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ACT Math
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Gravity
Terms in this set (73)
(A) Getting started stuff
If I assigned certain cards ("study the Bs, Cs, and Ds" or something) see the letter in parentheses on each card. If not, study all.
*If using the app*
Click the "cards" button
Click the settings icon in upper right corner
Turn on "Start with term"
Click the back arrow to go back to the deck
Read and try the first card
Click to flip it over
Star it if you didn't know it
Scroll down to go to the next one
(B) What are the steps for answering any math question?
1. look at the end and underline what the question is asking
2. scratchwork & strategies
3. Did you answer the underlined question?
(B) Which of these are even?
-5
-4
0
2
3,145
3,146
-4
0
2
3,146
(B) arsenal of strategies
1. use answer choices
2. plug in your own numbers
3. guess and check
(B) What's the definition of a rational number?
can be written as a fraction
(B) which of the following are rational?
i
0
.5
1.285
√2
π
6
0
.5
1.285
6
(B) smallest prime number
2
(B) What does "a set of distinct numbers" mean?
all different numbers, no repeats
(B) Is 0 positive?
no
not positive
not negative
non-positive
non-negative
(B) Give three multiples of 12
24, 36, 48, etc
(B) Give three factors of 12
2,3,4,6, etc
(B) which of these are prime?
0
1
3
5
7
9
3
5
7
(B) Is 3 a complex number?
Yes, because you can write 3+0i
(B) Which of these are integers?
-2
0
.5
1
2
345
-2
0
1
2
345
(B) When do you plug in answers?
This is the first thing to try when you get stuck on a problem.
Phrasing like "what is the value of x...?" and "for what value of b..." is a clue that using answer choices is likely to work.
(C) When do you make up your own numbers?
1. variables in the answer choices
2. changing fractions (the population of flies increased by 1/5...)
3. changing percents (the company marks up the price 10%...)
4. changing variables in an equation (what happens if x is doubled and y is halved?)
(C) What are the steps for making up numbers and getting an answer?
1. make up values and box them
2. get an 'answer' for your values using the QUESTION and box it
3. put your values into the answer choices
4. pick the one that matches
(C) What do you do when you see variables in the answer choices?
make up numbers
(D) What values should you always test for a must be/ could be problem (unless that value is prohibited by the question)?
-3 (a negative number)
0
.5 (a fraction/decimal)
1
2
100 (a big number)
(E) midpoint formula
(avg x₁ & x₂, avg y₁ & y₂)
(E) slope-intercept form of a line
y=mx+b
m is the slope and b is the y-intercept
(E) median
middle number
(E) slope formula
(y²-y¹)/(x₂-x₁)
(E) percent change formula
(amount of change/original amount)*100
(E) slope of a horizontal line
0
(E) mode
most frequently occurring number
(E) What is the slope of a line parallel to the line y=3x+4
3
(E) slope of a vertical line
undefined
(E) How do you find the equation of a line if you're given two points?
use (y₂-y₁)/(x₂-x₁) to find slope. Plug the slope and one of the points into the equation y=mx+b to find b.
(E) if f(x)=x²+2, what is f(3)?
11
f(3)=3²+2
anything in parentheses is an x value
(E) What trick can you use for hard average problems?
pretend every value is exactly equal to the mean
(E) if f(x)=x²+2 and f(n)=27, what is n?
5 (or -5)
27=n²+2
put whatever's in parentheses in for x
anything not in parentheses is a y-value
(E) A basket of apples contains red apples and green apples. There are 4 red apples for every 3 green apples. If there are 70 apples all together, how many are red?
40
(E) On the ACT, what are the three best ways to solve a system of equations?
1. substitution (solve for one variable, plug what you get in for that variable in the other equation)
2. elimination (line up, add or subtract left sides and right sides to get rid of a variable)
3. use answer choices
(E) What is the slope of a line perpendicular to the line y=-3x+4
1/3
(F) x²+x³=
NO!!
These do not simplify. 1²+1³≠1⁵
(F) How should you solve exponent questions?
Use exponent rules, then plug in a number to confirm your answer choice
(F) x²*x³=
x⁵
(F) (x²)³=
x⁶
(F) x³/x²=
x¹
(F) x⁻³=
1/x³
(F) How can you rewrite x^½?
√x
(G) area of a circle
πr²
you can remember this by remembering that area is in square units
(G) side lengths of a 45, 45, 90 triangle
x, x, x√2
(G) side lengths of a 30, 60, 90 triangle
x, x√3, 2x
(G) area of a triangle
½BH
(G) complementary
adds up to 90⁰
people compliment you on your posture if your back's at a 90 degree angle
(G) supplementary
adds up to 180⁰
you need vitamin supplements if you're 180 years old
(G) name two situations where angles add up to 180
The three angles of a triangle
any two angles along a line together
(G) what do you need to know about similar triangles?
They have the same angles. Set up a proportion and cross multiply.
(G) volume of three dimensional solids
area of the base * the height
(G) circumference of a circle
2πr or πd
(G) Pythagorean theorem
a²+b²=c²
c is the hypotenuse
(G) area parallelogram
(G) what's the area of an equilateral triangle with side length 4?
4√3 ≈ 6.9
(G) volume of a cylinder
πr²*h
(G) Bisect
split in half
(G) What's the area of a right triangle with side lengths 3, 4, and 5?
6
(H) what does the graph of (x+4)²+(y+3)²=4 look like?
A circle with a center point of (-4,-3) and a radius of 2.
(H) cosine graph
(H) Is the tangent of 4π/3 radians positive or negative?
positive
(H) How do you flip a parabola?
Put a negative in front of the equation
examples: y=-x²+2x+1 and y=-(x+3)²
(H) what does the graph of y=(x+4)²+3 look like?
A parabola opening upward with vertex (-4,3)
(H) How do you convert from radians to degrees?
π radians = 180°
(H) How can you recognize a sine graph?
Goes through (0,0)
(H) How can you recognize a cosine graph?
Goes through (0,1)
(H) What is the vertex of the parabola y=2x²-4x+11?
(1,9)
use x=-b/2a to get the x-value of the vertex, then plug it into the equation to get the y-value.
(H) quadratic formula
-b±√(b²-4ac)
--------------
2a
(H) sine=
opposite/hypotenuse
(H) cosine=
adjacent/hypotenuse
(H) tangent=
opposite/adjacent
(H) sine graph
(H) If two sides of a triangle are 4 and 7, what can the third side be?
3<x<11
Add the side lengths to get 11 and subtract them to get 3. The third side must be greater than 3 and less than 11.
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