Heart of Algebra
Passport to Advanced Mathematics
Problem Solving & Data Analysis
Additional Topics in Math
No Calculator Allowed!
100

If 16 - 7w  = w + 14 - 6w

What is the value of w - 1? 

What is 0? 
100
100 - 121(k^2) = 0


What are the solutions for the equation above? 

A. k = 100/121

B. k = -100/121 and k = 100/121

C. k = 10/11

D. k = 10/11 and  k = -10/11

What is D? 
100
During a typing test, Alex typed 742 words in 14 minutes. Assuming Alexander works at this rate for the next hour, which of the following best approximates the numbers of words he would type in that hour?

A. 342 B. 4,324 C. 3,180 D. 14,000

What is C 
100
What is the equation for the pythagorean theorem? 
What is a^2 + b^2 = c^2
100

If a = 1 and b = 2

and C = 2^a + 2^b 

What is the value of C?

What is 5? 
200

5.5B + 4R = 28

The above equation is true if Amit is true if Amit buys B pounds of blueberries and R pounds of raspberries at a farm, where blueberries cost $5.50 per pound and raspberries cost $4.00 per pound. According to the equation, how much does Amit spend in total on both types of berries? 

What is 28? 
200
(2x - 3)(x +4) = 0


Let x = a, and x = b. What is the value of (-a) - b ? 

What is 2.5 or 5/2? 
200

Elena is conducting an experiment on the affect of toxins fish. She surveyed 350 male fish, 150 of the surveyed fish were affected by the toxins. According to Elena, What is the ratio of male fish with egg cells to male fish without egg cells in the river?

A. 3:4 B. 3: 7 C. 3:8 D. 2:5 

What is A? 
200
Part 1: What is the equation for a circle? 

Part 2:What does (h,k) represent? 

What is (x-h)^2 + (x-k)^2 = r^2?

What is the center of a circle?


200
What are the solutions to the equation

(x^2 - 1)? 

What is +1 and -1? 
300
Which of the following is an equation of the line A graphed in the xy-plane that passes through the point (-1,3,5) and is perpendicular to the line B whose equation is 

x + 4.5 = 0? 

A. y = x + 4.5 

B. y = 3.5

C. x = y

D. x = -4.5 

What is B?
300
h = − 4.9(t^2) + 25t 

The equation above expresses the approximate height h, in meters, of a ball t seconds after it is launched vertically upward from the ground with an initial velocity of 25 meters per second. After approximately how many seconds will the ball hit the ground?

What is 5.1?
300
s = 320 + 115t

The equation above approximates the relationship wildlife vets have found between the amount of t cortisol in micrograms per deciliter, in a wild harbor seal's tear to the amount of s cortisol, in the seals blood stream. Which of the following statements best describes the relationship between the amount of cortisol in the seals tears and blood stream? 

A. It is linear because there is an 11.5 increase in s for every .1 increase in t. 

B. It is linear because there is a 32 increase in s for every .1 increase in t.

C. It is exponential because there is a 15% increase in s for every .01 increase in t.

D. It is exponential because there is a 220% increase in s for every .01 increase in t. 

What is A? 
300
Which of the following is an equation of a circle in the xy-plane with center (0, 4) and a radius with endpoint (4/3, 5)?
What is x^2+(y-4)^2=25/9?
300
If b^3 * (b^4)^2 = b^x 

What is the value of x? 

What is 11? 
400

The change machine at an arcade gives change in the form of 25- cent coins and one dollar bills. The manager would like at least $50 worth of quarters and $100 worth of one-dollar bills in the machine at all times. Also the manager does not allow more than $500 in the machine at any time. What is the maximum number of quarters the manager would allow in the change machine? 

A. 400 B. 850. C. 4,000 D. 1,600

What is 1,600 quarters? 
400
For a polynomial p(x), the value of p(3) is −2. Which of the following must be true about p(x) ?

 A) x − 5 is a factor of p(x). 

B) x − 2 is a factor of p(x). 

C) x + 2 is a factor of p(x). 

D) The remainder when p(x) is divided by x − 3 is −2.

What is D?
400
A local television station sells time slots for programs in 30-minute intervals. If the station operates 24 hours per day, every day of the week, what is the total number of 30-minute time slots the station can sell for Tuesday and Wednesday?
What is 96?
400
A dairy farmer uses a storage silo that is in the shape of the right circular cylinder with height 8. If the volume of the silo is 72pi cubic yards, what is the diameter of the base of the cylinder, in yards?
What is 6?
400
What is the value of the expression below: 


(1/2)^-2 + 3^0

What is 5?
500
z + w - 3 = k

6z - 10w = 8

Consider the sytem of equations above, where K is a constant. For which value of K are there infinitely many (w,z) solutions? 

A. 9/6 B. 4 C. 8 D. None of the above

What is none of the above? 
500
(Equation to be written on the board) 

What is the value of x in the equation above? 

What is 4? 
500
I will pull up this question on the computer. 
What is 6? 
500
In the figure on the board, JLK and JNM are both right triangles. Which of the following expressions must be equation to the length of the line segment KL?


A. sin(y)*(JK/JL)

B. 1/cos(y) *(JK/JL)

C. tan(y)*JL

D. 1/tan(y)*JL

What is D?
500
What is the value of x in the following expression: 


To be written on the board.... 

What is 1,000 
M
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