SAT math, sat math part 2, omg

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The exponential graph increases below the X axis (from left to right) when _____ OR ______

"a" is NEGATIVE, b≥1, "c" is NEGATIVE OR "a" is NEGATIVE, 0<b<1, "c" is POSITIVE

The exponential graph decreases below the X axis (from left to right) when _____ OR ______

"a" is NEGATIVE, b≥1, "c" is POSITIVE OR "a" is NEGATIVE, 0<b<1, "c" is NEGATIVE

The exponential graph decreases above the X axis (from left to right) when _____ OR ______

"a" is POSITIVE, b≥1, "c" is NEGATIVE OR "a" is POSITIVE, 0<b<1, "c" is POSITIVE

The exponential graph increases above the X axis (from left to right) when _____ OR ______

"a" is POSITIVE, b≥1, "c" is POSITIVE OR "a" is POSITIVE, 0<b<1, "c" is NEGATIVE

How to solve: What is P percent of T?

(P/100) (t)

How to solve: S is P percent of what total amount?

(S/total) = P percent convert P percent to decimal

a² - b²

(a - b)(a + b)

Area of a sector (central θ in degrees) =

(central angle) / (360°) * (π * r²)

Area of a sector (when θ is in radians)

(central θ in radians / 2) * r²

x²-y²

(x + y) (x - y)

All points INSIDE of a CIRCLE follow the inequality

(x-h)² + (y-k)² < r²

general form of a circle

(x-h)² + (y-k)² = r²

All points OUTSIDE of a CIRCLE follow the inequality

(x-h)² + (y-k)² > r²

Absolute value graph parent function

- shaped like a V - f(x) = |x|

slope of a line in a Standard form linear equation

-(A) / B

For quadratic equations, the formula for sum of the solutions is

-(b)/a

The roots of the product (AC) method are

-(r)/a & -(s)/a

How to find the x-value of the vertex

-b /2a

If Solution A is 20% glucose by mass and we have "A" kilograms, then amount of glucose in Solution A is

0.2A

If Solution B is 30% glucose by mass and we have "B" kilograms, then amount of glucose in Solution B is

0.3B

When a value is increased by a percentage, you need to multiply the value by

1 PLUS the decimal form of the percent increase

{1, 2, 3, 2, x}, Mean = 4. Solve for x

1+2+3+2 =8 8+x / 5 values = 4 8 + x = 5*4 x =12

How to find the center given the 2 endpoints of a diameter,

1. (x1 + x2)/2 = X value of the center 2. (y1 + y2)/2 = Y value of the center

Paula bought a dress at a store that gave her a 30 percent discount off the original price. The total amount she paid to the cashier was "p" dollars, including a 9 percent sales tax on the discounted price. What represent in the original price of the dress in terms of p?

1. 0.7X 2. 9/100 +1 =1.09 3.You multiply with percentage so (0.7x)(1.09) 4. 1.09(0.7)(x) = P 5. Divide 1.09 and 0.7 6. p/ (1.09)(0.7) = X

If 6 guests are assigned to each table, 3 additional tables will be needed. If 12 guests are assigned to each table, 3 tables will not be used. How many guests are there?

1. 6 guests * 3 tables = 18 guests 12 guests * 3 = 36 guests. 2. 6(tables) + 18 = guests 12(tables) - 36 = guests 3. 6T + 18 = 12T -36 T = 72

product (AC) method

1. Find 2 numbers, r & s, that add up to (B) and equal (A*C) when multiplied r+s = B r * s = A*C

Kenny enlarged the area of the photograph to 150% of its original size. The original dimensions of the photograph were 3 inches by 5 inches. What is the area of the new enlarged photograph.

1. Find the area of the original dimension 3 x 5 =15 2. Realize the problem says enlarged TO 150% not BY so Area(1.5) equals the original dimension 3. 15(1.5) = 22.5

When given a set of data box plot and asked to find Q1 & Q3, you must

1. First find the position of the median 2. Divide that position by 2. (lets call the answer Y) 3. Add Y to the position of the median. This answer is the position of the value that makes Q3 4. Subtract Y from the position of the median. This answer is the position of the value that makes Q1

485] Greasy Stank slop has a serving size of 7/8 cup and provides 280 calories. Chris mixes Greasy Stank slop with Unctuous Stank slop for his breakfast. Unctuous Stank slop provides 300 calories per cup. If the total number of calories in one cup of Chris's mixture is 315, how much Unctuous Stank slop is one cup of the mixture.

