1
Which expression is equivalent to (9y+12x)+(7y-4x)?
- A2y+8x
- B2y+16x
- C16y+8x
- D16y+16x 2y+8x
C
2024.10 US A
Math · 44 questions Go to Reading and Writing
Module 1 (Medium)
2
A line in the xy-plane has a slope of-1/6 and passes through the point ( 0, 19 ) . Which equation represents this line?
- Ay=-1/6x-19
- By=-1/6x+19
- Cy=1/6x-19
- Dy=1/6x+19
B
3
A certain dove species can fly at an average speed of 16 meters per second when in continuous flight. At this rate, how many meters would this dove species fly in 3 seconds?
- A48
- B19
- C16
- D13
A
Each of 181 flowers can be classified as one of three colors, as shown in the frequency table.
4
If one of the flowers is selected at random, what is the probability of selecting a flower of color Y?
- A8/181
- B70/181
- C103/181
- D173/181
A
5
If 6x = 5 , what is the value of 24x ?
- A10/3
- B4
- C20
- D120
C
6
Which expression is equivalent to 49x2+ 49 ?
- A49(x^2+1)
- B49(x^2+49)
- C49(49x^2+1)
- D49(x^2+1/49)
A
7
A sample was selected at random from a population. Based on the sample, it is estimated that the mean value of a variable for this population is 88, with an associated margin of error of 1.5. Based on the estimate and associated margin of error, which of the following best describes the range of plausible values for the population mean?
- AAny value between 85 and 88
- BAny value between 86.5 and 89.5
- CAny value less than 86.5
- DAny value greater than 89.5
B
8
In triangle J K L, the measures of ∠K and ∠L are each 32°. What is the measure of ∠ J, in degrees? (Disregard the degree symbol when entering your answer.)
116
9
A point is plotted on the x-axis of the xy-plane at (20, 0). The point is then moved 5 units to the right a certain number of times until it is at (40, 0). How many times is the point moved to the right?
- A4
- B8
- C20
- D40
A
10
f(x)=x^5+6x+11
For the given function f , the graph of y=f(x) in the xy-plane passes through the point (0, b), where b is a constant. What is the value of b?
11
11
The equation 7p + 7w = 420 represents the number of purple tiles, p, and the number of white tiles, w, a designer needs to cover a 420-square-inch section of a wall. The designer needs 32 purple tiles for the wall. How many white tiles does she need?
28
12
For the linear function f , the graph of y = f (x) in the xy-plane has a slope of 42 and passes through the point ( 0, 0 ). The function f is defined by f (x) = ax , where a is a constant. What is the value of a?
42
13
g(x)=5(x^2-14x+49)+k
The function g is defined by the given equation, where k is a constant. For what value of x does g(x) reach its minimum?
- A49
- B7
- C-7
- D-49
B
14
What is the x-intercept of a line in the xy-plane that has a slope of-8/5 and passes through the point (0, 16) ?
- A(10,0)
- B(5,0)
- C(-8,0)
- D(-10,0)
A
15
A sample of a certain isotope takes 29 years to decay to half its original mass. The functions(t)=208(0.5)^(t/29) gives the approximate mass of this isotope, in grams, that remains t years after a 208-gram sample starts to decay. Which statement is the best interpretation of s(87)=26 in this context?
- AApproximately 26 grams of the sample remains 87 years after the sample starts to decay.
- BThe mass of the sample has decreased by approximately 26 grams 87 years after the sample starts to decay.
- CThe mass of the sample has decreased by approximately 87 grams 26 years after the sample starts to decay.
- DApproximately 87 grams of the sample remains 26 years after the sample starts to decay.
A
The scatterplot shows the relationship between two variables, x and y. A line of best fit is also shown.
16
Which of the following best represents the line of best fit shown?
- Ay=130.12+0.02x
- By=130.12+0.4x
- Cy=130.12+30.04x
- Dy=130.12+40.04x
D
17
If (1/2x-33/2)^2-49=0, what is the value of (x-33)^2 ?
- A196
- B98
- C33
- D7
A
18
P(t)=260(1.03)(6/4)^tP(t)=260(1.03)^((6/4)t)
The function P models the population, in thousands, of a certain city t years after 2001. According to the model, the population is predicted to increase by n % every 8 months. What is the value of n?
- A0.22
- B1.03
- C2
- D3
D
19
In △ ABC , ∠ B is a right angle and the length of BC is 236 millimeters. If cos A=3/5, what is the length, in millimeters, ofoverrightarrowAB AB ?
- A59
- B177
- C236
- D295
B
20
(x-3)^2+(y-9)^2=6
In the xy-plane, the graph of the given equation is a circle. Which point lies on this circle?
- A(-3,-9)
- B(-3-√3,-9-√3)
- C(3,9)
- D(3-√3,9-√3)
D
21
The function f is defined by f(x)=a^x+b, where a and b are constants and a > 0. In the xy-plane, the graph of y=f(x) has a y-intercept at (0,-28) and passes through the point (2, 35). What is the value of a + b?
-21
22
7x-2y=2y+5
hy=4+7x
In the given system of equations, h is a constant. If the system has no solution, what is the value of h?
4
Module 2 (Advanced)
1
The function g is defined by g(x)=-9x+70 . What is the value of g(x) whenx=-3?
- A67/9
- B43
- C58
- D97
D
2
A certain blue whale calf weighed 5,200 pounds when it was born, and its weight increased at an average rate of 250 pounds per day for the first n days after birth, where n is an integer. If the calf's weight was greater than 8,700 pounds but less than 9,700 pounds n days after birth, what is one possible value of n?
