Deck 1: Precalculus Diagnostic

Question 1

Solve. (If your solution has more than one interval, list them in order from left ot right, separate by commas as necessary.)

Answer 1

Question 2

Solve for x .

Answer 2

Question 3

Solve for x. (If there is more than one solution, separate each solution for x with a
comma.)

Answer 3

Question 4

Solve for x and y .

Question 5

The front of an aircraft hanger is being built in the shape of a parabola, which is
162 ft. wide, and has a maximum height of 95 ft. AND must have a rectangular
doorway that is 60 ft. tall. What is the maximum width of the doorway? (Round
your answer to the nearest tenth of a foot.)

Question 6

Factor completely:

Question 7

If g(t)=9 t² - t + 10 , find, expand, and simplify g(t - 5) .

Question 8

Solve for x . (Write your answer in interval notation.)

Question 9

List any vertical or horizontal asymptotes, if they exist, for the following function.

Question 10

Factor and simplify:

Question 11

Find the vertex of the following fuction.

Question 12

Simplify:

Question 13

Write the intersection or union of the following inequalities in interval notation:

Question 14

Rationalize the denominator:

Question 15

What is the domain of the following function? (Write your answer in internal notation.)

Question 16

Simplify:

Question 17

Write the equation of a circle, in standard form, whose diameter is AB,
where A = (-2, 11) and B = (6, 23).

Question 18

Solve for x

Question 19

What is the x -value of any hole(s) in the graph of the following function?

Question 20

The volume of a right rectangular solid with a square base is 108 in3. Find the
dimensions of the box, if the height of the box is the same as the perimeter of the
base.

Question 21

The hypotenuse of a right triangle is 18 cm. more than one of the legs. If the other
leg is 108 cm., how long is the hypotenuse (in cm.)?

Question 22

In an arithmetic sequence, if a₁ = 15 and the eighth term is 50 , find the 90^th term in the sequence.

Question 23

Evaluate:

Question 24

Simplify completely:

Question 25

Given https://d2lvgg3v3hfg70.cloudfront.net/TB34225555/. Evaluate

Question 26

Kyle went to the post office and spent $23.73 on 55 stamps. He bought 27¢ stamps
for the postcards, 42¢ stamps for the letters addressed to friends in the U.S., and 94¢
stamps for each letter to England. Kyle bought 3 times as many postcard stamps as
those for the letters to England. How many postcard stamps did Kyle buy? (Hint:
use matrices.)

Question 27

A straight line, l, passes through . For a point which lies on line l, as the value of x decreases by 2, what happens to the
value of y?

Question 28

Find the quotient and remainder, using long division, of the following expression. What is the remainder?

Question 29

Two ships leave port in different directions. The first ship leaves at 8 a.m. traveling
due east at 32 knots. The second ship leaves three hours later traveling due north
at 36 knots. How far apart are the two ships at 11 p.m.? (1 knot = 1 nautical mile
per hour. Round your answer to two decimal places.)

Question 30

Given ∆ABC whose vertices are A = (6, -4), B = (-5, 9), and C = (16, 9). Find the area
of ∆ABC.

Question 31

Given the following matrices, find AB, if possible.

Question 32

Solve for x . (Round your final answer to one decimal place, but do NOT round until the final step!)

Question 33

Question 34

Suppose M is jointly proportional to x and y and inversely proportional to the square
of z. If x is doubled, y is decupled, and z is tripled, is the value of M changed, and if
so, by what factor?

Question 35

Find the EXACT values for x and y