) of her term paper. If she has edited 15 pages, how many pages does she have left to edit?

Question 5 of 44 | Algebra · Level 2

7, 12, 22, 42, 82 Which of the following gives a rule for finding each term in the sequence after the first?

Add 5 to the preceding number.

Add 5 to the sum of all of the preceding terms.

Double the preceding term and then subtract 2 from the result.

Add 14 to the preceding term and divide that result by 2.

Question 6 of 44 | Algebra · Level 2

If \(3 - \dfrac{1}{b} = \dfrac{3}{2}\), what is the value of \(b\)?

Question 7 of 44 | Geometry · Level 3

The figure shows a rectangular box with dimensions 3, 4, and 5. What is the longest length of a diagonal of one of the faces of this box?

\(\sqrt{24}\)

\(\sqrt{41}\)

\(\sqrt{50}\)

\(\sqrt{60}\)

Question 8 of 44 | Algebra · Level 2

Which of the following points is NOT on the graph of the line \(-2x - 3y = 36\) in the xy-plane?

\((-9, 6)\)

\((-24, 4)\)

\((6, -16)\)

\((12, -20)\)

Question 9 of 44 | Algebra · Level 3

During a coyote repopulation study, researchers determine that the equation \(P = 250(1.32)^t\) describes the population P of coyotes t years after their introduction into a new region. Which of the following gives the values of I, the initial population of coyotes, and r, the annual percent increase in this population?

I = 250, r = 32%

I = 250, r = 132%

I = 330, r = 32%

I = 330, r = 132%

Question 10 of 44 | Algebra · Level 3

Which of the following is equal to \(\dfrac{1}{\sqrt{3} + 1}\)?

\(\dfrac{\sqrt{3}}{2} - \dfrac{1}{2}\)

\(\dfrac{\sqrt{3}}{2} + \dfrac{1}{2}\)

\(\dfrac{\sqrt{3}}{4} - \dfrac{1}{4}\)

\(\dfrac{\sqrt{3}}{4} + \dfrac{1}{4}\)

Question 11 of 44 | Algebra · Level 2

The square of a positive number is 0.24 greater than the number itself. What is the number?

Question 12 of 44 | Algebra · Level 3

Which of the following could be the x-intercept and y-intercept of a line that is perpendicular to the line \(3x + 6y = 0\)?

\((-6, 0)\) and \((0, 3)\)

\((3, 0)\) and \((0, -6)\)

\((3, 0)\) and \((0, 6)\)

\((6, 0)\) and \((0, 3)\)

Question 13 of 44 | Algebra · Level 3

The function f is defined by the equation \(f(x) = x - x^2\). Which of the following represents a quadratic with no real zeros?

\(f(x) + \dfrac{1}{2}\)

\(f(x) - \dfrac{1}{2}\)

\(f\left(\dfrac{x}{2}\right)\)

\(f\left(x - \dfrac{1}{2}\right)\)

Question 14 of 44 | Algebra · Level 3

The function f is a quadratic function with zeros at \(x = 1\) and \(x = 5\). The graph of \(y = f(x)\) in the xy-plane is a parabola with a vertex at \((3, -2)\). What is the y-intercept of this graph?

Question 15 of 44 | Algebra · Level 3

In the xy-plane, the graph of the line \(y = \dfrac{15}{4}\) intersects the graph of the equation \(y = x^2 + x\) at two points. What is the distance between these two points?

\(\dfrac{3}{2}\)

\(\dfrac{5}{2}\)

\(\dfrac{15}{4}\)

Question 16 of 44 | Advanced Math · Level 4

If \(i^{2k} = 1\), and \(i = \sqrt{-1}\), which of the following must be true about k?

k is a multiple of 4.

k is a positive integer.

When 2k is divided by 4, the remainder is 1.

k/2 is an integer.

Question 17 of 44 | Geometry · Level 4

When graphed in the xy-plane, the line \(y = m x - 4\) intersects the x-axis at an angle of \(\theta\). If \(m > 0\), \(0^{\circ} < \theta < 90^{\circ}\), and \(\cos \theta = \dfrac{3}{\sqrt{58}}\), what is the value of m?

Question 18 of 44 | Algebra · Level 3

For all numbers x and y, let z be defined by the equation \(z = |2^2 - x^2 - y^2| + 2^2\). What is the smallest possible value of z?

Question 19 of 44 | Algebra · Level 3

If the polynomial \(P(x)\) has factors of 12, \((x - 5)\), and \((x + 4)\), which of the following must also be a factor of \(P(x)\)?

\(2x^2 + 8\)

\(4x^2 - 20\)

\(6x^2 - 6x - 120\)

\(x^2 - 10x + 25\)

Question 20 of 44 | Algebra · Level 2

If \(f(x) = -x + 7\) and \(g(f(x)) = 2x + 1\), what is the value of \(g(2)\)?

-11

-5

Question 21 of 44 | Problem Solving · Level 2

What number is 40% greater than the sum of 40 and 80?

Question 22 of 44 | Statistics · Level 3

A researcher is trying to estimate the daily amount of time undergraduate computer science majors spend on nonrecreational computer activities. She surveys 120 students. The mean is 210 minutes per day, with a standard deviation of 16.5 minutes. Which subject group would most likely yield a smaller margin of error?

