Precalculus S1 Review

chapter 1

100

Find the distance between (2,3) and (4,-5).

\sqrt(68)

200

Find the distance between (2,5) and (-4,13).

10

300

Find the slope between the points (2,5) and (-4,13)

-4/3

400

Find the slope intercept form of the equation that passes through (2,3) and the slope m=1/2

y=1/2x+2

500

Given f(x) = x^3-x if -1<=x<0

f(x) = x^3+x if 0<=x<=1

find f(1/2)

5/8

chapter 2

100

What are the domain and range of the function y=x²-1

D: All real numbers

R: y (greater than and equal to) -1

200

For the graph of the quadratic function, find the direction of the opening and the coordinates of the vertex. 

f(x) - 3(x-2)²+6

opens up 

vertex: (2,6)

300

Use synthetic division to divide 

(-9x⁴+10x³+7x²-6)/ (x-1)

-9x³+x²+8x+8+(2/x-1)

400

What would the equation of the function y=x² be if its vertex is moved 1 unit to the right and 2 units up?

y=(x-1)²+2

500

Find the inverse of 

f(x) = 3x-5

f^-1(x) = (x+5)/3

chapter 3

100

Evaluate log₂(1/8)

-3

200

Let Q represent a mass of radioactive radium (in grams), whose half-life is 1599 years. The quantity of radium present after t years if Q=25(1/2)^t/1599

^{(A) Determine the initial quantity (when t=0)}

(A) 25grams

300

Condense the logarithm 

1/2ln(2x-1)-2ln(x+1)

ln((2x-1)^1/2/(x+1)²)

400

Find the domain, x-intercept, and vertical asymptote of the logarithmic function. 

f(x) = log₅(x-4)

domain: x(greater than or equal to 4)

x-intercept: (5,0)

V.A: x=4

500

Solve the exponential equation algebraically. Approximate the result to 3 decimal places. 

-4(5^x)=-68

x=1.760

chapter 4

100

Given sin(60)=sqrt(3)/2 and cos(60)=1/2 find tan(60)

tan(60)=sqrt(3)

200

What is sin(135degrees)

sin(135degrees)=sqrt(2)/2

300

The angle of elevation from a point is 116 meters from the base of the Eiffel Tower to the top of the tower is 67(degrees). Find the approximate height of the tower. 

height: 273.28 meters

400

The angle of elevation to the top of the Egyptian pyramid Cheops is 36(degrees), measured from a point 350 feet from the base of the pyramid. Find the height of Cheops. 

height: 254.29 meters

500

A 50ft pole has a support wire that runs from its top to the ground with an angle of depression of 75(degrees). How far from the base of the pole does the wire connect to the ground? How long is the wire? 

the base of the pole connects to ground:51.76 ft.

length of wire: 13.4ft.