Math, No Calc - Round I
The mean number of students per classroom, y, at Central High School can be estimated using the equation y=0.8636x + 27.227 where x represents the number of years since 2004 and x ≤ 10. Which of the following statements is the best interpretation of the number 0.8636 in the context of this problem?
A) The estimated mean number of students per classroom in 2004
B) The estimated mean number of students per classroom in 2014
C) The estimated yearly decrease in the mean number of students per classroom
D) The estimated yearly increase in the mean number of students per classroom
Choice D is correct.
When an equation is written in the form y equals m x plus b comma the coefficient of the x-term (in this case 0.8636) is the slope. The slope of a linear equation gives the amount that the mean number of students per classroom (represented by y) changes per year (represented by x).
Question Difficulty: Easy
The equation y = 36 + 18x models the relationship between the height y, in inches, of a typical golden delicious apple tree and the number of years, x, after it was planted.
If the equation is graphed in the xy-plane, what is indicated by the y-intercept of the graph?
A) The age, in years, of a typical apple tree when it is planted
B) The height, in inches, of a typical apple tree when it is planted
C) The number of years it takes a typical apple tree to grow
D) The number of inches a typical apple tree grows each year
Choice B is correct.
If the equation y = 36 + 18x is graphed in the xy-plane, the y-intercept is at (0, 36). Since y represents the height, in inches, of a typical apple tree and x represents the number of years after it was planted, it follows that the number 36 represents the height, in inches, of a typical apple tree when x = 0; that is, the height, in inches, at the time the apple tree is planted.
DIFFICULTY: Medium
What does "subjugate" mean?
Example:
The village next door was subjugated by the raiding pirates without question.
bring under domination or control; conquer, defeat
What does "paramount" mean?
Example: It is paramount that my grandfather takes his medicine if he wants to feel better.
critical, most important
THIS COLLEGE is a private, historically black men's college located in Atlanta, Georgia. The college is one of the few remaining men's liberal arts colleges in the United States.
Morehouse College
If a2 + 14a=51 and a>0, what is the value of a + 7?
10
Question Difficulty: EASY
Giovanni wants to buy shirts that cost $19.40 each and sweaters that cost $24.80 each. An 8% sales tax will be applied to the entire purchase. If Giovanni buys 2 shirts, which equation relates the number of sweaters purchased, p, and the total cost in dollars, y?
A) 1.08 (38.80 + 24.80 p) = y
B) 38.80 + 24.80p = 0.92y
C) 38.80 + 24.80p = 1.08y
D) 0.92 (38.80 + 24.80p) = y
Choice A is correct.
The cost, in dollars, of Giovanni’s 2 shirts is 19.40 × 2 = 38.80, and the cost, in dollars, of his p sweaters is 24.80 × p = 24.80p. Additionally, he paid an 8% sales tax. To include the sales tax in the total cost, the combined cost of shirts and sweaters should be multiplied by 1.08. Therefore, the total cost, in dollars, of Giovanni’s purchases, y, can be expressed as 1.08(38.80 + 24.80p).
DIFFICULTY: Medium
What does "despondent" mean?
Example: After learning about her brother's death, Lisa became so despondent that she didn't show up to school for a week.
disheartened; discouraged
What does "periphery" mean?
Example: The dogs are confined by an invisible electronic fence that runs along the periphery of the yard.
the outer limits/edge
Zion Williamson was a freshman star player for THIS UNIVERSITY'S basketball team when he destroyed his shoe in the first 36 seconds of a game.
Jason Tatum, of the Celtics, also attended this school for one year before he joined the NBA.
Duke University
Which of the following is an equivalent form of the expression 15x + 24ax?
A) 39ax2
B) 39 (a+2x)
C) (5+8a) x
D) (15 + 24a) x
Choice D is correct.
The expression 15x + 24ax contains two terms with common factors. One of the common factors is x. Factoring x from the expression gives x(15 + 24a), which can also be written as (15 + 24a)x.
DIFFICULTY: Medium
−3x − 4y = 20
x − 10 y = 16
If (x, y) is the solution to the system of equations above, what is the value of x ?
A) −14
B) −12
C) −4
D) 16
Choice C is correct.
