SAT Pastpaper with Solutions

Chapter 33

2025.9 : B-C (analysis included)

MATH2 · 22 questions

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Chapter 33 · 2025.9 : B-C (analysis included) · MATH2

Which expression is equivalent to (3x³−4x+9)−(6x⁶+8x−4)?

−3x ⁹−12x−13

−6x ⁶+3x ³−12x+13

−6x⁶+3x²+4x+5

−3x ⁹−4x+5

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Chapter 33 · 2025.9 : B-C (analysis included) · MATH2

x ²+13x=−9

What are all possible solutions to the given equation?

C0D

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Chapter 33 · 2025.9 : B-C (analysis included) · MATH2

y<x

y>−3x−11

For which of the following tables are all the values of x and their corresponding values of y solutions to the given system of inequalities?

x	Y
4	2
5	3
6	4

x	Y
4	9
5	8
6	7

x	Y
-9	-11
-8	-10
-7	-9

x	Y
-9	-2
-8	-3
-7	-4

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Chapter 33 · 2025.9 : B-C (analysis included) · MATH2

f(x)=5(g(x))−2

g(x)=∣13x−9∣

The functions f and g are defined by the given equations. What is the value of f(−10)?

A139B-52C685D693

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Chapter 33 · 2025.9 : B-C (analysis included) · MATH2

In the xy-plane, an equation of circle A is (x−3)²+(y−9)²=25. Circle B has the same center as circle A but has a radius that is twice the radius of circle A. Which equation represents circle B?

(x−3)²+(y−9)²=625

(x−3)²+(y−9)²=250

(x−3)²+(y−9)²=50

(x−3)²+(y−9)²=100

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Chapter 33 · 2025.9 : B-C (analysis included) · MATH2

The length of the diagonal of a square is

units. What is the area, in square units, of the square?

A88B15,488C7,744D352

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Chapter 33 · 2025.9 : B-C (analysis included) · MATH2

Each of the following frequency tables represents a data set. Which data set has the greatest mean?

Value	Frequency
30	4
40	3
50	3
60	4

Value	Frequency
30	3
40	3
50	3
60	3

Value	Frequency
30	1
40	2
50	3
60	4

Value	Frequency
30	5
40	2
50	2
60	5

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Chapter 33 · 2025.9 : B-C (analysis included) · MATH2

A partially filled container containing 21 milliliters of water is placed under a leaky faucet that produces one 0.06-milliliter drop of water every 6 seconds. Until the container is full, which of the following can be used to represent the volume v, in milliliters, of water in the container t seconds after it is placed under the faucet, where t is a multiple of 6?

Av=6tBv=0.36t+21Cv=0.01t+21Dv=0.06t+21

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Chapter 33 · 2025.9 : B-C (analysis included) · MATH2

A science club from a certain high school in Ohio conducted an experiment to study the effects of smell on taste. A sample of 80 students was selected at random from the high school to participate in the experiment. First, the students tasted a pureed food sample while wearing covered goggles and nose plugs. Then, the students tasted the same pureed food sample without nose plugs. 32 students were able to correctly identify the pureed food sample while wearing nose plugs. Which of the following is the largest population to which the results of the experiment can be generalized?

AAll students from high schools in OhioBThe 80 students who participated in the experimentCAll students from the high schoolDThe 32 students who were able to correctly identify the pureed food sample while wearing nose plugs

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Chapter 33 · 2025.9 : B-C (analysis included) · MATH2

At the beginning of an experiment, the temperature of a liquid is 23 degrees Celsius (°C). During the first 4.0 minutes of the experiment, the temperature of the liquid increases at an average rate of 6.5°C per minute. Then, the temperature of the liquid increases at a constant rate of 2.4°C per minute. If the temperature of the liquid reaches 63°C x minutes after the beginning of the experiment, where x>4.0, which equation represents this situation?

