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Semester 1 Problems Review
Semester 1 Definitions Review
Semester 2 Problems Review
Semester 2 Definitions Review
Important things to remember
100
Write f(x)= 3 (x-4)^2+6
= 3(x^2-8x+16) + 6 = 3x^2-24x+48+6 final answer= 3x^2-24x+54
100
Convert 5pi/6 from radians to degrees?
150 degrees
100
Find the range relation of {(-2,-3),(1,0),(5,-2)}
{-3,0,-2}
100
What are csc,sec,and cot equal to?
csc= 1/sin sec= 1/cos cot= cos/sin
100
What is SOHCAHTOA?
A way to remember sin,cos,and tangent
200
Simplify (x+3+4x^2)-3(x^2-2x+1)
=x+3+4x^2-3x^2+6x-3 final answer = x^2 + 7x
200
How do you decide whether to use long division or synthetic division when dividing polynomials?
Synthetic division=only works if the divisor is in the form of (x-some constant) such as (x-5) or (x+3) Long division=(2x+3) or (x^2-3)
200
Simplify: 12(x-1)-3(x-1)
=12x-12-3x+3 final answer=9x-9
200
Write the standard form of the equation of the line that has slope -3 and passes through the point (4,3)
3x + y =15
200
What is the quadratic formula?
-b+- b^2-4ac/2a
300
Solve the quadratic:n^2-3=2n
n^2+-2n+-3=0 n^2+1n+-3n+-3=0 n(n+1) -3(n+1)=0 (n-3)(n+1) n+-3=0 n=3 n+1=0 n=-1
300
What is the polynomial, describe end behavior, and give the leading coefficient? -3n^7+8+n^2-7n^6+5n-8n^4
Degree: 7 Leading Coefficient: -3 End behavior: downwards
300
Find the slope of the line passing through the points (-3,3) and (6,2)
y1-y2/x1-x2 = 3-2/-3-6 = -1/9
300
What is the tan of 270 degrees?
sin=0 cos=-1 tan=0
300
What the sin of a triangle?
Opposite/adjacent!
400
Condense to a single logarithm: 5 log z + 1/3log x
5/3log2x
400
How to write the inverse of each function using function notation?
A mathematical function (usually denoted as f(x)) can be thought of as a formula that will give you a value for y if you specify a value for x. The inverse of a function f(x) (which is written as f-1(x))is essentially the reverse: put in your y value, and you'll get your initial x value back.
400
solve the equation
2+ 3/x-1 =10 (x-1)2 + (x-1)(3/x-1)= (x-1)10 2x-2+3=10x-10 1=8x-10 11=8x 11/8=x
400
What are the degrees of the two special triangles?
30,60,90 and 45,45,90
400
Which quadrant(s) of the unit circle are tangent positive in?
1st and 3rd
500
Solve 6^.3x=64. Round answer to the nearest ten-thousandth?
log6^.3x=log64 .3xlog6/.3log6=log64/(.3log6) x=7.7371
500
What are the three log rules?
logb(mn) = logb(m) + logb(n) logb(m/n) = logb(m) – logb(n) logb(mn) = n · logb(m)
500
A boat travels at a rate of 15 kilometers per hour in still water. it travels 60 kilometers upstream in the same time that it takes to 90 kilometers downstream. What is the rate of the current?
upstream: distance= 60 rate= 15-x time= 60?15-x downstream: distance=90 rate=15+x time= 90/15+x 60/15-x=90/15+x 90(15-x)=60(15+x) 13509(-90x)=900+60x 450/150=150x/150 final answer: 3.014r
500
A lamp post casts a 48 foot shadow. The angle of elevation from the end of the shadow to the top of the lamp post is 58 degrees. Find the height of the lamp post.
tan58=x/48 48tan58=x x=76.82ft
500
What is the pattern of the y coordinates of a sine graph?
y= 0 a 0 -a 0