Heart of Algebra

Passport to Advanced Mathematics

Problem Solving & Data Analysis

Additional Topics in Math

No Calculator Allowed!

If a/b = 2, what is the value of 4b/a?

What is 2?

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?

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?

what is the sum (7 + 3i) + (−8 + 9i) ?

What is -1+12i?

If
(x− 1)/3=k and k = 3, what is the value of x ?

What is 10?

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?

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?

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)?

In a right triangle, one angle measures x°, where
sin x° =4/5. What is cos(90° − x°) ?

What is 4/5?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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

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?

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?

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?

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?

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