2024.8 B

Math · 44 questions Go to Reading and Writing

Module 1 (Medium)

1

9x-8x+120=240
What value of x is the solution to the given equation?

120Algebra / Solve linear equation
2

A company studied a random sample of 70 lawns in a small town. The company found that 10 of these lawns contain acidic soil. If there are 910 lawns in the town, which of the following is the best estimate of the number of lawns that contain acidic soil?

  1. A7
  2. B8
  3. C13
  4. D130
DProblem Solving and Data Analysis / Data inferencing
3

f(x)=10x+9
The function gives the total number of people on a city tour with x tour guides. What is the total number of people on a city tour with 10 tour guides?

109Algebra / Linear functions word problem
4

A total of 263 toothpicks of equal length were used to construct two types of figures: triangles and squares. The triangles and squares were constructed so that no two figures had a common side. The equation 3x+4y=263 represents this situation, where x is the number of triangles constructed and y is the number of squares constructed. What is the best interpretation of (x,y)=(21,50)in this context?

  1. AIf 21 triangles were constructed, then 50 squares were constructed.
  2. BIf 21 triangles were constructed, then 50 toothpicks were used.
  3. CIf 50 triangles were constructed, then 21 toothpicks were used.
  4. DIf 50 triangles were constructed, then 21 squares were constructed.
AAlgebra / Interpreting linear equation
5

The function k is defined by k(x)=x^3+600. What is the value of k(x)when x=2?

  1. A600
  2. B605
  3. C606
  4. D608
DAdvanced Math / Function notations and transforms
6

Each side of square A has a length of 34 inches. Each side of square A is multiplied by a scale factor of 2 to create square B. What is the length, in inches, of each side of square B?

  1. A32
  2. B34
  3. C36
  4. D68
DGeometry and Trigonometry / Congruence and similarity
7

f(x)=-8x^2+118x
The function f models the depth below sea level, in meters, of a certain seal x minutes after the seal dives into the water. What is the best interpretation of f(2)=204 in this context?

  1. A2 minutes after the seal dives into the water, its estimated depth is 204 meters below sea level.
  2. BApproximately 2 minutes after diving into the water, the seal returns to sea level.
  3. CThe seal reaches an estimated maximum depth of 204 meters below sea level.
  4. D204 minutes after the seal dives into the water, its estimated depth is 2 meters below sea level.
AAdvanced Math / Interpreting nonlinear expressions

The scatterplot shows the relationship between two variables, x and y. A line of best fit is also shown.

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8

Which of the following equations best represents the line of best fit shown?

  1. Ay=x-19.9
  2. By=-x+19.9
  3. Cy=-x+5.7
  4. Dy=x-5.7
CProblem Solving and Data Analysis / Scatter Plot
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9

For the function h, the table gives three values of x and their corresponding values of h(x). Which equation could define h?

  1. Ah(x)=2^x+18
  2. Bh(x)=2^x+17
  3. Ch(x)=2^x+2
  4. Dh(x)=2^x
AAdvanced Math / Exponential word problems
10

As part of a science experiment on evaporation, Ella measured the height of water in a glass over a period of time. The function f(x)=39-0.17x gives the estimated height, in centimeters (cm), of the water in the glass x days after the start of the experiment. What is the best interpretation of 0.17 in this context?

  1. AThe estimated height, in cm, of the water at the start of the experiment
  2. BThe estimated height, in cm, of the water at the end of the experiment
  3. CThe estimated change in the height, in cm, of the water each day
  4. DThe estimated number of days for all the water in the glass to evaporate
CAlgebra / Interpreting linear equation
11

If 4(x+3)=3(x+3)+59, what is the value of x+3?

  1. A-3
  2. B56
  3. C59
  4. D62
CAlgebra / Solve linear equation
12

For the linear function h, h(0) = 0 and h(5) = 3. Which equation defines h?

  1. Ah(x)=5/3x
  2. Bh(x)=5/3x+5
  3. Ch(x)=3/5x
  4. Dh(x)=3/5x+3
CAlgebra / Linear functions word problem
13

The product of a positive number x and the number that is 7 more than x is 18. What is the value of x?

  1. A1
  2. B2
  3. C9
  4. D18
BAdvanced Math / Quadratic word problems
14

The measure of angle B is 7π/4 radians. What is the value of cos(B)?

