SAT Math

Given an equation of f(x) and asked to evaluate

Define f(x) on desmos, then type in new f(x) equation and will give answer

Equation of a circle(center form)

(x-h)² + (y-k)² = r²

Variables in the question and answers

1. Pick values for variables, any that are NOT 1 and 0, different numbers, and if variables depend on each other then pick all but 1 and solve for 1

2. Re read the question with values plugged in and answer to find target value

3. plug in variables in answers to see which matches up

Given One equation where there is infinite solutions asked to solve for missing constant

1. Get both sides to ax+b form

2. both a’s must be the same and both b’s must be the same

3. So solve for variable to find this number

Given One equation with no solutions, asked to solve for constant

1. Get both sides in ax+b form

2. a’s must be the same but the b’s on both sides must be different

3. solve for variable

Given a System of equations with either no or infinite solutions

1. Get both equations in ax+by=c form

2. no solutions: set a1/b1 = a2/b2 and solve

3. Infinite: set previous OR c1/b1=c2/b2 and solve

4. double check answer on desmos

Given system of Linear equations with no missing constants, asked which point lies on the graph each equation, answers are coordinate points that include random letter

1. solve either equation for x in terms of y

2. If that’s not an option solve for y in terms of x

OR DESMOS:
Graph equations and then make slider for variable in points, graph each point answer choice

y=ax²+bx+c

a=up, down, narrow, wide

b=-b/2a tells you the x coordinate of the vertex, aka the axis of symmetry

c=y-intercept

y=a(x-h)²+k

h=x coordinate

k=y coordinate

a=up,down,wide,narrow

a(x-p)(x-q)

p and q show the x-intercepts/roots

A question about number of solutions given that there are 1,2, or no real solutions of a quadratic and solve for missing constant

DESMOS or

Use discriminant rules to solve for variable:

2 real solutions- b²-4ac>0

1 real solution- b²-4ac=0

No real solutions- b2-4ac<0

1 linear equation + 1 quadratic, solving for missing constant

If answer choices try on Desmos or….

1. Use substitution to combine equations

2. Get quadratic in standard form

3. Use discriminant rule to find missing value

Given a polynomial or table, asked about “factor” of it

1. find x-intercepts(the x when y=0)

2. factors of polynomials are (x - x-intercept)

Quadratic word problems

1. write down what x and y represent

2. use one of following definitions:

   y-int: y value when x=0 or initial value

   x-int: x value when y=0

   max/min: y coordinate of vertex

   x-value: where the function reaches max/min

Percents

Read carefully and translate into algebra

of - multiply

is - =

what is % - x/100

n% increase/decrease - 1+n/100 or 1-n/100

A percent question with no normal numbers given only percents

plug in 100 for the number you’re taking percent of

y=a(b)^x

a= y-intercept

b is <1 decrease b is >1 increase

Median from a list

The number in the middle of an ordered list from least to greatest

Can use Desmos

Mean

Average

Range

max-min

Standard deviation

measure of how spread out values are from mean

Questions involve sin and cos but not tan, include complementary angles

Rule if:

angleA + angleB=90 then sinA=cosB and sinB=cosA

Unit conversion or rate questions usually with more than two units

When converting units put them over each other(like a fraction) then multiply so you cancel units until you get correct ones.

Beware of square or Cubic Units you must square or cube the conversion factor

Given the equation of a graph and the coordinates of a point(s) on the graph

1. Plug the point in for x and y in the equation

2. Solve for any missing constants

What you should do to one ratio element to maintain the original ratio after changing the other element

If you add/subtract do not do the same to other instead make proportion

Word problems, 1 charge for first item(s) and a different charge for each additional item(s)

Find two points that can be found in the context of the word problem, use regression table to find equation

Percents but no real numbers

Plug in 100 for unknown variable

Given equation and x find y or vise versa

1. graph original equation

2. graph x=___ or y=___(whatever is given)

3. Intersection point is answer

Solve for one variable in terms of others

1. Make sure there is an x in original equation

2. Set sliders for all other variables

3. Graph original equation

4. Graph each answer choice as an equation

You are asked to solve for constants not solutions when given an equation or two equivalent expressions

Type in the first given equation and then a ~ then the next equation with the missing constants. Make sure a x’s are written as x₁

Create an x₁=[1,2,3,4,5,6]

What do I do when I’m stuck?

PI(plug in numbers)TA(Try answers)ME(Make an equation)

Word Problems with two unknowns

Write down what x and y represent

Make a system of equations

Given a normal system of linear equations, answers are points on a graph with constants(ex: (n,5/3n-8)

1. Graph either equation

2. Set a slider for the random letter in the answers

3. Graph each point and see which lies on line

y=original(1±r)^nt

“n times per t”

n= a number

t= unit of time

y=original(1±r)^t/n

“once every n t’s”

t= unit of time

n= a number

y=original(1±r)^at/b

“once every b/a t’s”

reciprocal! Flip a and b

a and b= numbers

t= unit of time

Asked to find arc length

Surface area of a cylinder

Given 3 points and asked to find area of a triangle

If any side is perfectly horizontal you can draw and easily find altitude and base length

If not then you must form a rectangle connecting the dots and find the area of that, and the three right triangles surrounding the triangle. Then subtract the three triangle areas with the total rectangle area

When given a “given that” statement in a probability question

Remember that will shrink the pool you are choosing from and will change the denominator. 

Solving for a missing constant in a quadratic when there are no real solutions

Start by asking can I use Desmos?

If not: b²-4ac<0

Solving for a missing constant in a quadratic when there is one real solution

Start by asking can I use Desmos?

If not:b²-4ac=0

Solving for a missing constant in a quadratic when there are 2 real solutions

Start by asking can I use Desmos?

If not:b²-4ac>0

Unit Conversion with square or cubic units

When a unit you are working with is squared or cubed the number must also be squared or cubed

ex: 1min² /60sec² is wrong it must be 1min²/3600sec²

Unclickable point when solving

Graph each side of the equation separately

If one side doesn’t include an x make it y=

Answer is the x coordinate of the intersection point 

Asked for Congruency or similarity of a triangle

Congruency rules: ASA, SSS, SAS, AAS

Similarity: Anything with AA or anything with proportional SSS, SAS

y=ab^x+c

a+c is the y-intercept

c=horizontal asymptote

Most commonly about room temperature

exponential function with “room temperature”

Room temperature will be the horizontal asymptote(The line it will never pass

y=ab^x-d

a is the y value when x =d

Point on graph (d,a)

y=ab^x-d+c

When x=d then y=a+c

Point on graph (d,a+c)

Given an Average/mean and the number of numbers(but usually not the numbers themselves)

Multiply the average times the number of numbers to find the sum of those numbers.

Probably use a fraction with adding and subtracting in numerator and the total in denominator

Median from histogram, frequency table, dot plot

n is the number of numbers-almost always given in the paragraph

n/2+.5 tells where the median falls

Interval Histograms, frequency tables, dot plots

impossible to find median, mean, etc. BUT can find max or min median, mean, ect.

Translations of lines in standard form

Always put line into y=mx+b form first and then apply function shifting rules.

Minimize/Maximize difference of mean/median for interval histograms

To minimize difference; make the bigger number smaller and the smaller number bigger

Maximize difference; Bigger number bigger and the smaller number smaller

drawing of right triangle

proportions

D=RT

HIGHER POLYNOMIALS