2024.10 A

Math · 44 questions Go to Reading and Writing

Module 1 (Medium)

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1

The scatterplot shows 5 measurements of the body length, in centimeters (cm), of a New Zealand fur seal from an age of 1 year to 6 years old. A line of best fit is also shown. For a New Zealand fur seal at an age of 3 years old, what is the body length predicted by the line of best fit, to the nearest 10 cm?

110Problem Solving and Data Analysis / Scatter Plot · Accuracy 93.89%
2

The function f is defined by f(x)=-3x+20. What is the value of f(x) when x=-7 ?

  1. A41
  2. B17
  3. C13
  4. D10
AAlgebra / Linear functions word problem · Accuracy 99.6%
3

A botanist estimates the number of oak trees in a forest to be at least 2,900 and not more than 3,100. Which inequality best represents the number of oak trees, x, in this forest?

  1. Ax≤200
  2. Bx≤2,900
  3. C2,900≤x≤3,100
  4. Dx≤2,900 or x≥3,100
CAlgebra / Linear inequality word problem · Accuracy 99.55%
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4

In the figure shown, line l intersects lines j and k. Which additional piece of information is sufficient to prove that lines j and k are parallel?

  1. Aw=60
  2. Bx=120
  3. Cy=60
  4. Dz=120
AGeometry and Trigonometry / Angles and Arc length · Accuracy 98.06%
5

Which expression is equivalent to 11x^3+2x^2+3x ?

  1. A16(x^3+x^2+x)
  2. Bx(11x^2+2x+3)
  3. C3x(11x^3+2x^2+1)
  4. D11x(x^2+2x+3)
BAdvanced Math / Operations of polynomials · Accuracy 98.16%
6

y=4/7x+5
One of the two equations in a system of linear equations is given. The system has infinitely many solutions. If the second equation in the system is y= mx + b, where m and b are constants, what is the value of b?

  1. A-5
  2. B-1/5
  3. C1/5
  4. D5
DAlgebra / Solving systems of linear equations · Accuracy 97.52%
7

Which expression is equivalent to (4nr^2+2nr)+(3n^2r+7nr)?

  1. A7n^2r^2+9nr
  2. B7n^3r^3+9n^2r^2
  3. C12n^3r^3+14n^2r^2
  4. D4nr^2+3n^2r+9nr
DAdvanced Math / Operations of polynomials · Accuracy 97.42%
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8

What is the slope of the line shown?

7/5,1.4,1.40Algebra / Graphing linear equations · Accuracy 90.04%
9

y=7,800(0.85)^x
The given equation estimates the value, in dollars, of a certain car x years after it was purchased. According to the given equation, what was the estimated value, in dollars, of the car at the time it was purchased?

  1. A780
  2. B6,630
  3. C7,800
  4. D8,500
CAdvanced Math / Exponential word problems · Accuracy 96.76%
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10

Triangle XYZ shown is a right triangle. Which of the following has the same value as sin X?

  1. AcosY
  2. Bcos X Y
  3. CtanY
  4. Dtan X
AGeometry and Trigonometry / Trigonometric functions · Accuracy 96.91%
11

The function f is defined byf(x)=3(1/4-x)^2+5/4. What is the value off(1/4) ?

5/4,1.25,1.250Advanced Math / Quadratic word problems · Accuracy 97.64%
12

A survey was conducted in Arlington to estimate the percent of adult residents who support the addition of a community pool in their town. Based on the survey, it is estimated that 40% of all adult residents of Arlington support the addition of a community pool in their town, with an associated margin of error of 7%. Which of the following is the most appropriate conclusion about all adult residents of Arlington?

  1. APlausible values for the percent of all adult residents of Arlington who support the addition of a community pool in their town are between 33% and 47%.
  2. BThe addition of a community pool in the town is supported by exactly 33% of all adult residents of Arlington.
  3. CPlausible values for the percent of all adult residents of Arlington who support the addition of a community pool in their town are either less than 33% or more than 47%.
  4. DThe addition of a community pool in the town is supported by more than 47% of all adult residents of Arlington.
AProblem Solving and Data Analysis / Spread of distribution · Accuracy 97.54%
13

Line t in the xy-plane has a slope of 1/4 and passes through the point (12,-8). Which equation defines line t?

  1. Ay=-11x+1/4
  2. By=x/4-11
  3. Cy=x/4-8
  4. Dy=12x-8
BAlgebra / Graphing linear equations · Accuracy 97.85%
14

7(x-4)=13+5(x-4)
If x is the solution to the given equation, what is the value of x-4?

13/2,6.5,6.50Algebra / Solve linear equation · Accuracy 94.74%
15

The ratio 12 to x is equivalent to the ratio 168 to y. Which expression represents y in terms of x?

