Passport to Advanced Math
Problem Solving & Data Analysis
Heart of Algebra
Miscellaneous
100

What are the solutions to 3x2 + 12x + 6 = 0

x = -2 +/- sqrt(2)

100
At Lincoln High School, approximately 7 percent of enrolled juniors and 5 percent of enrolled seniors were inducted into the National Honor Society last year. If there were 562 juniors and 602 seniors enrolled at Lincoln High School last year, which of the following is closest to the total number of juniors and seniors at Lincoln High School last year who were inducted into the National Honor Society?
69 or 70
100
Table:

n    | 1 | 2 | 3 | 4

f(n) |-2| 1 | 4 | 7

The table above shows some values of the linear function f. Which of the following defines f?

f(n) = n - 3

f(n) = 2n - 4 

f(n) = 3n - 5

f(n) = 4n - 6

f(n) = 3n - 5
100

In the xy-plane, the parabola with equation y = (x - 11)2 intersects the line with equation y = 25 at two points, A and B. What is the length of AB?

10
200

(-3x2 + 5x -2) - 2(x2 - 2x -1)

If the expression above is rewritten in the form ax2 + bx + c, where a, b, and c are constants, what is the value of b? 

9
200
Nate walks 25 meters in 13.7 seconds. If he walks at this same rate, what is the distance he will walk in 4 minutes?
436 or 437 meters
200

If (3w)/5 = 4/3; what is the value of w?

20/9
200
The average number of students per classroom at Central High School from 2000 to 2010 can be modeled by the equation y = 0.56x + 27.2, where x represents the number of years since 2000, and y represents the average number of students per classroom. Which of the following best describes the meaning of the number 0.56 in the equation?
The estimated increase in the average number of students per classroom each year.
300

3x2 - 5x + 2

5x2 - 2x - 6

Which of the following is the sum of the two polynomials shown above?

8x2 - 7x - 4

300
Of the following four types of savings account plans, which option would yield exponential growth of the money in the account?


Each successive year, 2% of the initial savings is added to the value of the account.

Each successive year, 1.5% of the initial savings and $100 is added to the value of the account.

Each successive year, 1% of the current value is added to the value of the account.

Each successive year, $100 is added to the value of the account.

Each successive year, 1% of the current value is added to the value of the account.

300
The cost of using a telephone in a hotel meeting room is $0.20 per minute. Which of the following equations represents the total cost c, in dollars, for h hours of phone use?
c = 0.20(60h)
300
Graphene, which is used in the manufacture of integrated circuits, is so thin that a sheet weighing one ounce can cover up to 7 football fields. If a football field has an area of approximately 1 and 1/3 acres, about how many acres could 48 ounces of graphene cover?
448
400
y = a(x-2)(x+4)


In the quadratic equation above, a is a nonzero constant. The graph of the equation in the xy-plane is a parabola with vertex (c,d). Which of the following is equal to d?

-9a
400

In order to determine if treatment X is successful in improving eyesight, a research study was conducted. From a large population of people with poor eyesight, 300 participants were selected at random. Half of the participants were randomly assigned to receive treatment X, and the other half did not receive treatment X. The resulting data showed that participants who received treatment X had significantly improved eyesight as compared to those who did not receive treatment X. Based on the design and results of the study, which of the following is an appropriate conclusion?


Treatment X is likely to improve the eyesight of people who have poor eyesight.

Treatment X is likely to improve eyesight better than all other available treatments.

Treatment X will improve the eyesight of anyone who takes it.

Treatment X will cause a substantial improvement in eyesight.

Treatment X is likely to improve the eyesight of people who have poor eyesight.
400
3x + b = 5x - 7

3y + c = 5y - 7

In the equation above, b and c are constants. If b is c minus 1/2, which of the following is true?

x is y minus 1/4

x is y minus 1/2

x is y minus 1

x is y plus 1/2

x is y minus 1/4
400

In a circle with center O, central angle AOB has a measure of (5pi)/4 radians. (pi means 3.1415....) The area of the sector formed by central angle AOB is what fraction of the area of the circle?


5/8 or 0.625
500
In planning maintenance for a city's infrastructure, a civil engineer estimates that, starting from the present, the population of the city will decrease by 10 percent every 20 years. If the present population of the city is 50,000, which of the following expressions represents the engineer's estimate of the population of the city t years from now?

50,000(0.9)(t/20)

500

A rectangle was altered by increasing its length by 10 percent and decreasing its width by p percent. If these alterations decreased the area of the rectangle by 12 percent, what is the value of p?

20
500

Mr. Kohl has a beaker containing n milliliters of solution to distribute to the students in his chemistry class. If he gives each student 3 milliliters of solution, he will have 5 milliliters left over. In order to give each student 4 milliliters of solution, he will need an additional 21 milliliters. How many students are in the class?


26
500

sin(ao) = cos(bo). ao and bo are acute angles.

If a = 4k -22 and b = 6k -13, what is the value of k?

12.5
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