1
Which expression is equivalent to6xy(2x^2+5y)xy(2x^2+5y)?
- A8x^3y+11xy^2
- B12x^2y+5y
- C12x^2y+30xy
- D12x^3y+30xy^2
D
2024.6 US A
Math · 44 questions Go to Reading and Writing
Module 1 (Medium)
2
Which expression is equivalent to7x^6-2x^5+9x^4? 7x^6-2x^5+9x^4
- Ax^5(7x-2)
- Bx^4(7x^2-2x+9)
- C9x^4(7x^2-2x+1)
- D2x^6(-2x^5+9x^4+1)
B
3
The height of a certain vehicle is 61 inches. The vehicle's length is 3 times its height. Which of the following systems of equations represents this situation, where x is the length of the vehicle, in inches, and y is the height of the vehicle, in inches?
- Ay=3x
x=61 - By=3x
y=61 - Cx=3y
x=61 - Dx=3y y=61
y=61
D
4
For the linear function f, the graph of y=f(x) in the xy-plane has a slope of -54 andpasses through the point (0,0). Which equation defines f?
- Af(x)=-54x
- Bf(x)=-36x
- Cf(x)=-18x
- Df(x)=x
A
5
The function g is defined by g(x)=5/9x-7/9. What is the value of g(18)?
- A38/9
- B52/9
- C83/9
- D97/9
C
6
The function f is defined by f(x)=x^2+x+61 . What is the value of f(2)f(2) ?
67
7
f(x)=5x+7
The function f gives the estimated height, in feet, of a poplar tree x years after its height was first measured. Which statement is the best interpretation of 77 in this context?
- AThe tree will be measured each year for 7 years.
- BThe tree is estimated to grow to a maximum height of 7 feet.
- CThe estimated height of the tree increased by 7 feet each year.
- DThe estimated height of the tree was 7 feet when it was first measured.
D
8
In the xy-plane, line k has a slope of 5 and a y-intercept of (0,-35). What is the x-coordinate of the x-intercept of line k?
7
9
(27(k+6))/(3(k+6))
The given expression is equivalent to c, where c is a constant and k>-6 . What is the value of c?
9
The table gives the perimeters of similar trianglesTUV and XYZ , where TU corresponds to XY . The length of TU is 6.
10
What is the length of XY ?
- A2
- B6
- C18
- D56
C
11
If 9(7-8x)+2=8(7-8x)+17 , what is the value of 7-8x ?
- A-15
- B-1
- C1
- D15
D
12
x+33=y
(x+33)^2=y
A solution to the given system of equations is (x, y). What is a possible value of x?
- A-32
- B0
- C1
- D33
A
13
A circle in the xy-plane has the equation(x-14)^2+(y-k)^2=36. Which of the following gives the center of the circle and its radius?
- AThe center is at (14, k) and the radius is 6.
- BThe center is at (k, 14) and the radius is 6.
- CThe center is at (k, 14) and the radius is 36.
- DThe center is at (14, k) and the radius is 36.
A
14
The town of Fillmore is planning its annual fireworks show. The equation y=-16(x-6.8)^2+740 gives the estimated height y, in feet, of a type of firework x seconds after it is launched into the air. Which of the following is the best interpretation of the vertex of the graph of the equation in the xy-plane?
- AThis type of firework reaches an estimated maximum height of 740 feet 16 seconds after it is launched into the air.
- BThis type of firework reaches an estimated maximum height of 740 feet 6.8 seconds after it is launched into the air.
- CThis type of firework reaches an estimated maximum height of 16 feet 740 seconds after it is launched into the air.
- DThis type of firework reaches an estimated maximum height of 6.8 feet 740 seconds after it is launched into the air.
B
15
The graph of y=f(x) is shown where f(x)=ax^3+bx^2+cx+d and a, b, c, and d are constants. For how many distinct values of x does f(x)=0 ?
- AOne
- BTwo
- CThree
- DFour
B
16
In the xy-plane, circle M is the graph of the equation (x-3)^2+(y-6)^2=4 . Circle P has the same center as circle M but has a radius that is twice the radius of circle M. Which equation represents circle P?
- A(x-3)^2+(y-6)^2=8
- B(x-3)^2+(y-6)^2=16
- C(x-6)^2+(y-12)^2=4
- D(x-6)^2+(y-12)^2=8
B
17
Which expression represents the length of line segment AB?
- A14sin58°
- B14/(sin 58°)
- C14cos58°
- D14/(cos 58°)
A
18
The product of a positive number x and the number that is 15 less than x is equal to 286. What is the value of x ?
26
19
In the figure, AC = CD. The measure of angle EBC is 29°, and the measure of angle ACD is 108°. What is the value of x?
65
20
The positive number a is 2,800% of the number c, and c is 25% of the number b. If a-b=wc , where w is a constant, what is the value of w?
24
21
Line j is defined by 4x+5y=55. Line k is parallel to line j in the xy-plane. An equation of line k is 24x+ry=15 , where r is a constant. If line k passes through the point (0,b) , what is the value of b?
1/2,0.5
22
The dot plot shows the distribution of capacity for a set of capacitors, set A, which a researcher used for a certain experiment. For another experiment, the researcher used a different set of capacitors, set B. Set B has the same number of capacitors as set A but the capacity of each capacitor of set B is 17 microfarads (μF) greater than the capacity of each respective capacitor in set A. Which of the following is true about the capacities of the capacitors in set B?
- AThe mean capacity is 8 μF, and the range of capacities is 12 μF.
- BThe mean capacity is 8 μF, and the range of capacities is 29 μF.
- CThe mean capacity is 25 μF, and the range of capacities is 12 μF.
