Heart of Algebra, No Calc
x + y = 75
The equation above relates the number of minutes, x, Maria spends running each day and the number of minutes, y, she spends biking each day. In the equation, what does the number 75 represent?
A) The number of minutes spent running each day
B) The number of minutes spent biking each day
C) The total number of minutes spent running and biking each day
D) The number of minutes spent biking for each minute spent running
C) The total number of minutes spent running and biking each day
Which of the following ordered pairs (x, y) satisfies the inequality 5x - 3y < 4?
I. (1, 1)
II. (2, 5)
III. (3, 2)
A) I only
B) II only
C) I and II only
D) I and III only
C) I and II only
In 1854, during the California gold rush, each ounce of gold was worth $20, and the largest known mass of gold found in California was worth $62,400 in that year. What was the weight, in pounds, of this mass of gold? (16 ounces = 1 pound)
3,120
Which of the following is equivalent to 3(x + 5) - 6?
A) 3x -3
B) 3x - 1
C) 3x + 9
D) 15x - 6
C) 3x + 9
(x^2 - 3) - (-3x^2 + 5)
Which of the following expressions is equivalent to the one above?
A) 4x^2 - 8
B) 4x^2 - 2
C) -2x^2 - 8
D) -2x^2 - 2
A) 4x^2 - 8
x = y - 3
(x / 2) + 2y = 6
Which ordered pair (x,y ) satisfies the system of equations shown above?
A) (-3, 0)
B) (0, 3)
C) (6, -3)
D) (36, -6)
B) (0, 3)
9ax + 9b - 6 = 21
Based on the equation of above, what is the value of ax + b?
A) 3
B) 6
D) 8
D) 12
A) 3
A market researcher selected 200 people at random from a group of people who indicated that they liked a certain book. The 200 people were shown a movie based on the book, and then asked whether they liked or disliked the movie. Of those surveyed, 95% said they disliked the movie. Which of the following inferences can be appropriately be drawn from this survey result?
A) At least 95% of people who go see movies will dislike this movie
B) At least 95% of people who read books will dislike this movie
C) Most people who dislike this book will like this movie
D) Most people who like this book will dislike this movie
D) Most people who like this book will dislike this movie
If f(x) = (x^2 - 6x + 3)/(x-1) what is f(-1)?
A) -5
B) -2
C) 2
D) 5
A) - 5
In the equation, (ax + 3)^2 = 36, a is a constant. If x = -3 is one solution to the equation, what is a possible value of a?
A) -11
B) -5
C) -1
D) 0
C) -1
[Free response]
If 2x + 8 = 16, what is the value of x+4?
8
y = 19.99 + 1.50x
The equation above models the total cost y, in dollars, that a company charges a customer to rent a truck for one day and drive the truck x miles. The total cost consists of a flat fee plus a charge per mile driven When the equation is graphed in the xy-plane, what does the y-intercept of the graph represent in terms of the model?
A) A flat fee of $19.99
B) A charge per mile of $1.50
C) A charge per mile of $19.99
D) Total daily charge of $21.49
A) A flat fee of $19.99
A customer paid $53.00 for a jacked after a 6 percent sales tax was added. What was the price of the jacket before the sales tax was added?
A) $47.60
B) $50.00
C) $52.60
D) $52.84
(7532 + 100y2) + 10(10y2 - 110)
The expression above can be written in the form ay2 + b, where a and b are constants. What is the value of a+b?
6632
h(t) = -16t^2 + 110t + 72
The function able models the height h, in feet, of an object above ground t seconds after being launched straight up in the air. What does the number 72 represent in the function?
A) The initial height, in feet, of the object
B) The maximum height, in feet of the object
C) The initial speed, in feet per second, of the object
D) The maximum speed, in feet per second, of the object
A) The initial height, in feet, of the object
Ken is working this summer as part of a crew on a farm. He earned $8 per hour for the first 10 hours he worked this week. Because of his performance, his crew leader raised his salary to $10 per hour for the rest of the week. Ken saves 90% of his earnings from each week. What is the least number of hours he must work the rest of the week to save at least $270?
A) 38
B) 33
C) 22
D) 16
C) 22
A four sided polygon has angles that have the following measurements (all in degrees): 45, x, x, x.
What is the value of x?
A) 45
B) 90
C) 100
D) 105
D) 105
If 50 one-cent coins were stacked on top of each other in a column, the column would be approximately 3 and 7/8 inches tall. At this rate, which of the following is closest to the number of once-cent coins it would take to make an 8-inch-tall column?
A) 75
B) 100
C) 200
D) 390
ax^3 + bx^2 + cx +d = 0
In the equation above, a, b, c, and d are constants. If the equation has roots -1, -3, and 5, which of the following is a factor of ax^3 + bx^2 + cx + d?
A) x - 1
B) x + 1
C) x - 3
D) x + 5
B) x + 1
The world’s population has grown at an average rate of 1.9 percent per year since 1945. There were approximately 4 billion people in the world in 1975. Which of the following functions represents the world’s population, P, in billions of people, t years since 1975? (1 billion = 1, 000,000,000)
A) P(t) = 4(1.019)^t
B) P(t) = 4(1.9)^t
C) P(t) = 1.19t +4
D) P(t) = 1.019t + 4
A) P(t) = 4(1.019)^t
[Free response]
The graph of a line in the xy-plane passes through the point (1,4) and crosses the x-axis at the point (2,0). The line crosses the y-axis at the point (0, b). What is the value of b?
8
The score on a trivia game is obtained by subtracting the number of incorrect answers from twice the number of correct answers. If a player answered 40 questions and obtained a score of 50, how many questions did the player answer correctly?
30
In 2012, an online news service sold 5,600 subscriptions. In 2013, it sold 5,880 subscriptions. The manager of this service estimated that the percent increase from 2012 to 2013 would be double the percent increase from 2013 to 2014.How many subscriptions did the manager expect would be sold in 2014?
A) 6,020
B) 6,027
C) 6,440
D) 6,468
The expression (x2/3) - 2 can be written as (1/3)(x-k)(x+k), where k is a positive constant. What is the value of k?
A) 2
B) 6
C) square root of 2
D) square root of 6
C) square root of 2
y = x^2 - 4x + 4
y = 4 - x
If the ordered pair (x, y) satisfies the system of equations above, what is one possible value of x?
x = 0 OR x = 3