1
In triangle PQR, the measure of ∠P is 47°, and the measure of ∠Q is 83°. What is the measure of ∠R?
- A36°
- B50°
- C94°
- D130°
B
2023.12 D
Math · 44 questions Go to Reading and Writing
Module 1 (Medium)
2
The table summarizes members of a local organization by age and whether they live north or south of Center St. If a member of the organization is selected at random, what is the probability that the selected member is at least 45 years old?
- A32/135
- B35/135
- C100/135
- D103/135
D
3
The function f is defined by f(x)=2x^2-5x . What is the value of f (7)?
63
4
Line q in the xy-plane has a slope of -2 and passes through the point (0, 12). Which equation defines line q?
- Ay=-2x+12
- By=2x+12
- Cy=12x-2
- Dy=12x+2
A
5
For a 2-week period in a town in Iowa, the lowest recorded temperature was 27 degrees Fahrenheit ( °F) and the highest recorded temperature was 69 °F, Which inequality is true for any recorded temperature t, in °F, in this town for this 2-week period?
- At≥ 96
- Bt≥69
- C27 ≤t ≤69
- Dt ≤ 27
C
6
j/8=k+11m
The given equation relates the distinct positive numbers j, k, and m. Which equation correctly expresses j in terms of k and m?
- Aj=k+8(11m)
- Bj=8(k+11m)
- Cj=8k+11m
- Dj=(k+11m)/8
B
7
A student council group is selling car stickers for a fundraiser. They use the function p(x)= 5x-220 to determine their profit p(x), in dollars, for selling x car stickers. In order to earn a profit of $400, how many car stickers must they sell?
124
The scatterplot shows the relationship between two variables, x and y.
8
Which of the following equations is the most appropriate linear model for the data shown?
- Ay= -6+27x
- By= 6-27x
- Cy= 27+6x
- Dy= 27-6x
D
9
A batch of smoothies consists of 4 cups of milk and 2 bananas and has 1,172 milligrams (mg) of calcium. There is 290 mg of calcium in 1 cup of milk. How much calcium, in mg, is in 1 banana?
- A6
- B12
- C441
- D1,160
A
10
A rectangular region of land is divided into 86 square plots of equal area R, in square units. The length of the region is 21.5 times the width of the region. If the width of the region is sqrt(R)x√R units, what is the value of x?
2
11
f(x)=8,000(0.75)^x
A conservation scientist implemented a program to reduce a certain invasive insect population in an area. The given function estimates this insect species' population x years after 2008, where x ≤ 8. Which of the following is the best interpretation of 8,000 in this context?
- AThe estimated initial insect population for this species and area in 2008
- BThe estimated insect population for this species and area 8 years after 2008
- CThe estimated percent decrease in the insect population for this species and area each year after 2008
- DThe estimated percent decrease in the insect population for this species and area every 8 years after 2008
A
12
Jasmin grows bean pods in her garden, This year, she harvested 490 bean pods and saved 10% of them to plant next year, How many of the harvested bean pods did Jasmin save to plant next year?
- A39
- B49
- C57
- D59
B
13
Which of the following expressions is equivalent to 12x^10-12x^9+48x ?
- Ax(11x^10-11x^9+47x )
- Bx(12^10-12^9+48 )
- C12x(x^10-x^9+4x )
- D12x(x^9-x^8+4 )
D
14
The measure of angle D is 5π/4 radians. What is the value of sin(D)?
- A-(√3)/2
- B-(√2)/2
- C-1/2
- D(√2)/2
B
15
Line k has a slope of 2 and a y-intercept of (0, 18). What is the x-coordinate of the x-intercept of line k?
-9
16
A hemisphere is half of a sphere. If a hemisphere has a radius of 57 inches, which of the following is closest to the volume, in cubic inches, of this hemisphere?
- A6,800
- B27,200
- C290,900
- D387,900
D
17
The function g is defined by g(x)=-x/5+12 . What is the x-intercept of the graph ofy=g(x)+7 in the xy-plane?
- A(-60, 0)
- B(-95, 0)
- C(60, 0)
- D(95, 0)
D
18
An auditorium has seats for 3,000 people. Tickets to attend a show at the auditorium currently cost $8.00. For each $1.00 increase to the ticket price, 100 fewer tickets will be sold. This situation can be modeled by the equation y=-100x^2+2,200x+24,000, where x represents the increase in ticket price, in dollars, and y represents the revenue, in dollars, from ticket sales. If this equation is graphed in the xy-plane, at what value of x is the maximum of the graph?
- A8
- B11
- C22
- D30
B
19
The function f gives the product of a number, x, and a number that is 94 more than x. Which equation defines f ?
- Af(x)=x^2+x+94
- Bf(x)=x^2+94
- Cf(x)=x^2+94x
- Df(x)=x^2+94x+94
C
20
ax +by=95
2ax +6y= 70
In the given system of equations, a and b are constants. The graphs of these equations in the xy-plane intersect at the point (x, 5). What is the value of b?
