Math SAT

vertex formula

x = -b/2a, make sure the equation is in ax²+bx+c

Mean score after something added or removed

Find the initial total score (so the initial mean times the amount of trials) then find the final total score (so the final mean plus or minus the initial amount of trials) then find the difference between the two and that is the score that was added or removed

Inscribed spheres

The side length of the cube or object is the diameter

C term rule

If you have 2 polynomials that are equal to each other then the c term is equal to the other c term, the b term is equal to the other b term and the a term is equal to the other a term.

Discriminant

b²-4ac, if that is positive there is 2 solutions, if it is 0 there is 1 solution, if it is negative no real solutions, if it is 0, 1 solution

make sure the equation is in ax²+bx+c

Exponent rules

Square root is a fractions as the exponent, negative exponents turn number into a fraction

SOHCAHTOA

cos(theta) = adjacent/hypothenuse, so to find a side plug in stuff you know, to find a angle you need cosine reverse of the two sides you know.

Inclinometer

Think about if the whole answer is raised by some amount of height depending on where the inclinometer is.

Vertex Formula

y = a(x-h)²+k

Final Term Rule

The final term of the polynomial is the product of all the factos of the polynomial(so (x+1)(x+p) has a c vlue of p, this is only when the a term = 1, otherwise the sum of the solutions is proportional to the c term (if the sum of the solutions is 4 and the c term is 16 than the a term has to be 4(because 4/14 and 1/4 - sum of solutions equation/actual equation)… only the proportional relationship between a term and c term

Cross Multiplication

Can be used for percentages

Ratios

When it says the ratio of boys to girls is 7 to 3 that means that for every 10 people 7 are boys and 3 are girls therefore divide the whole group by 10 (how many groups of boys and girls there are)and then multiply by 7 or 3 to find the amount of boys or girls in the whole group

Ratios

Convert things into the squared version or the normal version based on the initial measurement you get

Similar triangles/ratios

Any 2 sides can be proportional to the same 2 sides on a similar triangle. This can be set up as a fraction of either T1S1/T1S2 = T2S1/T2S2 or it can be T1S1/T2S2 = T1S2/T2S2

Area scaling

When you get the area and only the length or width is scaled down you should assume the other is also scaled down to fit the question, so therefore you square the scale and then apply that to the initial area

Point Slope Form

y-y1 = m(x-x1)

When In Doubt

Just plug numbers in, and follow any restrictions in the problem.(but if no restrictions just try it)

Calculator

Use regression wherever you can, its very helpful

Cant tell the answer on the calculator

Lets say you are trying to find the answer to |3x-1|=2, Instead of doing that make it |3x-1|=y and then create a second equation with y=2, then you can easily see the answer because it will be the intercept of those two equations

Usage of discriminant

To use the discriminant make sure all GCF’s are taken out and the equation equals 0 on the other side

Same X intercepts

If two quadratics have the same x intercepts that means they have the same zeros, therefore the a,b, and c terms will either be equal to each other or will be a factor of each other(like c for one equation = 12, and the other c = 36). Just make sure in these problems to find all of the terms in on of the equation and have one term in the other equation to know the scale.

Rate of Change

When you have 2 things being done at different speeds if you combine those two speeds thats how long it would take if both of those things happened at the same time(so you can find out how long it takes to fill a bath tub from two different water sources that are at two different speeds.

Density

d=m/v

Dimensional Anaylsis

The unit your trying to cancel out has to be on the opposite side of the denominator or numerator, and if you are trying to convert seconds to minute squared just do the conversion of seconds twice, so multiply it by 60 seconds/1 minute and then again 60 seconds/1 minute

Spinning ratios

For questions that have the diameter or radius and something spinning at a certain rotation per time unit. First calculate the circumference and that is how far the object is moving per rotation, then multiply that by the rotations and that is how fast the object is initially moving per time unit

How many times something gets done in a certain amount of time

If you have a rate of speed like 3 carrots per 2 hours eaten and you need to find how many carrots are eaten in a hour all you have to do is divide 1 by 3/2. You can also use this with other time units if you convert them to the same time units

Usage of C term rule

Try to get the coefficients of the x² term and the x term to be one thing times x² or x. For example (b-1)x instead of bx-x

Equivalent Equations

When you are given one quadratic or polynomial without any unknown variable that is equal to another quadratic or polynomial with a lot of unknown variables, plot the quadratic you can( it can help a lot)

