Heart of Algebra
A line in the xy-plane passes through the origin and has a slope of 3/4. Which of the following points lies on the line?
A) (0, 4) B) (3, 4) C) (3, 3) D) (4, 3)
What is D) (4, 3)?
For what value of h is h 24 = h/10 − 6 ?
What is h = 300?
Refer to Graph D
The scatterplot shows the widths and the heights of 12 types of rectangular envelopes. What is the width, in inches, of the envelope represented by the data point that is farthest from the line of best fit (not shown) ?
A) 2 B) 5 C) 7 D) 12
What is C) 7?
A babysitter earns $8 an hour for babysitting 2 children and an additional $3 tip when both children are put to bed on time. If the babysitter gets the children to bed on time, what expression could be used to determine how much the babysitter earned?
A) 8x + 3, where x is the number of hours
B) 3x + 8, where x is the number of hours
C) x(8 + 2) + 3, where x is the number of children
D) 3x + (8 + 2), where x is the number of children
What is A) 8x + 3, where x is the number of hours
If (x− 1)/3 = k and k = 3, what is the value of x ?
A) 2 B) 4 C) 9 D) 10
What is D) 10?
If a/b = 2, what is the value of 4b/a?
A) 0 B) 1 C) 2 D) 4
What is C) 2?
The posted weight limit for a covered wooden bridge in Pennsylvania is 6000 pounds. A delivery truck that is carrying x identical boxes each weighing 14 pounds will pass over the bridge. If the combined weight of the empty delivery truck and its driver is 4500 pounds, what is the maximum possible value for x that will keep the combined weight of the truck, driver, and boxes below the bridge’s posted weight limit?
What is 107?
Refer to graph A
The line graph shows the monthly rainfall from March to October last year in Chestnut City. According to the graph, what was the greatest change (in absolute value) in the monthly rainfall between two consecutive months?
A) 1.5 inches B) 2.0 inches
C) 2.5 inches D) 3.5 inches
What is C) 2.5 inches?
A soda company is filling bottles of soda from a tank that contains 500 gallons of soda. At most, how many 20-ounce bottles can be filled from the tank? (1 gallon = 128 ounces)
A) 25 B) 78 C) 2,560 D) 3,200
What is D) 3,200?
If f(x - 1) = 2x + 3 for all values of x, what is the value of f(-3)?
A) -7 B) -5 C) -3 D) -1
What is D) -1?
If y = kx, where k is a constant, and y = 24
when x = 6, what is the value of y when x = 5 ?
A) 30 B) 20 C) 4.8 D) 4
What is B) 20?
Wyatt can husk at least 12 dozen ears of corn per hour and at most 18 dozen ears of corn per hour. Based on this information, what is a possible amount of time, in hours, that it could take Wyatt to husk 72 dozen ears of corn?
What is any number between 4-6 inclusive?
Refer to graph C
The histogram shows the distribution of the heights, in meters, of 26 pyramids in Egypt. Which of the following could be the median height of the 26 pyramids represented in the histogram?
A) 44 meters B) 48 meters
C) 63 meters D) 77 meters
What is B) 48 meters
A car traveled at an average speed of 80 miles per hour for 3 hours and consumed fuel at a rate of 34 miles per gallon. Approximately how many gallons of fuel did the car use for the entire 3-hour trip?
A) 2 B) 3 C) 6 D) 7
What is D) 7 ?
To cut a lawn, Allan charges a fee of $15 for his equipment and $8.50 per hour spent cutting a lawn. Taylor charges a fee of $12 for his equipment and $9.25 per hour spent cutting a lawn. If x represents the number of hours spent cutting a lawn, what are all the values of x for which Taylor’s total charge is greater than Allan’s total charge?
A) x > 4 B) 3 < x < 4 C) 4 < x < 5 D) x < 3
What is A) x > 4 ?
A high school basketball team won exactly 65% of the games they played last season. Which of the following could be the total number of games the team played last season?
A) 22 B) 20 C) 18 D) 14
What is B) 20?
What is the value of a if (2a + 3) − (4a − 8) = 7 ?
What is a = 2?
Refer to chart E
Which of the following is closest to the percent of those surveyed who had a summer job?
A) 22% B) 35% C) 47% D) 53%
What is B) 35% ?
In a certain game, a player can solve easy or hard puzzles. A player earns 30 points for solving an easy puzzle and 60 points for solving a hard puzzle. Tina solved a total of 50 puzzles playing this game, earning 1,950 points in all. How many hard puzzles did Tina solve?
A) 10 B) 15 C) 25 D) 35
What is B) 15 ?
h = 3a + 28.6
A pediatrician uses the model above to estimate the height h of a boy, in inches, in terms of the boy’s age a, in years, between the ages of 2 and 5. Based on the model, what is the estimated increase, in inches, of a boy’s height each year?
A) 3 B) 5.7 C) 9.5 D) 14.3
What is A) 3?
y < -x+a
y > x+b
In the xy-plane, if (0, 0) is a solution to the system of inequalities above, which of the following relationships between a and b must be true?
a) a = b b) a > b c) a < b
d) cannot be determined
What is b) a>b
In a college archaeology class, 78 students are going to a dig site to find and study artifacts. The dig site has been divided into 24 sections, and each section will be studied by a group of either 2 or 4 students. How many of the sections will be studied by a group of 2 students?
What is 9?
Refer to graph B
What is the minimum value of the function graphed on the xy-plane, for −4 ≤ x ≤ 6 ?
A) −∞ B) −4 C) −2 D) 1
What is C) -2?
Boyd grows only tomatoes and raspberries in his garden. Last year, he grew 140 pounds of tomatoes and 60 pounds of raspberries. This year, the production, by weight, of tomatoes declined by 20 percent, and the production, by weight, of raspberries declined by 50 percent. By what percentage did the total yield, by weight, of Boyd’s garden decline?
A) 29 percent B) 30 percent
C) 35 percent D) 70 percent
What is A) 29 percent?
g(x) = ax^2 + 24 For the function g defined above, a is a constant and g(4) = 8. What is the value of g(−4) ?
A) 8 B) 0 C) -1 D) -8
What is A) 8?