1. Mark the Greasy Stank slop as "A", Unctuous Stank slop as "B" and the new mixture as C 2. Set up a proportion to figure out how many calories are in one cup of Greasy Stank slop. 7/8 = 280/ x 3. A + B = C 4. The question states that the mixture uses 1 cup, so C = 1 (A+B = 1) 5. Set up the other equation 320A + 300B = 315 6. Realize that A + B = 1, meaning that x + (1-x) = 1 7. 320(1-B) + 300B = 315 8. solve for B

Completing the square for Circle Equations

1. Move the constant term to the opposite side of the variable 2. Divide both sides of the equations by the coefficients of x² & y². (the coefficients must be 1) 3. Complete the square for the X terms & Y terms x² + bx --> (x + b/2)² y² + qy --> (y + q/2)² 4. Add (b/2)² & (q/2)² to the side with the constant

Victor gets paid 30% of the total retail value of the cars he sells, but he can also earn a bonus. When he earns a bonus, he is paid an additional 5% of his normal pay. During one pay period, Victor sold $8400 in used cars and earned a bonus. How much was he paid, in dollars, for this pay period?

1. Multiply 0.3(8400) 2. Multiply that value by 1.05

In a company, 15% are executives, 40% are programmers, 15% are graphic designers and the remaining 12 people are marketing representatives. How many more programmers are in the company than executives?

1. Notice that the percentages do not fully add to 100%, 15% + 15% + 40% = 70% 2. This means that the remaining 12 people represent 30% of the company 3. Set a proportion. 30/100 = 12/X X =40 4. Programmers are 40% / 0.4(40) = 16 5. Executives are 15% / 0.15(40) = 6 6. 16 - 6 = 10 Answer is 10 more people

The table shows the distribution of the number of sports that high school students play. If the number of students who participate in one sport(45%) is 80 more than the number of students who participate in two sports (20%), what is the total number of students at the school?

1. Realize that 0.45 * (the total) equals the number of students at the school 0.2 * (the total) + 80 equals the 0.45(T) 2. Set the equation to 0.2T + 80 = 0.45T and solve

The angles are acute and cos(a°) = sin(b°). If a = 5k + 15 and b = 4k -24, what is the value of k?

1. Realize that cos A = sin(90-A) or sin B=cos(90-B) 2. So either plug cos(5k+15) =sin(90-(4k-24) and solve for K OR 3. sin(4k-24) = cos(90-(5k+15) and solve for K

f(x) = 3x² + 5 and f(x+a) = 3x² - 24x + 53. What is the value of "a"?

1. Realize that if you add "a" to the original f(x) equation, the equation becomes f(x+a) 2. Plug (x+a) into the f(x) equation 3. Set the equations equal to each other 4. Match the equations

An escape room gives ratings from 0 to 100. In the first 8 ratings the escaperoom received, the average was 82. What is the least value the escaperoom can receive for the 9th rating and still be able to have an average of at least 90 for the first 15 ratings.

1. Realize that there are three parts to this problem. (The 8 ratings, 9th ratings, 10-15 ratings) 2. 90 * 15 values = 1350 ( the sum of all the values 3. 8 ratings*82 = 656 (sum of the first 8 values) 4. Realize to find the least value of the 9th rating, we need to maximize the value of the other 10-15 ratings. The average of 10-15 ratings (6 numbers) equals 100 5. 6 values * 100 = 600 6. 656 + 9th rating + 600 ≥ 1350 7. 656+600 = 1256 8. 1256 + 9th rating ≥ 1350 9. {1350-1256 = 94} 9th rating ≥ 94 Answer is 94

The function f(x) = x³ and the function g(x) = x³ - 2. Which of the following translations of the graph of "F" in xy plane causes the graph of "G"