240 randomly selected computer science majors

240 randomly selected liberal arts majors

80 randomly selected computer science majors

80 randomly selected liberal art majors

Question 23 of 44 | Algebra · Level 2

If \(a = \dfrac{1}{2} b\) and \(2a + 4b = 20\), what is the value of b?

2.5

Question 24 of 44 | Statistics · Level 2

The spinner for a board game has 10 sectors, numbered 1 through 10. It is spun 20 times and the results summarized in the table. What is the median value of these 20 spins?

Question 25 of 44 | Algebra · Level 2

The table shows ordered pairs that correspond to the function \(h(x) = \dfrac{x^2}{2} + k\). What is the value of k?

Question 26 of 44 | Problem Solving · Level 2

A 48-gram serving of breakfast cereal contains 8 grams of sugar. How many grams of sugar are there in a 57-gram serving of the same cereal?

9.5

10.5

11.5

12.5

Question 27 of 44 | Statistics · Level 2

The graph shows the number of applicants and finalists for a statewide college scholarship program over four consecutive years. For which year was the ratio of finalists to applicants the greatest?

2010

2011

2012

2013

Question 28 of 44 | Algebra · Level 3

If \(y^3 = 20\) and \(z^2 = 10\), what is the value of \((y z)^6\)?

\(2 \times 10^5\)

\(4 \times 10^4\)

\(2 \times 10^5\)

\(4 \times 10^5\)

Question 29 of 44 | Algebra · Level 2

\(h x + 4y = -3\). The equation above is the equation of a line in the xy-plane, and h is a constant. If the slope of this line is \(-13\), what is the value of h?

Question 30 of 44 | Algebra · Level 2

If the sum of a, b, and c is three times the sum of a and b, which of the following expresses the value of a in terms of b and c?

\(\dfrac{(c - 2b)}{2}\)

\(\dfrac{(2b - c)}{2}\)

\(\dfrac{(c - 3b)}{3}\)

\(\dfrac{(3b - c)}{3}\)

Question 31 of 44 | Geometry · Level 3

In the figure, BCDE is a rectangle, \(A C = 14\), \(B C = 12\), and \(E C = 13\). What is the value of \(\tan x\)?

0.4

0.6

1.3

2.5

Question 32 of 44 | Algebra · Level 2

Which of the following binomials is a factor of \(x^2 - 6x + 8\)?

\(x - 4\)

\(x + 4\)

\(x + 2\)

\(x - 8\)

Question 33 of 44 | Algebra · Level 2

Let the function f be defined by \(f(x) = 2 - |x - 4|\) for all real values of x. What is the greatest possible value of f?

-2

Question 34 of 44 | Algebra · Level 2

If \(\dfrac{3}{b} - \dfrac{2}{5} = 1\), what is the value of b?

\(\dfrac{5}{7}\)

\(\dfrac{6}{5}\)

\(\dfrac{15}{7}\)

Question 35 of 44 | Algebra · Level 2

The sum of two numbers is four times their difference. The smaller of these numbers is 15. What is the greater number?

Question 36 of 44 | Algebra · Level 2

For the function f, \(f(1) = 4\) and \(f(2) = 13\). Which of the following equations could describe f?

\(f(x) = x^2 + 3\)

\(f(x) = x^2 + 9\)

\(f(x) = 2x^2 + 2\)

\(f(x) = 3x^2 + 1\)

Question 37 of 44 | Algebra · Level 2

Which of the following is NOT equivalent to \(12b^2\)?

\((6b)(6b)\)

\(12b(b)\)

\((b \sqrt{12})^2\)

\(6b^2 + 6b^2\)

Question 38 of 44 | Statistics · Level 3

If m is a number chosen randomly from the set {2, 3, 4, 6} and n is a number chosen randomly from the set {1, 2, 3, 4}, what is the probability that \(m n\) is a multiple of 12?

\(\dfrac{1}{16}\)

\(\dfrac{1}{8}\)

\(\dfrac{1}{4}\)

\(\dfrac{1}{2}\)

Question 39 of 44 | Geometry · Level 4

If \(0 < x < 2 \pi\) and \(5 \cos x = \sqrt{5}\), what is the value of \(\sin^2\left(\dfrac{x}{3}\right)\)?

Question 40 of 44 | Algebra · Level 2

If \(y = 3x + 4\) and \(x < 3\), which of the following represents all the possible values of y?

\(y > 7\)

\(y < 13\)

\(7 < y < 13\)

\(y > 13\)

Question 41 of 44 | Algebra · Level 3

If \(g(x + 1) = x^2 + 2x + 4\) for all values of x, which of the following is equal to \(g(x)\)?

\(x^2 + 4\)

\(x^2 + 3\)

\((x - 1)^2 + 4\)

\((x - 1)^2 + 3\)

Question 42 of 44 | Geometry · Level 3

In the figure, the circle with center O has a circumference of 50, and \(A B = B C\). What is the length of arc AB?

Question 43 of 44 | Algebra · Level 3

A: 2, 7, 12, 17, 22, ... B: 5, 15, 25, 35, 45, ... Two sequences, A and B, follow the patterns shown above. If the nth term of sequence A is 72, what is the nth term of sequence B?

125

135

145

155

Question 44 of 44 | Problem Solving · Level 2

A website received 2,100 visitors in July from both subscribers and nonsubscribers. If the ratio of subscribers to nonsubscribers among this group was 2:5, how many more nonsubscribers visited the site in July than subscribers?

126

630

900

1,260

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