  1. A1/14x
  2. B14x
  3. C1/12x
  4. D12x
BProblem Solving and Data Analysis / Ratios and proportion · Accuracy 93.5%
16

Rectangles ABCD and EFGH are similar. The length of each side of EFGH is 8 times the length of the corresponding side of ABCD. The area of ABCD is 48 square units. What is the area, in square units, of EFGH ?

  1. A6
  2. B64
  3. C384
  4. D3,072
DGeometry and Trigonometry / Congruence and similarity · Accuracy 96.47%
17

1/x+1/(x-9)=10/(x^2-9x)
What are all the solutions to the given equation?

  1. A-1 and10
  2. B0 and9
  3. C5
  4. D19/2
DAdvanced Math / Rational transformation · Accuracy 93.95%
18

Circle A in the xy-plane has the equation (x+3)^2+(y-3)^2=16. Circle B has the same center as circle A. The radius of circle B is two times the radius of circle A. The equation defining circle B in the xy-plane is (x+3)^2+(y-3)^2=k , where k is a constant. What is the value of k?

64Geometry and Trigonometry / Circle equation · Accuracy 92.8%
19

How many centimeters are equivalent to 47 meters?
(1 meter = 100 centimeters)

4700Problem Solving and Data Analysis / Units · Accuracy 98.25%
20

|x-8|=11
What is the sum of the solutions to the given equation?

  1. A0
  2. B16
  3. C19
  4. D22
BAlgebra / Solve linear equation · Accuracy 92.87%
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21

The graph of y=f(x)-k is shown in the xy-plane. If k, a, and b are positive constants, which equation could define f ?

  1. Af(x)=(x-a)^2(x+b)
  2. Bf(x)=(x+a)^2(x-b)
  3. Cf(x)=(x-a)^2(x+b)^2
  4. Df(x)=(x+a)^2(x-b)^2
AAdvanced Math / Nonlinear equation graphs · Accuracy 76.75%
22

The linear function g is defined by g(x)=b-18x, where b is a constant. If g(c+6)=c/5, where c is a constant, which of the following expressions represents the value of b?

  1. A18c+108
  2. B91c/5+108
  3. C23c/5+6
  4. D18c/5
BAlgebra / Linear functions word problem · Accuracy 94.5%

Module 2 (Advanced)

1

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)=38-0.22x gives the estimated height, in centimeters (cm), of the water in the glass x days after the start of the experiment. Which of the following is the best interpretation of 38 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 to evaporate
AAlgebra / Interpreting linear equation · Accuracy 99.28%
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2

The roofs on the buildings of a public garden are designed to allow water to drain into the garden. The table shows the relationship between the area x, in square feet, of a roof and the amount of water f(x), in gallons, drained from the roof into the garden over a certain period of time. Which equation could define f?

  1. Af(x)=0.6x
  2. Bf(x)=2.4x
  3. Cf(x)=1,320.0x
  4. Df(x)=2,640.0x
BProblem Solving and Data Analysis / Linear growth · Accuracy 97.88%
3

In 2010, a skating team had a total of 37 skaters, each classified as either advanced or intermediate. From 2010 to 2020, the number of advanced skaters on the team increased by approximately 23%, and the number of intermediate skaters on the team increased by approximately 33%. The total number of skaters on the team increased by approximately 27%. Which equation best represents this situation, where a represents the number of advanced skaters on the team in 2010 and b represents the number of intermediate skaters on the team in 2010?

  1. A1.23a+1.27b=37(1.33)
  2. B1.27a+0.23b=37(1.33)
  3. C1.23a+1.33b=37(1.27)
  4. D1.33a+1.23b=37(1.27)
CAlgebra / Linear equation word problem · Accuracy 96.45%
4

b-65=x/y
The given equation relates the positive numbers b, x, and y. Which equation correctly expresses x in terms of b and y?

  1. Ax=(by-65)/y
  2. Bx=by-65
  3. Cx=by-65y
  4. Dx=(b-65)/y
CAdvanced Math / Isolating quantities · Accuracy 95.15%
5

The function f is defined by f(x)=3x^2. What is the value of f(7)?

  1. A21
  2. B27
  3. C42
  4. D147
DAdvanced Math / Quadratic word problems · Accuracy 99.1%
6

y=6x+17
-7x-y=35
What is the solution (x, y) to the given system of equations?

  1. A(-4,-7)
  2. B(-18/13,-72/13)
  3. C(4,41)
  4. D(18,125)
AAlgebra / Solving systems of linear equations · Accuracy 93.52%
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7

The histograms summarize the distributions of scores for team A and team B. Which statement best compares the standard deviations of scores for these teams?

  1. AThe standard deviation of scores for team A is less than the standard deviation of scores for team B.
  2. BThe standard deviation of scores for team A is greater than the standard deviation of scores for team B.
  3. CThe standard deviation of scores for team A is equal to the standard deviation of scores for team B.
  4. DThere is not enough information to compare the standard deviations.
AProblem Solving and Data Analysis / Spread of distribution · Accuracy 87.44%
8

x^2-5x-36=0
What is the sum of the solutions to the given equation?