1. Realize that there isn't any parentheses in the equation meaning that point has x=0 2. The y value equals = -2 3. This means that the value goes 2 units downward

Ex: (x-4)² + 2(x-4) -15 = 0

1. Replace (x-4) with the letter U 2. Write x - 4 = U 3. Solve for U 4. After solving for U, plug the answers into x - 4 5. Solve for X. This is your answer

In the equation, B(p) = 500(1.45)ᵖ, what is the growth B(h) that gives the number of bacteria as a function of hours,h, instead of as a function of 18 minute periods, p?

1. Set a proportion between P and H 2. Realize that the value that we are trying find equals 1 in the proportion so we're trying to find "h" so H = 1 3. P/H = /1 4. Ask how many times does 18 min fit in "H" 1 hr or 60 mins 60/18 5. Set the proportion P/H = 60/18 / 1 6. Solve for P (because we are replacing P in the original equation)

The equation, -12x²+28x-44 / ax -4 = -6x+2 - (36/ax-4), is true for all values of x≠4/a, where "a" is a constant. What is the value of "a"?

1. The quotient of this division equation is -6x+2. This means that -12x²/ax = -6x Basically, what number divided by -12 equals -6?

Franklin created a scale model of a bus where 1 inch on the model equals 4 feet on the bus. The length of the model is 9.3 inches. He makes a new model where 1 inch on the model equals 2 feet on the bus. How will the length of the new model compare to the old model?

1. The ratio of model to real bus is 1:4. 1/4 = 9.3/x x = 37.2. The length of the real model is 37.2 The new model's ratio to real bus is 1:2. 1/2 = x/ 37.2 x = 75 So the new model is 2 times the length of the first

How to figure out what the area will equal when both the length and width doubles OR when the length triples and the width doubles?

1. Write the formula for area. A = L*W 2. Follow the instruction of the question, let's say the length triples and the width doubles: Write: Area = 3L * 2W So Area is 6 times the L*W

How to figure out what the volume will equal when the length, width & height double OR when the length triples, the width doubles & height quadruples?

1. Write the formula for volume. V = L*W*H 2. Follow the instruction of the question, let's say the length triples, the width doubles & height quadruples: Write: Volume = 3L * 2W *4H So Volume is 24 times the L*W*H

A baseball coach uses the formula, K = ½mv², to find the kinetic energy of a ball moving with velocity, V, and the same ball moving with the velocity 2.5V. What is the ratio of the kinetic energy of the faster ball to the kinetic energy of the slower ball?

1. Write the ratio for K of fast ball to K of slow ball--> Kf/Ks 2. write the kinetic energy formula for Kf and Ks. 3. Replace the v in the Kf formula as 2.5v and in the Ks formula as V 4. Kf/Ks = ½m(2.5v)² / ½m(v)² 5. Cancel out ½m on the numerator & denominator 6. Because the question asks for ratio, convert 2.5 into a fraction--> 5/2 7. Distribute the ² in (5/2v)²/(v)² 8. It becomes (25/4 v²) / v² 9. Cancel out the v² 10. The answer is 25/4

What is the y intercept of the graph when y=2ˣ?

1. Y int means the value when X=0 2. Plug 0 into 2ˣ 3. 2⁰ = 1 4. The y int is (0,1)

To determine the median with a data set that has an even number of values (100 values in a dataset),

1. divide the number of values in the dataset by 2 2. The answer you get is the 1st position 3. Add 1 to the 1st position to get the second position 4. The median is between the 1st & 2nd position 5. After finding the values that make up those positions, add and divide them by 2 to get the MEDIAN

complete the square to get X

1. make sure the equation is in Ax² + Bx + C = 0 2. Move C to the other side of the equation, Ax² +Bx = C 3. Convert Ax² + Bx into (x+ (b)/2)² 4. Add (b/2)² to the side where C is & Combine 5. square both sides that are, (x+ (b)/2)² = C + (b/2)^2 6. After squaring the side of (C) + (b/2)², the answer must be written as "±" 7. Solve for the roots, zeroes

To recognize perfect square expressions

1. middle terms are products of 2 2. the last term & first term can be square rooted

The expression [ 5x + 23/ (x+4)² - 5/ (x+4) ] is equal to a /(x+4)², where a is a positive constant and x ≠ 4. What is the value of a?