  1. A-(√2)/2
  2. B-1/2
  3. C(√2)/2
  4. D(√3)/2
CGeometry and Trigonometry / Trigonometric functions
15

A model estimates that a gray whale travels 74 to 79 miles each day during its migration. Based on this model, which inequality represents the estimated total number of miles, x, a gray whale could travel in 49 days of its migration?

  1. A(74)(49)≤x≤(79)(49)
  2. B74+49≤x≤79+49
  3. C74≤49x≤79
  4. D74≤49+x≤79
AAlgebra / Linear inequality word problem
16

-3x+6rx=42
In the given equation, r is a constant. The equation has no solution. What is the value of r?

  1. A1/7
  2. B1/2
  3. C2
  4. D7
BAlgebra / Solve linear equation

The table summarizes the number of objects in each group.

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17

The number of objects in group C is p% of the number of objects in group A. What is the value of p?

176Problem Solving and Data Analysis / Percents
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18

The graph of a system of two linear equations is shown. If a third equation, x+2y=-8, is added to this system, how many solutions will the resulting system of three equations have?

  1. AZero
  2. BExactly one
  3. CExactly two
  4. DInfinitely many
AAlgebra / Solving systems of linear equations
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19

Data set A and data set B each consist of 33 values. The table shows the frequencies of the values for each data set. Which of the following statements best compares the means of the two data sets?

  1. AThe mean of data set A is greater than the mean of data set B
  2. BThe mean of data set A is less than the mean of data set B.
  3. CThe mean of data set A is equal to the mean of data set B.
  4. DThere is not enough information to compare the means of the data sets.
AProblem Solving and Data Analysis / Mean, mode, median
20

The function g is defined as g(x)=(2x-6)/(x+13)(x-8) . If g(a+7)=0, where a is a constant, what is the value of a?

-4Advanced Math / Rational transformation
21

｜x-7｜=-｜x-7｜+16
What is the sum of the solutions to the given equation?

14Algebra / Solve linear equation
22

The floor of a library has an area of 4,375 square feet. An architect creates a scale model of the floor of the library, where the length of each side of the model is 1/25times the length of the corresponding side of the floor of the actual library. What is the area, in square feet, of the scale model?

7Geometry and Trigonometry / Congruence and similarity

Module 2 (Advanced)

1

The water depth in a certain river is 77.9 feet (ft). During a 30-day period, the water depth in this river is predicted to increase by a minimum of 1 ft and a maximum of 4 ft. What is the predicted maximum water depth, in feet, during this time?

  1. A73.9
  2. B76.9
  3. C78.9
  4. D81.9
DAlgebra / Linear inequality word problem
2

4(y-19)+11=3(y-19)+11
What value of y is the solution to the given equation?

  1. A0
  2. B1
  3. C11
  4. D19
DAlgebra / Solve linear equation
3

If f(x)=x+5 and g(x)=5x, what is the value of 2f(3)-g(3)?

1Algebra / Linear functions word problem
4

(7y+9)-(5y+3)
The given expression is equivalent to by+c, where b and c are constants. What is the value of b?

2Algebra / Linear equation word problem
5

What is the slope of the graph of y=1/3(23x+19)+5x in the xy-plane?

  1. A23/3
  2. B38/3
  3. C23
  4. D28
BAlgebra / Graphing linear equations
6

Which expression is equivalent to 10√x^9y^9 , where x and y are positive?sqrt[10]x^9y^9

  1. A(xy)^(10/9)
  2. B(xy)^(9/10)
  3. C(xy)^19
  4. D(xy)^90
BAdvanced Math / Radical and rational exponent problems
7

In 7 days, a polar bear ate 31.5 pounds of fat. Which equation describes the amount of fat y, in pounds, the polar bear ate in these 7 days?

  1. Ay=7
  2. By=31.5/7
  3. Cy=31.5
  4. Dy=31.5+7
CAlgebra / Linear equation word problem
8

If (x+3)^2=24, what is the value of x^2+6x ?

15Advanced Math / Transform of quadratic expressions
9

In the xy-plane, line s passes through the point (0, 0) and is parallel to the line represented by the equationy=16x+2. If line s also passes through the point (4, d), what is the value of d?

  1. A2
  2. B16
  3. C64
  4. D66
CAlgebra / Graphing linear equations
10

In triangle FGH and triangle KLM, the measures of angles G and L are each 60°. The lengths of GH and LM are each 52 centimeters, and GH/GF=LM/LK. Which additional piece of information would be necessary to prove that triangle FGH is congruent to triangle KLM?