Multiplying each side of the second equation by 3 and then adding the equations eliminates x, as follows: 3 4 20 3 30 48 0 34 68 x y x y y −− = − = − = Solving the obtained equation for y gives y = −2. Substituting −2 for y in the second equation of the system gives x − 10(−2) = 16, which simplifies to x + 20 = 16, or x = −4.
DIFFICULTY: Medium
What does "nuance" mean?
Example: Because she is a chef, Mina notices every nuance of flavor in the meal.
a subtle difference in meaning, expression or sound; variation
What does the word "cynical" mean?
Example: He was cynical about politicians' promises on forgiving all student loan debt?
skeptical or distrustful of human motives
How many Ivy League colleges are there in the United States?
There are eight total colleges that are considered to be Ivy League.
Which of the following ordered pairs (x, y) satisfies both equations y= x2 + 3x − 4 and x= y −4 ?
A) (0, −4)
B) (2, 6)
C) (3, 14)
D) (5, 9)
Choice B is correct.
The equation x = y − 4 can be rewritten as y = x + 4. Substituting x + 4 for y in the other equation gives x + 4 = x 2 + 3x − 4, which can be rewritten as x 2 + 2x − 8 = 0. Since −4 and 2 are the two numbers whose sum is −2 and whose product is −8, they are the solutions to the equation x 2 + 2x − 8 = 0. From the equation y = x + 4, it follows that the solutions of the system are (−4, 0) and (2, 6). Therefore, of the given choices, (2, 6) is the correct answer.
DIFFICULTY: Medium
A line is graphed in the xy-plane. If the line has a positive slope and a negative y-intercept, which of the following points cannot lie on the line?
A) (−3, −3)
B) (−3, 3)
C) (3, −3)
D) (3, 3)
Choice B is correct.
Any line that passes through the point (−3, 3) and has a positive slope will intersect the y-axis at a point (0, b) with b > 3; that is, such a line will have a y-intercept greater than 3. Therefore, a line that has a positive slope and a negative y-intercept cannot pass through the point (−3, 3).
DIFFICULTY: Medium
What does "jargon" mean?
Example: On top of working at the local library, Hamilton is a good storyteller and a clear writer who avoids the pitfalls of pretentious art-world jargon.
Specialized language; slang
What does the word, "dissipate" mean?
Example: According to meteorologists, the storm will dissipate after a few hours and make way for the sunshine
disappear or cause to disappear; squander; waste; scatter
Over the last 5 years, which TWO Posse schools have Boston Prep seniors NOT matriculated (attended) to:
A) Bryn Mawr College
B) Centre College
C) Bucknell University
D) Denison University
E) Union College
A) Bryn Mawr College
B) Centre College
Which of the following is a solution to the equation: 2x2+4x = 3+3x2?
A) −1
B) 0
C) 3
D) 6
Choice C is correct.
The given equation can be rewritten as x 2 − 4x + 3 = 0. Since 1 and 3 are two numbers whose sum is 4 and whose product is 3, it follows that they are the solutions to the equation x 2 − 4x + 3 = 0. Therefore, of the choices given, only 3 can be a solution to the original equation.
DIFFICULTY: Medium
Juliene practiced her dance routine for twice as many minutes on Monday as she did on Tuesday. She practiced her routine those two days for a total of 2 hours and 15 minutes. For how many minutes did Juliene practice her dance routine on Monday?
The correct answer is 90.
Juliene practiced twice as long on Monday as she did on Tuesday. Therefore, if x is the number of minutes Juliene practiced on Tuesday, then 2x is the number of minutes she practiced on Monday. The total amount of time Juliene practiced on the two days is 2 hours and 15 minutes, which is equal to 135 minutes. Thus, the equation x + 2x = 135 must be true. This simplifies to 3x = 135, and so x = 45. The number of minutes Juliene practiced on Monday is 2x, which is equal to 2x = 2(45) = 90
DIFFICULTY: Hard
What does "lampooning" mean?
Example: Brandon was always scared to post his story ideas on the writing forum because critics might lampoon his work.
publicly criticize; mock; ridicule
What does the word, "scrutinize" mean?
Example: Because of recent alerts, the airline screeners closely scrutinize all bags that are going on board airplanes.
examine closely and critically
Name AT LEAST 5 of the Ivy League colleges/universities.
Brown, Harvard, Cornell, Princeton, Dartmouth, Yale, Columbia and the University of Pennsylvania.