1. set the expression equal to "a" /(x+4)² 2. multiply both sides by (x+4)² 3. Cancel the denominators of 5x + 23/ (x+4)² & "a" /(x+4)² 4. The (x+4)² cancels out the denom. in 5/ (x+4) but leaves 5(x+4) left. 5. Distribute and combine like terms to get "a"

2 < -3x + 2 < 8

1. subtract 2 from both sides 0 < -3x < 6 2. Divide by -3 0 > x >-2

No solution in a system of equations means

1. the lines are parallel 2. the lines do not intersect 3. the lines have same slope, different y intercepts

Infinitely many solutions in a system of equations means

1. the lines are the same line 2. the lines have the same slope and same y intercept

Using the formula [weight = 13/2 (height) + 15], and we wanted to see how much taller the object would grow to increase the weight by 1 lb,

1. we should set a proportion using the slope 13/2 2. Realize that 13/2 means (change in weight / change in height) 3. Match the values with the slope. 13/2 = 1/X 4. Solve for X

Solutions to a system (synonyms)

1. zeros 2. x coordinates of the points of intersection 3. "values that satisfy" 4. roots

With mixture problems, you need to set up 2 equations. What are they?

1st equation talks about the total amount of ONE THING 2nd equation talks about total amount of the mixture (the percentages)

A central angle of 2 radians intercepts an arc that measures

2 radiuses

Surface area =

2(height*length) + 2(length * width) + 2(width * height)

Pythag triple

20-21-29

Pythag triple

5-12-13

surface of a cube

6 * length²

Pythag triple

7-24-25

Pythag triple

8-15-17

aᵇ * aᶜ

= a ᵇ⁺ᶜ

X⁰

sum of interior angles

=180(number of sides - 2)

The factored form of the product (AC) method

A(x + (r)/a) (x+ (s)/a)

kx - y =3 y = x² - k In the system of equations above, "k" is a constant. When the equations are graphed in the xy-plane, the graphs intersect at exactly two points. Which of the following CANNOT be the value of "k"?

A) 2 B) 3 C) 4 D) 5 1. Move the y in the first equation 2. Set both equations equal to each other kx - 3 = x² - k 3. Move kx -3 to the other side of the equation. x² -kx -k +3 = 0 4. Realize the equation is in Ax² +Bx +C = 0 a = 1 b=-k c= -k+3 5. The problem states that the graph has an intersection at TWO POINTS meaning that there are TWO REAL ZEROS The equation is b² - 4ac >0 6. (-k)² - 4(1)(-k+3) = k² +4k -12 7. k² +4k -12 > 0 8. Factor out k² +4k -12 --> (k+6) (k-2) 9. (k+6) (k-2) > 0 10. k = -6 & k= 2 > 0 11. K has to be greater than -6 & 2 12. The answer is A.

The line of best fit passes through the point (15, -0.31). Which of the following can be concluded?

A) A hardware store cannot have more than 14 competitors B) A hardware store with 14 competitors cannot decrease in price any further C) A hardware store with 14 competitors can no longer sell screwdrivers D) The line of best fit will not model the price well for a store with a large number of competitors.

Which option yields exponential decay of the money and why?

A) Each successive year, 5% of the initial account balance is withdrawn from the account B) Each successive year, 2% of the initial account balance and $500 is withdrawn from the account C) Each successive year, 3% of the current value is withdrawn D) Each successive year, $500 is withdrawn from the account The answer is C because 3% is taken from every CURRENT value in the account. Taking money from the initial account makes it a linear relationship

The graph of the exponential function, h, in the xy plane where y=h(x), has a y intercept of "D", where "D" is a negative constant. What is the function?