5Advanced Math / Transform of quadratic expressions · Accuracy 95.61%
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9

The graph of y=f(x) is shown, where f(x)=ab^x+c , and a, b, and c are constants. For how many values of x does f(x)=0?

  1. AThree
  2. BTwo
  3. COne
  4. DZero
DAdvanced Math / Nonlinear equation graphs · Accuracy 79.04%
10

To study fluctuations in leaf water potential, samples of wood were taken from 25 trees and cut in the shape of a cube. The length of the edge of one of these cubes is 3.000 centimeters. This cube has a density of 0.210 grams per cubic centimeter. What is the mass of this cube, in grams?

5.67,5.670Geometry and Trigonometry / Volume · Accuracy 83.62%
11

Function f is a quadratic function where f(-21)=0 and f(-5)=0. The graph of y=f(x) in the xy-plane has a vertex at (r,-64). What is the value of r?

-13Advanced Math / Transform of quadratic expressions · Accuracy 90.77%
12

The function f gives the product of a number, x, and a number that is 77 more than x. Which equation defines f?

  1. Af(x)=x^2+x+77
  2. Bf(x)=x^2+77
  3. Cf(x)=x^2+77x
  4. Df(x)=x^2+77x+77
CAdvanced Math / Quadratic word problems · Accuracy 91.62%
13

-25x^2-10x+c=0
In the given equation, c is a constant. The equation has exactly one solution. What is the value of c?

  1. A-3
  2. B-1
  3. C0
  4. D1
BAdvanced Math / Transform of quadratic expressions · Accuracy 91.72%
14

The positive number a is 2,024% of the sum of the positive numbers b and c, and b is 88% of c. What percent of b is a?

  1. A4,324%
  2. B2,112%
  3. C43.24%
  4. D21.12%
AProblem Solving and Data Analysis / Percents · Accuracy 79.62%
15

The functions f and g are defined by the given equations below, where x≥0. Which of the following equations displays, as a constant or coefficient, the minimum value of the function it defines, wherex≥0?
Ⅰ.f(x)=14(1.3)^(x+5)
Ⅱ.f(x)=14(1.09)(1.3)^x+3g(x)=14(1.09)(1.3)^(x+3)

  1. AⅠ only
  2. BⅡ only
  3. CⅠ and Ⅱ
  4. DNeither Ⅰ nor Ⅱ
  5. AⅠ only
  6. BⅡ only
  7. CⅠ and Ⅱ
  8. DNeither Ⅰ nor Ⅱ
DAdvanced Math / Exponential word problems · Accuracy 69.07%
16

(12x+16)/4-s/13=r(x-9)
In the given equation, s and r are constants, and s>0. If the equation has infinitely many solutions, what is the value of s?

403Algebra / Solve linear equation · Accuracy 71.87%
17

The perimeter of an isosceles right triangle is 28+28√2 inches. What is the length, in inches, of the hypotenuse of this triangle?

  1. A14
  2. B14√2
  3. C28
  4. D28√2
CGeometry and Trigonometry / General triangle · Accuracy 70.01%
18

A right triangular pyramid has exactly six edges. Each of these edges is 74 centimeters long. If the surface area of the pyramid is k√3 square centimeters, what is the value of k?

5476Geometry and Trigonometry / Volume · Accuracy 65.33%
19

In right triangle RST, the sum of the measures of angle R and angle S is 90 degrees. The value of sin(R) is (3√17)/13. What is the value of cos(S)?

  1. A(4√17)/51
  2. B(3√17)/13
  3. C(13√17)/51
  4. D(3√17)/4
BGeometry and Trigonometry / Trigonometric functions · Accuracy 96.0%
20

The cost of renting a piece of construction equipment for up to 10 days is $230 for the first day and $115 for each additional day. Which of the following equations gives the cost y, in dollars, of renting the equipment for x days, where x is a positive integer and x≤10?

  1. Ay=115x+115
  2. By=115x+230
  3. Cy=230x-115
  4. Dy=230x+115
AAlgebra / Linear functions word problem · Accuracy 86.67%
21

A line intersects two parallel lines, forming four acute angles and four obtuse angles. The measure of one of these eight angles is (9x-310)°. The sum of the measures of four of the eight angles is k°. Which of the following could NOT be equivalent to k, for all values of x?

  1. A360
  2. B-36x+1,960
  3. C18x-440
  4. D-18x+1,780
DGeometry and Trigonometry / Angles and Arc length · Accuracy 59.69%
22

8x+7y=3
40x+35y=15
For each real number r, which of the following points lies on the graph of each equation in the xy-plane for the given system?

  1. A(r/5+3,-r/5+15)
  2. B(-7r/8+3/8,r)
  3. C(r,8r/7+3/7)
  4. D(r,-7r/8+3/8)
BAlgebra / Solving systems of linear equations · Accuracy 73.39%