- DThe mean capacity is 25 μF, and the range of capacities is 29 μF.
C
Module 2 (Advanced)
The bar graph shows the distribution of flower type for the 700 flowers that a florist has in stock.
1
For which two types of flowers is the total number of flowers of the two types exactly 2/5 of the florist's stock?
- ADaisy and orchid
- BOrchid and lily
- COrchid and sunflower
- DLily and sunflower
B
2
The scatterplot shows the relationship between two variables, x and y, for data set A. A line of best fit for the data is also shown. Data set B is created by subtracting 11 units from the value of y for each data point from data set A. Which of the following is closest to the y-coordinate of the y-intercept of the line of best fit for data set B?
- A62.75
- B53.75
- C42.75
- D31.75
C
3
If 4(2x+11)-2(2x-5)=-9+13x , what is the value of 12x ?
- A7/12
- B7
- C12
- D84
D
4
An object has a mass of 308 grams and a volume of 28 cubic centimeters. What is the density, in grams per cubic centimeter, of the object?
- A11
- B280
- C336
- D8,624
A
5
In the xy-plane, which of the following does NOT contain any points that are part of the solution set to 3x-7y>21 ?
- AThe region where x<0 and y>0
- BThe region wherex<0 and y<0
- CThe region where x>0 and y>0
- DThe x-axis
A
6
Which equation defines the linear function f ?
- Af(x)=-14x-9
- Bf(x)=-5x-1
- Cf(x)=-5x+8
- Df(x)=-14x+8
B
7
In triangle FGHand triangle KLM , the measures of angles GG and LL are each 30°. The lengths of GH and LM are each 34 centimeters, andGH/GF=LM/LK. Which additional piece of information would be necessary to prove that triangle FGH is congruent to triangle KLM ?
- AThe lengths of FG and KM are each 17 centimeters.
- BThe measures of angles HMH andM M are each 60°.
- CThe measures of angles F and K are each 90°.
- DNo additional information is necessary.
D
8
y=3x+9
3y=8x-6
The solution to the given system of equations is (x, y). What is the value of x-y ?
- A-123
- B33-33
- C3
- D57
D
9
An exponential function f is defined by f(x)=c^x, where c is a constant greater than 1. If f(6)=9·f(4), what is the value of c ?
3
10
In the right triangle shown, what is the value of sin x°?
- A1/73
- B10/73
- C63/73
- D136/73
C
11
-x-wy=-337
2x-wy=47
In the given system of equations, w is a constant. In the xy-plane, the graphs of these equations intersect at the point (q, 19), where q is a constant. What is the value of w?
11
12
The table shows the distribution of two types of trees at two different sites. If a tree represented in the table is selected at random, what is the probability of selecting tree from site A, given that the tree is a red maple? (Express your answer as a decimal or fraction, not as a percent.)
0.7,7/10,35/50
13
A beaker containing a liquid is placed on a table. The function g(t)=295+(361-295)(2.72)^(-0.104t) gives the approximate temperature, in kelvins, of the liquid t minutes after the beaker was placed on the table. According to this function, what was the approximate temperature, in kelvins, of the liquid when the beaker was placed on the table?
361
14
For the exponential function f, the value of f (1) is k, where k is a constant. Which of the following equivalent forms of the function f shows the value of k as the coefficient or the base?
- Af(x)=50(1.7)^(x+1)
- Bf(x)=85(1.7)^x
- Cf(x)=144.5(1.7)^(x-1)
- Df(x)=245.65(1.7)^(x-2)
C
15
y=9(a/6)^(x+c)-b
How many times does the graph of the given equation in the xy-plane cross the x-axis, where a, b, and c are positive constants such that a>6 andb>c ?
- AZero
- BOne
- CTwo
- DThree
B
16
For a polynomial function f , the graph of y=f(x) in the xy-plane contains the points(-6,0), (7,0 ), (0,0 ), and (4,0 ). Which of the following must be a factor of f(x) ?
- Ax^2-2x-24
- Bx^2-x+42
- Cx^2-11x-28
- Dx^2-7x
D
17
In the given figure, NP is the diameter of semicircle O. Angles Q, R, and S are right angles, and point P is the midpoint of NQ . If PQ = 52 feet and NS = 18 feet, the area of the figure can be expressed as aπ+b square feet, where a and b are integers. What is the value of a-b ?
-1534
18
1/5xy+xyz=1/4yz
In the given equation, x, y, and z are positive numbers. Which expression is equivalent to y?
- A(5x-4z)/(20x^2z^2)
- B√(5x-4z)/(20x^2z^2)
- C1/(4xz^2-5x^2-z)
- D√1/(4xz^2-5x^2-z)
B
19
The equation 2|x-5|=k,where k is a constant, has exactly one solution. Which of the following could be the value ofk/2 ?
- A-5 only
- B-5 or 5
- C0 only
- D5 only
C
20
The percent increase in mass of a certain red kangaroo from 80 days old to 160 days old was 676%. If this red kangaroo's mass was k grams at 80 days old, which expression represents its mass, in grams, at 160 days old?
- A7.76k
- B6.76k
- C1.08k
- D0.08k
A
21
The table shows three values of x and their corresponding values of g(x), where g(x)=(f(x))/(x+3) and f is a linear function. What is the y-intercept of the graph of y=f(x) in the xy-plane?
- A(0,-9)
- B(0,3)
- C(0,9)
- D(0,27)
D
22
For groups of 25 or more people, a museum charges $28 per person for the first 25 people and $17 for each additional person. Which function f gives the total charge, in dollars, for a tour group with n people, where n≥25 ?
- Af(n)=17n+275
- Bf(n)=17n+28
- Cf(n)=17n+700
- Df(n)=45n-425
A