A) h(x) = d(2)ˣ B) h(x) = d(-x)² 1. The formula is y = a * bˣ 2. So "D" is in the place of "a". 3. Realize that bc the y int is "D", when X=0, y=D 4. Plug 0 where the X is

When a system of linear equation has INFINITE solutions, the ratio

A1 / B1 = A2 / B2 C1 / B1 = C2 / B2

if a model car is built at a 1:20 scale,

ANY MEASUREMENT on the model will be 1/20 of the same measurement on the real car.

Formula for mean

Average = (sum of values) / (size of data set)

distance/time/speed equation

Average speed = (total distance)/(total time)

When parallel lines are written in Standard form, the

Ax + By = Ax + By C≠C x & y coefficients match in both equations

Standard form linear equation

Ax + By = C

When a system of linear equation has NO solutions, the ratio

Ax1 + By1 =C1 Ax2 + By2 = C2 A1 / B1 = A2 / B2 C1 / B1 ≠ C2 / B2

y intercept slope of a line in a Standard form linear equation

C/B

Radians =

Degrees * (π/180)

INSCRIBED ANGLE and its measure is

HALF THE MEASURE OF THE CENTRAL ANGLE

If Solution C is made by mixing Solution A (20%) & B (30%), and it contains "K" kilograms of glucose, what is the formula?

K = 0.2A + 0.3B

When a value X is increased by 200%, you need to multiply the value by what and why?

Multiply by 3 because 1 + 2 (the decimal form of 200) equals 3.

150 is 50% more than 100 (bc of 1.5*100), but 100 is

NOT 50% LESS THAN 150

Given the statement: X is 80% of Y, you should

NOT WRITE y=1.2x

If a jacket originally priced at "J" dollars was on sale for 10% off and you paid P dollars for the jacket, what is the equation?

P = 0.9(J)

The line of best fit in a scatterplot is a ________, so we must make __________ claims about the values it gives.

PREDICTION, GENERAL

For a polynomial p(x), the value of p(6) is 4. What is true about p(x)?

The remainder of p(x) when divided by (x - 6) is 4

How to find median of frequency table?

Use the Sum of the frequencies. They will tell you the positions of the values

high standard deviation

When all the values are more spread out and away from the mean (kinda forms a box if it was a bar graph)

low standard deviation

When all the values cluster/circle/focus around the mean (kinda looks like a peak)

horizontal line equation

Y = a number

percent change formula

[(New value - original value)/ original value] * 100

With frequency tables, the mean is equal to

[value(frequency) + value(frequency) + value(frequency) / sum of all the frequencies

For polynomial long division, you must STOP when

a constant is left over and write the (constant/divisor)

when the inequality sign is > or ≥, you shade

above the line

To determine the median with a data set that has an odd number of values (99 values in a dataset),

add 1 to the size of the data set and then divide by 2 to determine the POSITION of the median Ex: 99 values in a data set + 1 = 100 100/2 = 50. The median is in the 50th position

angles formed by crossing parallel lines

all the obtuse angles are equal to each other all the acute angles are equal to each other

In the formula to calculate percent change, the denominator is

always the original value

Perpendicular lines have

an opposite reciprocal of the other line

proportion w/ arc length & circumference

arc length / circumference = x° / 360°

(a+b)²

a² + 2ab + b²

(a-b)²

a² - 2ab + b²

1/a⁻ᵇ

aᵇ

aᵇ / aᶜ

aᵇ⁻ᶜ

when the inequality sign is < or ≤, you shade

below the line

When a polynominal raised to an even power, the line

bounces off the point

For quadratic equations, the formula for product of the solutions is

c / a

In the equation, weight = 13/2 (height) + 15, what does the slope mean

change in weight /change in height. An object that weight 15 lbs will increase by 13 lbs as the height increases by 2 inches

slope can equal

change in y value / change in x value

sin (x) =

cos(90 -x)

when the inequality sign is a < or >, the line is a

dashed line

density formula

density = mass / velocity

when you are unsure about the ratios,

draw a picture

When a polynomial f(X) is divided by a binomial x - r, the remainder is

equal to f(r)/ you must plug in "r" into the polynomial to find the remainder

When a polynomial f(x) is divided by a binomial, ax - r, the remainder is

equal to f(r/a)

