Graph
Algebra
Vocabulary
Trig
Random
100
A line passes through
(2,3) and (6,11)
Find its slope.
(11-3)/(6-2) = 2
100
Solve:
5−2(3x−4)=4x+7
5−6x+8=4x+7
6=10x
x=3/5
100
What is cardinality?
The number of elements in a set.
100
This is the longest side of a right triangle.
Hypotenuse
100
Whos the greatest superhero ever???
200
Write the equation of a line with slope 3 and y -intercept -5 .
y=3x−5
200
Solve:
(2x-3)/4 - (x+5)/3 =2
Multiply by 12:
3(2x−3)−4(x+5)=24
6x−9−4x−20=24
2x=53
x=53/2
200
This transformation occurs when all y-values of a graph are multiplied by −1.
A REFLECTION across the x-axis
200
What does trigonometry study?
Relationships between sides and angles of triangles
200
Is this statement always, sometimes, or never true?
Squaring a number makes it larger.
Sometimes!
3^2 = 9 > 3
but (1/2)^2 = 1/4 < 1/2
300
Given
f(x)=2x^2−3
find f(−2) .
f(−2)=2(−2)^(2)−3
=8−3
=5
300
What is the quadratic formula?
x=(−b±sqrt(b^2−4ac))/ (2a)
300
What symbol means “is congruent to”?
≅
300
What does sin(theta), cos(theta), and tan(theta) equal to according to SOH-CAH-TOA?
sin(theta)= (opp)/(hyp)
cos(theta)= (adj)/(hyp)
tan(theta)= (opp)/(adj)
300
In a class, 12 students like basketball, 9 like soccer, and 4 like both. This many students like only basketball.
8
400
Line A has equation
y=−1/2x+7
What slope would a line perpendicular to Line A have?
Negative reciprocal:
2
400
Explain why the product of two consecutive integers is always even.
One of every two consecutive integers must be even, so their product contains a factor of 2
400
This set contains every element in the universal set that does not belong to A.
The complement of A (A')
400
Complete the exact value:
cos45∘=
sqrt(2) / 2
400
A line passes through (5,−1).
and (−3,7)
Find its equation.
First find the slope:
m=(-1-7)/(5-(-3))=-8/8=−1
Use:
y=mx+b
7=−(−3)+b
7=3+b
b=4
Therefore: y=−x+4
500
A line passes through (5,−1).
(−3,7)
and
(5,−1).
Find its equation.
First find the slope:
m=(-1-7)/(5-(-3))=-8/8=−1
Use:
y=mx+b
7=−(−3)+b
7=3+b
b=4
Therefore: y=−x+4
500
Given
f(x)=2x+3
and
g(x)=x^2−1 ,
find
(f∘g)(2) .
f(g(x))=2(x^2−1)+3
=2x^2+1
Plugging in 2 gives us 9
500
This is the set of all possible input values of a function, ___.
This is the set of all possible output values of a function, ___.
Domain and range
500
Without a calculator, evaluate:
(sin60∘)/(cos60∘)
((sqrt(3)/2)/(1/2))
=sqrt(3)
500
A rectangle has perimeter 50 units.
Its length is 5 units greater than its width.
Find its dimensions.
Let width =x.
Length:
x+5
Perimeter:
2x+2(x+5)=50
4x+10=50
4x=40
x=10
So:
Width=10, Length=15