Heart of Algebra (No Calculator)
f(x) = 3x/2 + b
In the function above, b is a constant. If f(6) = 7, what is the value of f(-2)?
A. -5
B. -2
C. 1
D. 7
A. -5
Last week Raul worked 11 more hours than Angelica. If they work a combined total of 59 hours, how many hours did Angelica work last week?
24
If a 3-pound pizza is sliced in half and each half is sliced into thirds, what is the weight, in ounces, of each of the slices? (1 pound = 16 ounces)
A. 4
B. 6
C. 8
D. 16
8
If f(x) = -2x+5, what is f(-3x) equal to?
A. -5x-5
B. 6x+5
C. 6x-5
D. 6x2-15x
B. 6x+5
In the xy-plane, the graph of the function f has x-intercepts at -3, -1, and 1. Which of the following could define f?
A. f(x) = (x-3)(x-1)(x+1)
B. f(x) = (x-3)(x-1)2
C. f(x) = (x-1)(x+1)(x+3)
D. (x+1)2(x+3)
C. f(x) = (x-1)(x+1)(x+3)
Which of the following expressions is equal to 0 for some value of x?
~ |x-1| - 1
~ |x+1| +1
~ |1-x| +1
~ |x-1| +1
|x-1|-1
One of the requirements for becoming a court reporter is the ability to type 225 words per minute. Donald can currently type 180 words per minute, and believes that with practice he can increase his typing speed by 5 words per minute each month. Which of the following represents the number of words per minute that Donald believes he will be able to type m months from now?
A. 5+180m
B. 225 + 5m
C. 180+5m
D. 180-5m
C. 180+5m
A partially filled pool contains 600 gallons of water. A hose is turned on, and water flows into the pool at the rate of 8 gallons per minute. How many gallons of water will be in the pool after 70 minutes?
1160
3(2x+1)(4x+1)
Which of the following is equivalent to the expression above?
A. 45x
B. 24x2+3
C. 24x2+18x+3
D. 18x2+6
C. 24x2+18x+3
f(x) = (x+6)(x-4)
Which of the following is an equivalent form of the function f above in which the minimum value of f appears as a constant or coefficient?
A. x2-24
B. x2+2x-24
C. (x-1)2-21
D. (x+1)2-25
D. (x+1)2-25
-3x + 4y = 20
6x + 3y = 15
If (x,y) is the solution to the system of equations above, what is the value of x?
x=0
If 3p − 2 ≥ 1, what is the least possible value of 3p+2?
A. 5
B. 3
C. 2
D. 1
The density of an object is equal to the mass of the object divided by the volume of the object. What is the volume, in milliliters, of an object with a mass of 24 grams and a density of 3 grams per milliliter?
8
If (t+5)/(t-5) = 10, what is the value of t?
55/9
q = 1/2nv2
The dynamic pressure q generated by a fluid moving with velocity v can be found using the formula above, where n is the constant density of the fluid. An aeronautical engineer uses the formula to find the dynamic pressure of a fluid moving with velocity v and the same fluid moving with velocity 1.5v. What is the ratio of the dynamic pressure of the faster fluid to the dynamic pressure of the slower fluid?
2.25 or 9/4
While preparing to run a marathon, Amelia created a training schedule in which the distance of her longest run every week increased by a constant amount. If Amelia’s training schedule requires that her longest run in week 4 is a distance of 8 miles and her longest run in week 16 is a distance of 26 miles, which of the following best describes how the distance Amelia runs changes between week 4 and week 16 of her training schedule?
A. Amelia increases the distance of her longest run by 0.5 miles each week.
B. Amelia increases the distance of her longest run by 2 miles each week.
C. Amelia increases the distance of her longest run by 2 miles every 3 weeks.
D. Amelia increases the distance of her longest run by 1.5 miles each week.
D. Amelia increases the distance of her longest run by 1.5 miles each week
Let x and y be numbers such that -y < x < y. Which of the following must be true?
I. |x| < y
II. x > 0
III. y > 0
A. I only
B. I and II only
C. I and III only
D. I, II, and III
C. I and III only
The pes, a Roman measure of length, is approximately equal to 11.65 inches. It is also equivalent to 16 smaller Roman units called digits. Based on these relationships, 75 Roman digits is equivalent to how many feet, to the nearest hundredth? (12 inches = 1 foot)
4.55
x3-5x2+2x-10=0
For what real value of x is the equation above true?
5
f(x) = 2x3+6x2+4x
g(x) = x2+3x+2
The polynomials f(x) and g(x) are defined above. Which of the following polynomials are divisible by 2x+3?
A. h(x) = f(x) + g(x)
B. p(x) = f(x) + 3g(x)
C. r(x) = 2f(x) + 3g(x)
D. s(x) = 3f(x)+2g(x)
B. p(x) = f(x) + 3g(x)
The mesosphere is the layer of Earth’s atmosphere between 50 kilometers and 85 kilometers above Earth’s surface. At a distance of 50 kilometers from Earth’s surface, the temperature in the mesosphere is −5° Celsius, and at a distance of 80 kilometers from Earth’s surface, the temperature in the mesosphere is −80° Celsius. For every additional 10 kilometers from Earth’s surface, the temperature in the mesosphere decreases by k° Celsius, where k is a constant. What is the value of k?
25
The normal systolic blood pressure P, in millimeters of mercury, for an adult male x years old can be modeled by the equation P = (x+220)/(2). According to the model, for every increase of 1 year in age, by how many millimeters of mercury will the normal systolic blood pressure for an adult male increase?
1/2 or 0.5
Nick surveyed a random sample of the freshman class of his high school to determine whether the Fall Festival should be held in October or November. Of the 90 students surveyed, 25.6% preferred October. Based on this information, about how many students in the entire 225-person class would be expected to prefer having the Fall Festival in October?
A. 50
B. 60
C. 75
D. 80
B. 60
x = 2y + 5
y = (2x-3)(x+9)
How many ordered pairs (x,y) satisfy the system of equations shown above?
A. 0
B. 1
C. 2
D. infinitely many
2
The stock price of one share in a certain company is worth $360 today. A stock analyst believes that the stock will lose 28 percent of its value each week for the next three weeks. The analyst uses the equation V = 360(r)t to model the value, V, of the stock after t weeks.
What value should the analyst use for r?
0.72