When the b in y = a * bˣ less than 1 and greater than 0, this is called

exponential decay

When the b in y = a * bˣ greater than 1, this is called

exponential growth

A town's population grows by 2% every year after 2000, what is the function

f(t) = P(1.02)ᵗ

Vertical shift of a parabola equation

f(x) + k, the graph has shifted "K" units vertically

Cubic graph parent function

f(x) = x³

Horizontal shift of parabola equation

f(x-h), the graph has shifted "H" units horizontally

To find the area of a trapezoid

find the area of the rectangle find the area of triangle (1/2 b*h) add the two areas together

When you multiply or divide a negative number in an inequality

flip the SIGN

When asked to solve for a specific variable, you must

get that variable to one side of the equation

When a polynominal raised to an odd power, the line

goes through the point (X,0)

negative values of A in the quadratic formula for a parabola

graph opens downwards

positive values of A in the quadratic formula for a parabola

graph opens upwards

What is the vertex in vertex form [y = a (x-h)² +k],

h,k

center point of a circle

h,k

The x coordinate of the vertex is

halfway between the two roots

When a polynominal raised to an odd power and the power is over 1, the line

has a slight curve (a point of inflection) as it goes through the point

A parabola in vertex form, y = (x-h)² + k, has shifted...

horizontally "H" units and vertically "K" units to the point (h,k)

the slope can tell you

how many units the y value increases (decreases) as the x values increases

If the arc length is 100°, the arc length

is 5/18 of the circle's circumference bc 100°/360°

if table is two and a half times as long as it is wide, the ratio is:

its length-to-width ratio is 2.5:1

The key for perfect square expressions

look if the middle term is a product of 2

A parabola that is turned into an absolute value function has a graph that

looks the same but the negative values will be moved over the X axis

Model car/ real object or geographical area

m/r = 1/20

With some average problems, you will need to

maximize or minimize a value

When an average/mean question asks for the "least/smallest" value,

maximize the other "unknown" values to the highest given quantity stated in the problem. Ex: An escape room gives ratings from 0 to 100. Maximize all the other unknown ratings, meaning that the average of all ratings is 100.

When an average/mean question asks for the "most/largest" value,

minimize the other "unknown" values to the lowest given quantity stated in the problem.

how to go from percent to decimal

move the percentage two places to the left

How to find P% of a value, x?

multiply the decimal form of the percentage by the value, x.

With percentage you usually

multiply the values

In a triangle when two angles are exactly the same, the third angle __________ and the triangles

must be the same and the triangles must be similar

If you are given a rational function and asked for what values of x makes the function undefined, you

need to find the zeros of the denominator

Absolute value produces a

negative & positive answer

When a system of linear equation has ONE solution, the ratio

of X to Y coefficient for each equation/each lines DOES NOT EQUAL EACH OTHER

In parabolas written in quadratic function, negative coefficients

of the x² term make the graph open downwards

In parabolas written in quadratic function, positive coefficients

of the x² term make the graph open upwards

b²-4ac = 0

one real number zero

In standard form (ax² +bx +c =y), the sign of the X-coordinate of the vertex is

opposite the sign of the product, A*B

you have insert/plug in values, always put

parentheses () around the value

With divided triangles, do ratios between

part-to-part (on the same side) part-to-whole

with fractions, consider if they are asking:

part-to-part or part-to-whole

If you see a radical sign in the original equation,

plug in answers and make sure they're valid

If you see x² or a radical sign in the original equation, you should

plug in the solutions you got to make sure they are valid

With mixture problems, when a quantity is given (10 ounces or grams), you must

plug that number in for any variable

equation for percentage

portion of the total / total = percentage

Similar Triangles have sides that are_______ and angles that are_______

proportional / EQUAL

Answer of polynomial long division is written as

quotient + remainder/ divisor quotient (answer of a division question)

Degrees =

radians * (180/π)

intercepted arc length

radius * # of radians {from the central angle}

arc length =

radius * (central angle in radians)