15,16,17
3
2x(x-4)(x+9)=0
What is one of the solutions to the given equation?
- A-4
- B0
- C2
- D9
B
4
y=x/3+8
y=-x/3+50
The solution to the given system of equations is (x, y). What is the value of 2y?
- A58
- B50
- C42
- D8
A
5
A hemisphere is half of a sphere. If a hemisphere has a radius of 59 inches, which of the following is closest to the volume, in cubic inches, of this hemisphere?
- A7,300
- B29,200
- C322,600
- D430,100
D
6
f(x)=18x^2-45x+16
The given equation defines the function f f . For what value of x does f (x) reach its minimum?
- A1.25
- B2.25
- C16
- D45
A
7
An exponential function f is defined byf(x)=c^x, where c is a constant greater than 1. If f (6) = 4 • f (4), what is the value of c?f(x)=c^x
2
8
How many solutions does the equation 11( x + 18) + 7x = 18( x +11) have?
- AExactly one
- BExactly two
- CInfinitely many
- DZero
C
9
A science class studied the feeding behavior of the birds that visited a bird feeder each school day for a period of time. The table summarizes the number of birds the class observed visiting the bird feeder each school day during this period of time. What is the median number of birds the class observed visiting the bird feeder each school day during this period of time?
18
10
H = 2.408L + 23.16
A group of biology students conducted an experiment to study the relationship between a person's femur length and the person's height. The given equation describes the relationship between the length L , in inches, of a student's femur and the student's estimated height H, in inches, for the students in the group. Which of the following is the best interpretation of 2.408 in this context?
- AThe increase in a student's femur length, in inches, for each increase of 1 inch in the student's estimated height
- BThe increase in a student's estimated height, in inches, for each increase of 1 inch in the student's femur length
- CThe increase in a student's femur length, in inches, for each increase of 23.16 inches in the student's estimated height
- DThe estimated height, in inches, of a student whose femur has a length of L inches
B
11
x ( x +11) - 7 = 0
What are the solutions to the given equation?
- Ax=(11±√93)/2
- Bx=(11±√149)/2
- Cx=(-11±√93)/2
- Dx=(-11±√149)/2
D
12
The histogram summarizes a data set of the weights, in pounds, of 14 salmon. If an additional weight of 66 pounds is added to the original data set to create a new data set of 15 weights of salmon, which of the following measures must be greater for the new data set than for the original data set?
I. The median
II. The mean
- AⅠ only
- BⅡ only
- CⅠ and Ⅱ
- DNeither Ⅰ nor Ⅱ
- AⅠ only
- BⅡ only
- CⅠ and Ⅱ
- DNeither Ⅰ nor Ⅱ
B
13
In the figure shown, WZ and overrightarrowWZXY ntersect at point Q, YQ = 36, WQ = 90, WX = 70, and XQ = 120.What is the length of YZ ?
- A28
- B48
- C120
- D175
A
14
A researcher surveyed undergraduate students, graduate students, and postdoctoral students. The number of undergraduate students surveyed was 7,050% of the number of postdoctoral students surveyed and the number of graduate students surveyed was 24% of the number of undergraduate students surveyed. If there were 3,384 graduate students surveyed, what was the sum of the number of undergraduate students and postdoctoral students surveyed?
14300
15
The function q is defined by q(x)=a|x-9|^2-87|x-9|+b , where a and b are constants, and a > b> 87. If q(439) = h and q(-421) = k , where h and k are constants, what is the value of9(-439)^(h-k)+421(9)^(k-h) ?
430
16
Which expression is equivalent to 8xy + 24x2y + 32xy2 ?
- A8xy(1 + 24x + 32y)
- B8xy(1 + 3x + 4y)
- C8xy(24x + 32y)
- D8xy(3x + 4y)
B
17
The graph of the linear function y = f (x) + 13 is shown. If c and d are positive constants, which equation could define f?
- Af(x)=-d-cx
- Bf(x)=d-cx
- Cf(x)=d+cx
- Df(x)=-d+cx
A
18
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, where x ≥ 0?
Ⅰ.f(x)=14(1.4)^(x+5)
Ⅱ.g(x)=14(1.16)(1.4)^(x+3)
- AⅠ only
- BⅡ only
- CⅠ and Ⅱ
- DNeither Ⅰ nor Ⅱ
- AⅠ only
- BⅡ only
- CⅠ and Ⅱ
- DNeither Ⅰ nor Ⅱ
D
19
A set designer is hammering nails along the top edge of a wall with a length of 3x feet, where x is an integer, that will be used to hang garland. The designer hammers the first nail at the left edge of the wall. The designer then hammers an additional nail every 3/10 feet along the entire length of the wall, starting from the first nail and with the last nail being hammered at the right edge of the wall. Which equation best represents this situation, where y is the number of nails the designer hammers along the entire length of the wall?3/10
- Ay=3/10x
- By=3/10x+1
- Cy=10x
- Dy=10x+1
D
20
The perimeter of an isosceles right triangle is94+94√2inches. What is the length, in inches, of the hypotenuse of this triangle?
- A47
- B47√2
- C94
- D94√2
C
21
The table shows three values of x and their corresponding values of g(x), where g(x)=(f(x))/(x+5) and f is a linear function. What is the y-intercept of the graph of y = f (x) in the xy-plane?
- A(0, 35)
- B(0, 7)
- C(0, 5)
- D(0, -7)
A
22
In the figure shown, points A, B, C, and E lie on the circle, and AB < BC . Segment AC is perpendicular to segment BE at point D, and BD =√390 .The diameter of the circle is 197. IfCD/AD=r, what is the value of r ?
195/2,97.5,97.50