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Heart of Algebra
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100

Peter wrote 120 SAT questions that consisted of m of multiple choices questions and s of short response questions. Each multiple choice question is worth 2 points while short responses are worth 5 points. 120 questions have 300 points in total. Write a system of equations to model this the situation.

m + s = 120

2m + 5s = 300

100
Simplify 2/(x+1) - 10/(2x+2) into one single term.
-6/2(x+1)
100
If y = kx, where k is a constant, and y = 24 when x = 6, what is the value of y when x = 5 ?
20?
100
what is the sum (7 + 3i) + (−8 + 9i) ?
-1+12i
100
If (x− 1)/3=k and k = 3, what is the value of x ?
10
200
A line in the xy-plane passes through the origin and has a slope of 1/7. Which of the following points lies on the line? 

A) (0, 7) 

B) (1, 7) 

C) (7, 7) 

D) (14, 2)

D
200

The freezing point of water at sea level is -23 degrees Fahrenheit (°F). For every increase of 10 feet above sea level, the boiling point of water increases approximately 0.25°F. Which of the following equations gives the approximate freezing point F, in °F, at h feet above sea level?

F = -23 + 0.25(h/100)
200
Alma bought a laptop computer at a store that gave a 20 percent discount off its original price. The total amount she paid to the cashier was p dollars, including an 8 percent sales tax on the discounted price. Which of the following represents the original price of the computer in terms of p ?
p/( .8 * 1.08)
200
In a right triangle, one angle measures x°, where sin x° =4/5. What is cos(90° − x°) ?
4/5
200
On Saturday afternoon, Armand sent m text messages each hour for 5 hours, and Tyrone sent p text messages each hour for 4 hours. Which of the following represents the total number of messages sent by Armand and Tyrone on Saturday afternoon?
5m+4p
300

T = 2k + 4n

Yeonjung spends all of her free time on Korean drama or napping. k represents the number of episodes of K-drama and n is the number of naps which she takes. Yeonjung has at most 12 hours of free time, T, and she watches at least 2 episodes of K-drama a day. What's the maximum of naps that she could take each day?



2
300
5| 2x + 1 | = 15,  what is the positive value of x?
1
300
Katarina is a botanist studying the production of pears by two types of pear trees. She noticed that Type A trees produced 20 percent more pears than Type B trees did. Based on Katarina’s observation, if the Type A trees produced 144 pears, how many pears did the Type B trees produce?
120
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)?
x^2+(y-4)^2=25/9
300
Kathy is a repair technician for a phone company. Each week, she receives a batch of phones that need repairs. The number of phones that she has left to fix at the end of each day can be estimated with the equation P = 108 − 23d, where P is the number of phones left and d is the number of days she has worked that week. What is the meaning of the value 108 in this equation?
Kathy will start each week with 108 phones to fix
400
If x cube = 3, what is the value of x to the power of 12.
81.
400

If the value of x square - y square = 200 and x+y=10, what is the value of x-y?

20
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?
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 72π cubic yards, what is the diameter of the base of the cylinder, in yards?
6
400
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?
3
500
x square + 6x + 8 = y

11x = 2 - y

Find the solutions.

(2, 24)

(3, 35)

500
Peter opened a bank account that earns 2 percent interest compounded annually. His initial deposit was $100, and he uses the expression $100(x)^t to find the value of the account after t years. What is the value of x in the expression?
1.02
500
p=(0.6t + 2)cube

Peter is so smart that he could easily fool you with all kinds of little tricks. He often likes to take t pounds of water and add two cats to it. Since cats hate water they will try to escape and scream to Peter. Peter is very nice and lets the cats go. May I ask you why you are still reading? Didn't I tell you to skip this paragraph for questions like this? What is t in terms of p?

(cubic root of p -2)/0.6
500
What is Peter's favorite animal?
Cats!!!!!!!! (I love dogs too)
500
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) ?
8