Equivalent expressions with fractions

Sometimes to make it less complicated just set the 2 polynomials equal to each other and do cross multiplication(especially when only one of the polynomials is a fraction)

Finding the b term

If you have the equation and it gives you the a term, the c term and a the y coordinate of any point then you can plug in what you know and replace the b term for y. Like so 11.5 = -5x²+yx+10 and the bottom of the curve/top of the curve will be the answer

Arc

The arc created by a angle is the angle itself. For example if the arc length is 8π then that is the portion of it of the circumference. Since the circumference is 2πr once you figure out the circumference which is 24π in this case you know that the angle is 1/3 of the total amount of degrees in a circle which is 120(24π/8π = 360/120)

central angle

An arc length created by the angle in the middle of the circle is equal to the angle in the middle of the circle. But to convert that arc length to pie from the center angle you have to think about the percentage that the central angle is out of 360 degrees, and then apply that proportion to 2pie

inscribed angles

These are when an angle is not a central angle but it is the same arc length as a central angle, this means it is half of the central angle. So convert that arc length to a central angle degree and then half it for the inscribed angle

Tangent

A line tangent to the circle is perpendicular to the line formed from the center of the circle

Radical

When converting things inside a radical both things inside the radical have to be given the fraction exponent

Equation Of a circle

(x-h)²+(y-k)²=r²

Word Problems with changing rates

If the rates of change changes after a certain x amount and it asks for the equation after the changed rate of change then you have to include that you are not counting the initial rate of change x values. You can do this by making a equation like y = 2.5(x-19)+76. This is because we don’t count the intial x’s in this equation but we still need a x intercept that starts at that x value so in this case the rate of change was 4, therfore 19 times 4 = 76 so thats the y intercepts but you discard the x’s

Interior Angle

(n-2)*180 = sum of the interior angles

Special Right Triangles

x,x,x√2 - x,x√3,2x

perfect square quadratics

If the quadratic is a perfect square then (b/2)² = c. You can know if there is a perfect square if the highest exponent is greater than the amount of solutions. Then just find the perfect square part of it and your set

Volume Scaling

If it is scaling the volume up 50% from a initial volume and is asking how the radius/height changed makes sure to not include π in the equation and if the radius is being scaled up remember to square the scale for example. 1.5v = (1.18r)²hπ, to find what the scale of the height has to be for the volume to increase 50% square the 1.18 which is being applied to the radius(because the equation is r² if the equation was r³ than you cube the scale) and discount π because that is constant in both equations so the equation would be 1.5v = (1.18r)²h, then solve for h and the coefiecent is the scale that needs to be applied to h

Degrees to Radians

Degrees*(π/180)=

Radians to Degrees

Radians*(180/π)=

Complementary angles

The sin of one complementary angle(they add up to 90) equals the cos of the other complementary angle. Therefore sin(90-x) = cos(x), cos(90-x) = sin(x)

Triangle congruency

Either all sides are equal(SSS), 2 sides are equal and the angle between those sides are equal(SAS), 2 angles and the side between them are equal(ASA), two corresponding angles and a non included side of the triangles are equal

Transformations

If you want to see how transformations affect a polynomial just do f(x)= 2x² , and in the next line do g(x)=f(x-2)

Commas

Connect independent and dependent clauses, commas can also be used after a introductory word,phrase, or clause - for example: (Before digital cameras,) or (in 1986,). Also use it before FANBOYS to connect independent clauses. Also to add unneeded information - For example: My car, which is blue, is in the garage. Also to separate month and day from year, and to separate city from the state or the country in a address.

Semi Colon

Before lists, or connects two independent sentences when those sentences are closely related

Colon

Introduces a list, an explanation,example,or quotation that is preceded by a independent clause

Commas Continued

Use commas to introduce quotations. For example: She said, "I love you". Or use a comma between adjectives that describe the same thing, For example: He bought a new, shiny car.  Finally you can use commas to set off titles or to indicate direct address. For example: My friend, Sarah, is coming to visit. 

Slider

If it asks for a question with one variable that is unknown and it isn’t a multiple choice question, just use a slider. For example what is the lowest number that c could be to have this quadratic have no solutions… then just put the quadratic into the calculator and use a slider

arc length

radius*angle = once converted to radians

Area of a sector

(degrees/360)*pie*r²