Pre-Calculus Review

Evaluating Expressions

100

If 𝑦=𝑥²+4⁢𝑥+5, evaluate 𝑦 given 𝑥=3⁢𝑖.

-4+12i

200

If 𝑦=𝑥²-𝑥-1, evaluate 𝑦 given 𝑥=1-3⁢𝑖.

-10+3i, -10-3i

300

Evaluate (1+5i)-(-3-3i).

-2+2i

400

Evaluate (5+4i)(2-i)

14+3i

500

Evaluate y=x³-2x²+15x-4 when x=6i-7

278+924i

Dividing Polynomials

100

Use long division to divide.

(3⁢𝑥²+7⁢𝑥-20)÷(𝑥+4)

3x-5

200

Use synthetic division to find the quotient. 

(𝑥³+5⁢𝑥²-16)÷(𝑥+4)

x²+x-4

300

Use the given length and area of a rectangle to express the width algebraically.

Length is 𝑥-3, area is 3⁢𝑥²-10⁢𝑥+3

3x-1

400

Use the Remainder Theorem to find the remainder.

(2⁢𝑥³+11⁢𝑥²+8⁢𝑥-19)÷(𝑥+4)

Remainder: -3

500

(𝑥⁴+4)÷(𝑥+1)

x³-x²+x-1+5/x+1

Linear Functions

100

Determine whether the lines given by the equations below are parallel, perpendicular, or neither.

4⁢𝑥+5⁢𝑦=4, 5⁢𝑥-4⁢𝑦=9

perpendicular

200

Given the set of information, find a linear equation satisfying the conditions, if possible. If not, enter "DNE".

𝑓⁡(3)=-2, and 𝑓⁡(-3)=-4

y=1/3x-3

300

A city's population in the year 1960 was 291,200. In 1981 the population was 289,100. Compute the rate of growth of the population.

The city declined by 100 people per year. 

400

Find the point of intersection of the pair of lines. Hint: Don't start your second line with a point you used for the first line.

4⁢𝑥=𝑦+5, 𝑦+2⁢𝑥=7

(2,3)

500

Find the equation of the line perpendicular to the line 𝑔⁡(𝑥)=-0.01⁢𝑥+3.02 through the point (2,3).

y=100x-197

Quadratic Functions

100

Graph the expression f(x)=2(x-4)²-6

look to board for answer.

200

Determine whether there is a minimum or a maximum value to each quadratic function. Find the value and the axis of symmetry.

𝑓⁡(𝑥)=3⁢𝑥²-6⁢𝑥-4

minimum

value=-7

axis of symmetry: x=1

300

Solve the equation over the complex numbers.

𝑥²-8⁢𝑥+41=0

x=4+5i, 4-5i

400

Use the vertex (ℎ,𝑘) and a point on the graph (𝑥,𝑦) to find the Standard Form
( 𝑓⁡(𝑥)=𝑎⁢(𝑥-ℎ)2+𝑘 ) of the equation of this quadratic function.

(ℎ,𝑘)=(-1,0) , (𝑥,𝑦)=(-2,1)

(x+1)²

500

A ball is thrown in the air from the top of a building. Its height, in meters above ground as a function of time, in seconds, is given by ℎ⁡(𝑡)=-4.9⁢𝑡2+25⁢𝑡+8. How long does it take to reach maximum height? Round to the nearest hundredth of a second.

2.55 seconds

Zeros

100

Use the Factor Theorem to find the real zero(s) for the given polynomial function and one factor. Answer exactly.

𝑓⁡(𝑥)=4⁢𝑥3-𝑥2-85⁢𝑥+100;   𝑥+5

x= -5, 4, 5/4

200

Use the Rational Zero Theorem to find the real solution(s). Answer exactly.

𝑥³-3⁢𝑥²-12⁢𝑥+18=0

x= -3, 3+3^1/2, 3-3^1/2

300

Find all complex solutions (real and non-real). Answer exactly.

𝑥³+6⁢𝑥²+13⁢𝑥+20=0

Real: x=-4

Non-real: x=-1+2i, -1-2i

400

Use the Rational Zero Theorem to find all possible rational zeros for the polynomial function.

𝑓⁡(𝑥)=𝑥³+5⁢𝑥²+𝑥+12

+/- {1,2,3,4,6,12}

500

Find the dimensions of the box described. The length, width, and height are consecutive whole numbers. The volume is 504 cubic inches.

Length: 7 inches

Width: 8 inches

Height: 9 inches