ACT

Punctuation, Commas

Extra information

Punctuation, Commas

Extra information

Dash or comma on either side

Usage and Mechanics

Avoiding Redundancy

Restating already shared information

Transitions: Same Direction v.s. Contrast

Transitions steps

1. Are the transitions needed

2. If so, form a bridge, determining whether in the same or a different direction

Usage and Mechanics

Moving, deleteing, or adding

Portion should be related to all parts of what comes before and after it

Usage and Mechanics

Main Goal

If it is the main goal, all paragraphs should give details on it.

Negative number to odd power

keep negative

Negative number to even power

becomes positive

Logarithms Solving: Rewriting Logarithms

Logx#=n

Ex: logx36=2

x^n=#

x²=36

Graphing points on a line

A,B,D,C

If B is between A and C

D is between B and C

CD<BC because CD is within BC

Log base is never

never negative

Order of operations

PEJMDAS, left to right

Coefficient

Number next to the variable

Constants

Real numbers

Algebra Fundamentals:Key Definitions

Greater Common Factor GCF

Largest Number that Goes into Both

Main Graphs and Transformations:

Porabola Vertical Axis of Symmetry

Vertical

Triangles: Pythagorean Theorem

a²+b²=c²

leg²+leg²=hypotenuse²

Geometry Fundamentals: Angles and Coordinate Plane

Slope

(Δy)/(Δx)=

(rise)/(run)=

(amount up or down)/(amount left or right)

Up and right: positive +

Down and left: negative -

Altitude of triangle

Vertical distance between vertex and base

(y-coords of vertex)- (y-coords of base)

Probability:Basic Probability

Probability of n

P(n)

x!

multiply all numbers from 0 to x

Product of all positive integers less than or equal to x

2!= 2×1= 2

Graphing sine and cosine; Graphing cosine

Amplitude

how high up and low down below and above the midline

coefficient in front of a trig function

Ex: ½cos (3x+pi)

½=amplitude

x*-x

-x²

Rare and Random: Matrices

row*column

r*c

Ex: [2×2]

2 rows, 2 columns

Rare and Random: Matrices

Multiplying Matrices

Must have same inner numbers, or undefined

Ex: [2×3][3×2] can multiply, while [2×3][4×3] undefined

Main graphs and transformations

General form of porabola

y=x²

Linear Systems Word Problems

How to cancel base of power

log on both sides

10(2x-1/x)=1
(2x-1)/x=log10 1

Probability: Advanced Probability

(want)/(total possible)

Distance and Average Speed: Average Speed

distance/time

Distance and Average Speed

1 Rev

Circumference

Circumference

πd

Solving Radicals and Exponents: Simplifying Radicals

Simplify x^√

x^1/n

Ex: √3=3^1/2

Solving Radicals and Exponents: Simplifying Radicals

Exponents Equal

Exponents equal when bases the same

Ex: 3²=3^x

x=2

Solving Radicals and Exponents: Simplifying Radicals

Solve Equation with Radicals

Want both sides to have the same base

Mean, Median, and Mode

Arithmetic Sequence

± the same # between each terms

Ex: .75, 1.75, 2.75, 3.75, 4.75, 5.75, 6.75

Mean, Median, and Mode

Mean the same as Median

An arithmetic sequence, add app up and divide, get the middle term

Ex: .75, 1.75, 2.75, 3.75, 4.75, 5.75, 6.75

Circles: arc length

θ/360

arc length/circumference

arc length/πd

Law of Sines: Area of a SAS Triangle

½(ab)(sin c°)

Probability: Advanced Probability

Expected Value of x given different values of x

1. Multiply all (x values) by the (probability of x values)

2. Add all of them together

Natural Science (Dual)/Social Science (Single) Specific Information

Don’t try to remember, find where it is introduced and read carefully

Science ACT tips

1. Don’t read for the data representation (graph) sections

2. Always Refer back fro debating scientists sections and experiments

3. Watch for trick questions where all agree on IF, but not HOW

4. Check units

5. Read the questions carefully and check for trick answers

6. Focus on the study with the most detail that rather than just saying the “repeated the steps of X study“

Experiments: Identifying Mathematical Relationships and Trends

Balanced Chemical Equations

The ratios of coefficients of chemicals in a chemical equation must remain balanced

Ex:

(Ni^2+)+(2Oh^-)+(H2O)=Ni(OH2)H20»»

(3Ni²+)+(6OH^-)+(3H2O)=3Ni(OH2)H2O

Experiments: Understand Experimental Design

Control

One where the independent variable is kept constant for comparison

Experiments: Find details from figure, table or diagram

Metric unit conversions

Experiments: Understand basic Scientific Content

Equation for Photosynthesis

Plants take in water, light, and carbon dioxide, then produce glucose (sugars) in their leaves for energy, and oxygen which humans breathe:

Carbon dioxide+water+light→glucose+oxygen

Experiments: Understand Scientific Design

Minimum and Maximum

Least and greatest amount

Experiments: Understand Scientific Design

y=0

Completely straight line, doesn’t go up or down

Experiments: Understand Scientific Design

Absolute value/Magnitude

Getting further away from 0

Experiments: Understand Scientific Design

Like and Opposite charges

Like charges repel

Opposite charges atrtact

How to evaluate for f(x) for c

1. Rewrite the equation

2. Plug in c for every x in the equation

How to solve for composite functions

1. Take f(x) and plug it into g(x) function etc.

Combining Units When Adding and Subtracting

1. Goal is to get the x on one side and numbers on the other

2. Need to be very careful that operations are performed on both sides

3. Make sure to remember rules about solving absolute value, simplifying exponents, combining fractions, and distributing negative signs

Multiplying & Dividing in Algebraic Equations

1. Goal is to get x on one side and numbers on the other

2. Be careful to perform operations on both sides

Linear Equations for Word Problems

1. Read the problem carefully to define the variables of interest (for which you are solving)

2. Create the linear equations based on the information in the problem

3. Use substitution or elimination to solve for one of the variables

4. Solve for the other variable based on your answer in 3.