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Heart of Algebra
Passport to Advanced Mathematics
Problem Solving & Data Analysis
Additional Topics in Math
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100
If a/b = 2, what is the value of 4b/a?
What is 2?
100
If 3x − y = 12, what is the value of 8^x/2^y? a. 2^12 b. 4^4 c. 8^2 d. It cannot be determined from information given.
What is a?
100

If y = kx, where k is a constant, and y = 24 when x = 6, what is the value of y when x = 5 ?

What is 20?

100
what is the sum (7 + 3i) + (−8 + 9i) ?
What is -1+12i?
100
If (x− 1)/3=k and k = 3, what is the value of x ?
What is 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)
What is D?
200
If (ax + 2)(bx + 7) = 15x^2 + cx + 14 for all values of x, and a + b = 8, what are the two possible values for c ? A) 3 and 5 B) 6 and 35 C) 10 and 21 D) 31 and 41
What is D?
200

The student population at University X consists of 63% undergraduate students and 37% graduate students. If 23% of undergraduate students and 42% of graduate students wear contacts, what percent of all students wear contacts?

What is 30%?

200
In a right triangle, one angle measures x°, where sin x° =4/5. What is cos(90° − x°) ?
What is 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. Write an expression that represents the total number of messages sent by Armand and Tyrone on Saturday afternoon.

What is 5m+4p?

300
The posted weight limit for a covered wooden bridge in Pennsylvania is 6000 pounds. A delivery truck that is carrying x identical boxes each weighing 14 pounds will pass over the bridge. If the combined weight of the empty delivery truck and its driver is 4500 pounds, what is the maximum possible value for x that will keep the combined weight of the truck, driver, and boxes below the bridge’s posted weight limit?
What is 107?
300

h = − 4.9t^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

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?

What is 120?

300

What is the 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

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?

What is Kathy will start each week with 108 phones to fix?

400
Wyatt can husk at least 12 dozen ears of corn per hour and at most 18 dozen ears of corn per hour. Based on this information, what is a possible amount of time, in hours, that it could take Wyatt to husk 72 dozen ears of corn?
What is any number between 4-6 inclusive?
400

What is the positive solution to the following equation?

(x+5)(2x-3)=0


What is 3/2?

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 a right circular cylinder with a height 8. If the volume of the silo is 72π cubic yards, what is the diameter of the base of the cylinder, in yards?

What is 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?

What is 3?

500

What is the sum of x and y in the solution to the following system of equations?

y=2x + 3

y=-(1/3)x - 4


What is -6

500

Jessica opened a bank account that earns 2 percent interest compounded annually. Her initial deposit was $100, and she 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?

What is 1.02?

500

Frank and his friends rent a boat at a lake that charges a safety fee and an hourly rate. The money spent y on the lake each hour x is represented by the equation y = 12.5x + 20. What is the meaning of the 20 in this equation?

What is the value of the safety fee?

500
A x feet D B A summer camp counselor wants to find a length, x, in feet, across a lake as represented in the sketch I draw. The lengths represented by AB, EB, BD, and CD on the sketch were determined to be 1800 feet, 1400 feet, 700 feet, and 800 feet, respectively. Segments AC and DE intersect at B, and ∠AEB and ∠CDB have the same measure. What is the value of x ?
What is 1600?
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) ?
What is 8?