A63=2.4(x−4.0)+26B63=2.4x+23C63=2.4(x−4.0)+49D63=2.4x+49

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Chapter 33 · 2025.9 : B-C (analysis included) · MATH2

The function f is defined by f(x)=24x³. The graph of y=f(−x)+c in the xy-plane, where c is a positive integer constant, has an x-intercept at (r,0) and a y-intercept at (0,t), where r and t are constants. Which of the following must be true about r and t?

Ar<0 and t>0Br>0 and t>0Cr>0 and t<0Dr<0 and t<0

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Chapter 33 · 2025.9 : B-C (analysis included) · MATH2

A certain investment account offers a special interest rate for the first 4 months the account is open followed by a lower interest rate for the remainder of the time the account is open. Bennett opened one of these accounts with an original account balance of $900 and did not make any other deposits or withdrawals. 4 months after Bennett opened the account, the balance had increased by 0.6% of the original balance. 6 months after Bennett opened the account, the balance had increased by an additional 0.1% of the balance at the end of the first 4 months. Every 2 months after the first 6 months, the balance had increased by an additional 0.1% of the balance 2 months before. Which of the following equations could represent the account balance B(x), in dollars, x months after the account was opened, where x≥4?

B(x)=905.40(1.001)^2x-8

B(x)=905.40(1.001)^2x-4

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Chapter 33 · 2025.9 : B-C (analysis included) · MATH2

In the xy-plane, the graph of the equation y=−x²+7x−76 intersects the line y=c at exactly one point. What is the value of c?

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Chapter 33 · 2025.9 : B-C (analysis included) · MATH2

The area of a rectangular region is increasing at a rate of 310 square feet per hour. Which of the following is closest to this rate in square meters per minute? (Use 1 meter = 3.28 feet.)

A28.81B1.58C16.95D0.48

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Chapter 33 · 2025.9 : B-C (analysis included) · MATH2

, the value of x+5 is between which of the following pairs of values?

A2 and 6B-2 and 2C-6 and -3D7 and 12

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Chapter 33 · 2025.9 : B-C (analysis included) · MATH2

What is the slope of the graph of y= $\frac {9} {17}$ x in the xy-plane?

17/9

9/17

-9/17

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Chapter 33 · 2025.9 : B-C (analysis included) · MATH2

Line k is defined by 6x+19y−7=0. Line j is perpendicular to line k in the xy-plane. What is the slope of line j?

19/6

-6/19

7/19

-19/7

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Chapter 33 · 2025.9 : B-C (analysis included) · MATH2

32x+81y=290

The given equation represents the volume of mulch x, in cubic feet, and the volume of soil y, in cubic feet, in a mixture of mulch and soil that weighs 290 pounds. If the volume of soil in the mixture is 2 cubic feet, what is the volume of mulch in the mixture, in cubic feet?

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Chapter 33 · 2025.9 : B-C (analysis included) · MATH2

The population of a certain city doubled every 75 years from 1663 to 1963. The population of this city was 240000 in 1963. What was the population of this city in 1663?

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Chapter 33 · 2025.9 : B-C (analysis included) · MATH2

For the positive quantities h, j, and k, 42% of h is equivalent to 84% of j, and j is equivalent to 64% of k. What percentage of k is h? (Disregard the % sign when entering your answer. For example, if your answer is 39%, enter 39)

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Chapter 33 · 2025.9 : B-C (analysis included) · MATH2

$\frac {1} {58}{x}^{2}+(s-\frac {1} {58}t)x-st=0$

In the given equation, s and t are positive constants. The product of the solutions to the given equation is −2kst, where k is a constant. What is the value of k?

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Chapter 33 · 2025.9 : B-C (analysis included) · MATH2

In triangle RST, angle T is a right angle, point L lies on RS, point K lies on ST, and LK is parallel to RT. If the length of RT is 72 units, the length of LK is 24 units, and the area of triangle RST is 468 square units, what is the length of KT, in units?

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