Heart of Algebra
Problem Solving & Data Analysis
Passport to Advanced Math
Other/Geometry
100
If 20 − x = 15 , what is the value of 3x ?
A) 5
B) 10
C) 15
D) 35
C-15
100
The maximum value of a data set consisting of 25 positive integers is 84. A new data set consisting of 26 positive integers is created by including 96 in the original data set. Which of the following measures must be 12 greater for the new data set than for the original data set?
A) The mean
B) The median
C) The range
D) The standard deviation
C- The range
100
Simplify the following.
2x(x^2-3x)
2x^3-6x^2
100
A right circular cone has a volume of 24π cubic inches. If the height of the cone is 2 inches, what is the radius, in inches, of the base of the cone?
A) 2 square root (3)
B) 6
C) 12
D) 36
B- 6
200
For the function f defined above, what is the value of
f (−1) ?
f(x)=(x+3)/2
A) −2
B) −1
C) 1
D) 2
C-1
200
700, 1200, 1600, 2000, x
If the mean of the five numbers above is 1600, what is the value of x ?
2500
200
The function h is defined below. What is h(5)-h(3)?
h(x)=2^x
A) 2
B) 4
C) 24
D) 28
C-24
200
146 degrees
300
Based on the equation below, what is the value of 3x-2?
2/3(9x-6)-4=9x-6
A) −4
B) − 4/5
C) − 2/3
D) 4
A- -4
300
A book was on sale for 40% off its original price. If the sale price of the book was $18.00, what was the original price of the book? (Assume there is no sales tax.)
A) $7.20
B) $10.80
C) $30.00
D) $45.00
C- $30
300
V=4/3pir^3
The volume of a sphere is given by the formula, where r is the radius of the sphere. Which of the following gives the radius of the sphere in terms of the volume of the sphere?
D-
root3((3V)/(4pi)
300
A-150 degrees
400
Clayton will mix x milliliters of a 10% by mass saline solution with y milliliters of a 20% by mass saline solution in order to create an 18% by mass saline solution. The equation above represents this situation. If Clayton uses 100 milliliters of the 20% by mass saline solution, how many milliliters of the 10% by mass saline solution must he use?
0.10x+0.20y=0.18(x+y)
A) 5
B) 25
C) 50
D) 100
B- 25
400
The first year Eleanor organized a fund-raising event, she invited 30 people. For each of the next 5 years, she invited double the number of people she had invited the previous year. If f (n) is the number of people invited to the fund-raiser n years after Eleanor began organizing the event, which of the following statements best describes the function f ?
A) The function f is a decreasing linear function.
B) The function f is an increasing linear function.
C) The function f is a decreasing exponential
function.
D) The function f is an increasing exponential
function.
D- The function f is an increasing exponential function.
400
In the equation above, a is a constant. The graph of the equation in the xy-plane is a parabola. Which of the following is true about the parabola?
A) Its minimum occurs at (−3, a).
B) Its minimum occurs at (3, a).
C) Its maximum occurs at (−3, a).
D) Its maximum occurs at (3, a).
D- It's maximum occurs at (3,a)
400
The system of equations above is graphed in the xy -plane. What is the x -coordinate of the intersection point (x,y) of the system?
2.4x-1.5y=0.3
1.6x+0.5y=1.3
A) −0.5
B) −0.25
C) 0.8
D) 1.75
A- -0.5
500
Lynne has $8.00 to spend on apples and oranges. Apples cost $0.65 each, and oranges cost $0.75 each. If there is no tax on this purchase and she buys 5 apples, what is the maximum number of whole oranges she can buy?
6
500
The relationship between x and y can be written as y = mx , where m is a constant. If y = 17 when x = a , what is the value of y when x = 2a ?
34
500
Keith modeled the growth over several hundred years of a tree population by estimating the number of the trees’ pollen grains per square centimeter that were deposited each year within layers of a lake’s sediment. He estimated there were 310 pollen grains per square centimeter the first year the grains were deposited, with a 1% annual increase in the number of grains per square centimeter thereafter. Which of the following functions models P(t), the number of pollen grains per square centimeter t years after the first year the grains were deposited?
D-
p9T)=310(1.01)^T
500
Some values of x and their corresponding values of y are shown in the table above, where a is a constant. If there is a linear relationship between x and y, which of the following equations represents the relationship?
A) x + 2y = a
B) x + 2y = 5a
C) 2x − y = −5a
D) 2x − y = 7a
A- x+2y=a