Heart of Algebra
Problem Solving & Data Analysis
No Calculator Allowed!

### 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

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 ?
What is p/( .8 * 1.08)?

### 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. Which of the following 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

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

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

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 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

y<-x+a, y>x+b In the xy-plane, if (0, 0) is a solution to the system of inequalities above, which of the following relationships between a and b must be true?
What is a>b

### 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

The graph above displays the total cost C, in dollars, of renting a boat for h hours. What does the C-intercept represent in the graph? A) The initial cost of renting the boat B) The total number of boats rented C) The total number of hours the boat is rented D) The increase in cost to rent the boat for each additional hour
What is A?

### 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?