Pre-Calculus Quiz

Math

100

Solve the system of equations 

6x+3y =9 

x-7y=9

x=2

y=-1

200

Simplify 2(x-1)(x+1)

2x²-2

300

Factor 27+125y³​​​​

(3+5y)(9-15y+25y²)

400

Solve the equation 4x²-4x=24

x=-2

x=3

500

There are 50 deer in a particular forest. The population is increasing at a rate of 15% per year. Write an exponential growth function that represents the number of deer, y, in the forest after x years.

y=50e^0.15x

More Math

100

log₃ 27

3

200

Solve 3^x+4=9^x-1

x=6

300

Write log 5=0.7 in exponential form.

10^0.7=5

400

Expand log(xy²)

log x + 2 log y

500

Solve log₃(3x + 1) = 0

x=0

Trigonometry

100

Hypotenuse = 13 and one leg = 5. Find the other leg.

12

200

Opposite = 8, Adjacent = 15. Find tanθ

tanθ = 8/15

300

Convert 2pi/3 to degrees

120^o

400

Convert 80^o to radians

4pi/9

500

A 20-foot ladder makes a 30^o angle with the ground. Find how high it reaches. 

10 feet

Advanced Functions

100

Is this a polynomial: x³ - 2x^1/2 + 1?

No

200

What is the leading coefficient and degree of this polynomial: 4x⁶ - 2x - 3

Leading Coefficient: 4

Degree: 6

300

The graph of y=x² is translated down 6 units and left 4 units. Write the equation that represents the translated graph?

y=(x+4)²-6

400

What are the zeros of x² - 9?

-3,3

500

Given f(x) = 2x² and g(x) = -4x, find (f o g)(x)

32x²

Linear Models

100

Find the slope of the line passing through (2,3) and (5, 6)

m=1

200

Write the equation of the line with slope 3 passing through (2,5)

y=3x-1

300

Solve 

x + y = 10

x - y = 4

x = 7, y = 3

400

A phone company charges a fixed monthly fee of $25 plus $10 per gigabyte of data used. Find the cost for 6 gigabytes.

$85

500

For the function f(x) = 0.25 (6)^x identify the y-intercept. Write answers as decimals when necessary.

y-intercept: (0, 0.25)