  1. AThe measures of angles H and M are each 30°.
  2. BThe measures of angles F and K are each 90°.
  3. CThe lengths of FG and KM are each 26 centimeters.
  4. DNo additional information is necessary.
DGeometry and Trigonometry / Congruence and similarity
11

For x>0 , the function f is defined as follows:
f(x)equals 300% of x
Which of the following could describe this function?

  1. ADecreasing exponential
  2. BDecreasing linear
  3. CIncreasing exponential
  4. DIncreasing linear
DProblem Solving and Data Analysis / Linear growth
12

A machine launches a baseball from ground level. The baseball reaches a maximum height of 134.56 meters above the ground at 2.9 seconds and hits the ground at 5.8 seconds. Which equation represents the height above ground h, in meters, of the baseball t seconds after it is launched?

  1. Ah=-t^2+5.8
  2. Bh=-t^2+134.56
  3. Ch=-16(t-2.9)^2-5.8
  4. Dh=-16(t-2.9)^2+134.56
DAdvanced Math / Quadratic word problems
13

f(x)=336(2)^x
The function f is defined by the given equation. If g(x)=f(x-4) , which of the following equations defines the function g?

  1. Ag(x)=21(2)^x
  2. Bg(x)=84(2)^x
  3. Cg(x)=336(16)^x
  4. Dg(x)=336(8)^x
AAdvanced Math / Function notations and transforms
14

(x-17)/6+(y+28)/3=-5
(x-17)/3-(y+28)/6=5
The solution to the given system of equations is (x,y). What is the value of x-y ?

69Algebra / Solving systems of linear equations
15

A rectangular region of land is divided into 40 square lots of equal area R, in square units. The length of the region is 1.6 times the width of the region. If the width of the region is x√R units, what is the value of x?

5Geometry and Trigonometry / General polygons
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16

The graph of y=f(x)+4 is shown. Which equation defines the function f ?

  1. Af(x)=5^x
  2. Bf(x)=3^x
  3. Cf(x)=5^x+4
  4. Df(x)=3^x+5
BAdvanced Math / Nonlinear equation graphs
17

A raised garden is in the shape of a right rectangular prism. Its base has a width of 3 feet and a length of 27 feet, and it will be filled 24 inches high with topsoil. The total cost of the topsoil needed to fill the garden to this height is 288 dollars. What is the unit cost, in dollars per cubic yard, for the topsoil? (1 yard = 3 feet; 1 foot = 12 inches)

48Problem Solving and Data Analysis / Units
18

The result of increasing the quantity x by 800% is 504. What is the value of x?

  1. A56
  2. B63
  3. C296
  4. D4,032
AProblem Solving and Data Analysis / Percents
19

32/p=32/q-32/r-32/s
The given equation relates the positive variables p, q, r, and s. Which of the following is equivalent to q?

  1. Ap+r+s
  2. B32(p+r+s)
  3. Cprs/(pr+ps+rs)
  4. Dprs/(32p+32r+32s)
CAdvanced Math / Isolating quantities
20

The perimeter of an equilateral triangle is 750 centimeters. The three vertices of the triangle lie on a circle. The radius of the circle is w√3 centimeters. What is the value of w?

250/3,83.33Geometry and Trigonometry / Circle theorems
21

f(x)=4(x-a)(x-b)(x-c)
The function f is defined by the given equation, where a, b, and c are distinct constants. Whena<x<b, the value of f(x) is positive. The graph of y=f(x) in the xy-plane contains the point (r,s), where r and s are constants. If s=3, which of the following could be true?
Ⅰ.r<a
Ⅱ.b<r<c
Ⅲ.r>c

  1. AⅠ only
  2. BⅢ only
  3. CⅠ and Ⅲ only
  4. DⅡ and Ⅲ only
  5. AⅠ only
  6. BⅢ only
  7. CⅠ and Ⅲ only
  8. DⅡ and Ⅲ only
BAdvanced Math / Polynomial factors and graphs
22

A right square pyramid has a total surface area of 56,784 square inches, and the combined surface area of the four lateral faces of this pyramid is 28,560 square inches. What is the height, in inches, of this pyramid?

  1. A13
  2. B84
  3. C85
  4. D168
AGeometry and Trigonometry / Volume