Vertex Form by Completing the Square

replace the (ax² + bx) part with: A( x + b/2a)² - a(b/2a)² and combine like terms

How to solve: S is what percentage of T?

s/t * 100

Parallel lines have the

same slope, different y intercept

To find the intersection point of two inequality lines,

set the two inequality equations equal to each other and solve for X. Then, Plug X into one of the equations to find Y.

instead of instantly guessing with an answer, you should try to

set up a proportion/ratio for the values

when a question acts to figure out the ratio

set up a proportion/ratio with the quantities in the question

30-60-90 in a equilateral triangle

side across the 90 side/2 across the 30 (side√3)/2 across the 60

cos(x) =

sin(90-x)

when the inequality sign is ≥ or ≤, the line is a

solid line

Intersection points are the

solutions to the system of quadratic & linear equations

If you are given a system of equations with one linear equation and one quadratic question, use

substitution method to solve, set the 2 equations equal to each other

If a problem states that the price of something is raised by 5% and then decrease by 10%

that DOES NOT mean that the price dropped by 5% OVERALL

If you are asked to find the max or min coordinate value in a system of linear inequalities,

that coordinate must be at the intersection point

if you can't figure how to solve a problem that uses decimals, try to convert

the decimals to fractions

In question that discusses ratios, the "if" statement in the question prompt is

the denominator

When "a" in y = a * bˣ is POSITIVE,

the graph will be above the X axis

When "a" in y = a * bˣ is NEGATIVE,

the graph will be below the X axis

If you're told that lines are TANGENT to a circle, know that

the lines intersect the circle at ONE point. At the point, they make a RIGHT ANGLE

When you have an odd number of consecutive odd integers,

the mean -- the median will always equal 0

The value of the discriminant, b² - 4ac, will tell you

the number and types of zeros in a quadratic equation

if a plumber from California is chosen at random, then the denominator is:

the number of plumbers from California

Margin of error applies to ____ and ______

the population and the unit that is being measured

the length along the intercepted arc is EQUAL to

the radius of the circle

When a circle is drawn on the xy plane,

the side lengths can be negative or positive depending on which quadrant they're in radius is always positive

What is "a" in y = a * bˣ

the starting value, y intercept

When two terms with the same base are multiplied by each other,

their exponents will be added together

If the mean is significantly lower than the median, then

there are a few values that weigh less than the majority

If the mean is significantly higher than the median, then

there are a few values that weigh more than the majority

When two lines intersect at one point

they have different slopes and ONE SOLUTION

Two percentages that apply ...

to the SAME reference amount can be added and subtracted

Trapezoid can be divided into a

triangle and rectangle

when there are pictures in the question

try to form connections between the two things

b² - 4ac < 0

two complex number zeros

how to go from decimal to percent

two places to the right

b² - 4ac > 0 (positive)

two real number zeros

Factor Label method looks like:

undesired unit * (desired unit)/ undesired unit

When you do not know the length of the sides of similar triangles

use variables instead of solving

standard deviation is a

way to measure how closely clustered a data set is around the mean

When is the product (AC) method used?

when the A in Ax²+Bx+C is not 1

In parabolas written in quadratic function, x² coefficients with higher absolute values

will make the graph look narrower

In parabolas written in quadratic function, x² coefficients with lower absolute values

will make the graph look wider

In the form "y = a(x+p)(x+q), when a is negative the graph

will open downwards

In the form "y = a(x+p)(x+q), when a is positive the graph

will open upwards

| x + a | > b ???

x + a > b x + a < -b

Quadratic Formula

x = -b ± √(b² - 4ac)/2a

Vertical line equation

x = Number

Sector =

x°/(360° or 2π radians)

arc length (w/ radius) =

x°/360° * (2π * radius)

arc length (w/ circumference) =

x°/360° * (circumference)

Vertex Form

y = a (x-h)² +k

General form of Exponential Equations

y = a * bᶜˣ

If john eats 25% of 8 slices of pizza and George eats 50% of the 8 slices of pizza, can you add the percentages?

yes you can because they ate from the SAME 8 slices of pizza

If a problem tells you something "DECLINES by" 20%, then