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AICE Math 1 Review Flashcards | StudBud
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AICE Math 1 Review
AICE Math 1 Review
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1
State the transformation of f onto g in vector form for g\left(x\right)=f\left(x+2\right)+3 !IGNORE THE FRACTION BAR!
Translation by the vector \left(\frac{2}{3}\right)
\left(\frac{-2}{-3}\right) Translation by the vector
\left(\frac{2}{-3}\right)Translation by the vector
\left(\frac{-2}{3}\right) Translation by the vector
2
Slope (gradient) formula
\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}
\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)
y=mx+b
\frac{y_2-y_1}{x_2-x_1}
3
Formula for the axis of symmetry of a quadratic in standard form, ax^2+bx+c
y=mx+b
x=\left(\frac{b}{2}\right)^2
b^2-4ac
x=-\frac{b}{2a}
4
To find the area under a curve...
Integrate and then plug the x (or y) valued limits of integration, subtract
Differentiate for sure
Just draw the swooshy integral symbol and call it a day
Integrate and add +c
5
The symmetry property for solving \cos x=k is
90 - x
2x
180 - x
360 - x
6
To find the tangent to a curve
Need a point and a slope, guess
Need a point and a slope, slope is found using derivative
You don't need a point and a slope
Need a point and a slope, use the slope formula
7
If f\left(x\right) is decreasing, then
Who is derivative?
f'\left(x\right)=0
f'\left(x\right)<0
f'\left(x\right)>0
8
To find the inverse of a quadratic it must be
in completed square form or vertex form
in standard form
a fraction
cube root
9
We like right triangles, because
we just don't though...
we can use trigonometry and the Pythagorean theorem
we can use the sector formula
pointy
10
In order for a function to have an inverse, it must be
one to one, pass the horizontal line test
quadratic
periodic, repeat itself horizontally
purple
11
This is the integration formula\int_{ }^{ }x^ndx=\frac{x^{n+1}}{n+1}+c
False
True
12
How do you go from \frac{dy}{dx} to the original curve?
Differentiate
Binomial expansion
Integrate
Switch x and y and solve for y
13
Find the range of g\left(x\right)=-3\left(x+3\right)^2-4, for x\ge-3
g\left(x\right)\le-4
g\left(x\right)\le-4
g\left(x\right)>-4
g\left(x\right)\le-4
14
The tangent and normal (or the tangent to a circle and the radius) are
Merry Christmas
best friends
intersect at the point of tangency on the curve and are parallel
intersect at the point of tangency on the curve and are perpendicular
15
The symmetry property for solving \sinθ=k
2x
360-x
90-x
180-x
16
The period of sine and cosine parent functions are
\pi
2\pi
\frac{\pi}{2}
100000\pi
17
180 degrees is
\pi rad
the degrees in a full circle
2\pi rad
\frac{\pi}{2} rad
18
fg\left(2\right) means
plug 2 into g and then plug what you get into f
substitute f inside of g, then plug in 2
multiply the functions f and g, then plug in 2.
plug 2 into f, then plug what you get into g
19
\sin^2θ=\cos^2θ-1
True
False
20
When you see a right triangle in a circular measure problem immediately think
SKIP!
trigonometry (soh, cah, toa)
about what you are eating for lunch
what you ate for breakfast
21
The tangent and normal (or the tangent to a circle and the radius) are
Merry Christmas
best friends
intersect at the point of tangency on the curve and are parallel
intersect at the point of tangency on the curve and are perpendicular
22
To find where a line intersects the x-axis
substitute x = 0
substitute y = 0
substitute x = 0 and y = 0
SKIP!
23
Volume of revolution about the x-axis formula is
\pi\int_a^by^2dx
\frac{1}{2}bh
\pi\int_a^bx^2dy
\frac{1}{2}\left(b_1+b_2\right)h
24
When you have to differentiate a composite function...
Don't use the Chain Rule
SKIP
Use the Chain Rule (outside/inside)
Use the Product Rule
25
How do you find the graph of an inverse function given the graph of the original function?
Switch x and y and solve for y.
Reflect the function over the x-axis, change the signs on all y values
Reflect the function over the y-axis, change the signs on all x-values
Reflect the function over the line y=x, swap all (x, y) coordinates
26
stationary point at x = a
f'\left(a\right)\ne0
f'\left(a\right)=0
27
How do find the domain of an inverse function?
Find the range of the inverse function first
Find the domain of the original function
Swap x and y and solve for y.
The domain of the inverse is the range of the original function
28
3f(x) is a stretch along the x-axis by a factor of 3
True
False
29
If a quadratic equation does not factor, it does not have solutions.
Factor anyway, it'll be okay
Check your work to be certain, but then use the quadratic formula
SKIP!
You definitely messed up
30
When solving a series question...
run, hide, scream
a = common difference, r = first term, n = term number
start to solve it in your head
givens, formulas, substitute
31
Connected rates of change formula
\frac{dy}{dx}=\frac{dy}{dt}\times\frac{dx}{dt}
\frac{dd}{dd}=\frac{dd}{dd}\times\frac{dd}{dd}
\frac{dy}{dt}=\frac{dy}{dx}\times\frac{dx}{dt}
\frac{dy}{dx}=\frac{dy}{dt}\times\frac{dx}{dt}
32
The following is a nice formula for arithmetic sequences that is not on your formula sheet
r=\frac{u_n}{u_{n-1}}
A=\pi r^2
d=u_n-u_{n-1}
Percentage increase or decrease is always geometric
33
The connected rates of change formula is on your formula sheet.
False
True
34
The discriminant
determines the number of solutions or points of intersection to quadratic
find the slope of the curve/tangent line
find the perpendicular slope
means there are no solutions when it is greater than zero
35
When you see a triangle like this, you can use this formula to find the area.
A=bh
A=\frac{1}{2}r^2hijkl\sinθ
A=\frac{1}{2}r^2θ
A=\frac{1}{2}r^2\sinθ
36
f(3x) is a stretch in the x-direction by a factor of 3
False
True
37
Derivative formula
idk man
Just look at your formula sheet, the exponent gets divided goes up one.
Just look at your formula sheet, the exponent gets mult and goes down one.
never use your formula sheet
38
3f(x) is a stretch along the x-axis by a factor of 3
False
True
39
Select the equation for a circle.
\left(x+a\right)^2-\left(y+b\right)^2=r^2
y=a\left(x-h\right)^2+k
\left(x-a\right)^2-\left(x-b\right)^2=r^2
\left(x-a\right)^2+\left(y-b\right)^2=r^2
40
Any time you have an equation where one exponent on a variable is double another
SKIP!
create a quadratic, u-world
square root the entire equation
cancel it out
41
When substituting into the binomial expansion formula, you will
remember parentheses but not bring the exponent to every factor
forget to use parentheses
remember parentheses and bring the exponent to every factor
not simplify all terms
42
\left(x+4\right)^2+\left(y-3\right)^2=25
Center is (-4, 3), r = 5
Center is (4, -3), r = 25
Center is (-4, 3), r = 25
Center is (4, -3), r = 5