- A3
- B5
- C6
- D15
D
21
If the perimeter of an equilateral triangle with a height of 23 is a√3 , what is the value of a?
46
22
An object's speed is increasing at a rate of 9.4 meters per second squared. What is this rate, in miles per minute squared, rounded to the nearest tenth? (Use 1 mile = 1,609 meters.)
- A0.4
- B21.0
- C171.2
- D252.1
B
Module 2 (Advanced)
1
The function f is defined by f (x)= 35x + 40. What is the value of f (x) when x = 2?
- A70
- B77
- C110
- D150
C
2
Which expression is equivalent to 80y+ 70y?
- A560y^2
- B560y
- C150y^2
- D150y
D
3
The table shows the amount of time it took a participant in a study to complete each of 5 tasks. What was the mean time, in minutes, for this participant to complete a task?
8
4
w(t)=600-3t
The function w models the volume of water, in milliliters, in a container t seconds after it begins draining from a hole at the bottom, According to the model, what is the predicted volume, in milliliters, draining from the container each second?
- A3
- B200
- C597
- D600
A
5
If 5(x+3)= 25, what is the value of x+ 3?
- A2
- B5
- C17
- D20
B
6
The graph of the polynomial function f in the xy-plane, where y = f(x), has x-intercepts of (-7,0) and (2, 0). Which of the following must be true?
- Af(0)=-7
- Bf(2)=-7
- Cf(-7)=0
- Df(-7)= 2
C
7
y> 9x-5
For which of the following tables are all the values of x and their corresponding values of y solutions to the given inequality?
- A
- B
- C
- D
D
8
When the linear function h is graphed in the xy-plane, where y= h(x), its slope is -2. If h(4)= 3, which equation defines h?
- Ah(x)=-2x+5
- Bh(x)= -2x + 11
- Ch(x)=-2x+3
- Dh(x)= -2x -5
B
9
A linear model estimates the population of a city from 1992 to 2016. The model estimates the population was 56 thousand in 1992, 218 thousand in 2012, and x thousand in 2016. To the nearest whole number, what is the value of x?
250
10
7/3x+4y=23
5/3x+4y=21
The solution to the given system of equations is (x, y). What is the value of
17/3x+12y?
- A3
- B4
- C44
- D65
D
11
1/x+1/(x-7)=2/(x^2-7x)
What are all the solutions to the given equation?
- A-1 and 2
- B0 and 7
- C1
- D9/2
D
12
According to a set of standards, pure biodiesel fuel can contain a maximum of 0.001% phosphorus by mass. If a sample of pure biodiesel fuel has a mass of 310 grams, what is the maximum mass, in grams, of phosphorus the sample can contain to meet these standards?
0.003,.003,.0031
13
A proposal for a construction project was included on a city election ballot, A TV news report stated that 8 times as many people voted in favor of the proposal as people who voted against it. An internet article reported that 31,500 more people voted in favor of the proposal than voted against it, Based on these data, how many people voted against the proposal?
4500
14
x^2+38x+c=0
In the given equation, c is a constant, The equation has no real solutions if c > n. What is the least possible value of n?
- A-361
- B-38
- C38
- D361
D
15
The function f is defined by f(x)=a^x+b , where a and b are constants. In the xy-plane, the graph of y= f(x) has an x-intercept at (2, 0) and a y-intercept at (0, -24). What is the value of b?
-25
16
The area of a triangle is equal to x^2 square centimeters. The length of the base of the triangle is 2x + 16 centimeters, and the height of the triangle is x - 4 centimeters. What is the value of x?
8
17
y=-4x^2-25
y=qx-21
In the given system of equations, q is a positive constant. The graphs of the equations in the given system intersect at exactly one point, (x, y), in the xy-plane. What is the value of x?
- A-46
- B-29
- C-8
- D-1
D
18
y=-1.5
y=x^2+4x+a
In the given system of equations, a is a positive integer constant. The system has no real solutions. What is the least possible value of a?
3
19
46x^2+(46s+r)x+rs=0
In the given equation, r and s are positive constants. The product of the solutions to the given equation is krs, where k is a constant. What is the value of k?
1/46,0.021,0.022,.0217
The table gives the areas and perimeters of two similar rectangles, where n is a constant.
20
What is the value of n?
540
21
The cost of renting a piece of construction equipment for up to 5 days is $390 for the first day and $195 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 ≤ 5?
- Ay=195x+195
- By=195x+390
- Cy=390x-195
- Dy=390x+195
A
22
In the figure, parallel lines a and b are intersected by lines c, d, and e. If z = 59, y = 126, and v < z, which statement about x and w must be true?
- Ax < w
- Bx > w
- Cx = w
- Dx + w = 90
B