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math for ACT

prime numbers are divisible by 1 and itself
composite number divisible by more than just 1 and itself eg..4,6,8,9,10,12,14,15...
squared means numbers are multiplied by themselves. eg..2x2=4 3x3=9 1,4,9,16,25,36...
cubed means numbers are multiplied by themselves twice 2x2x=8 3x3x3=27
triangle formulas perimeter=side+side+side area=1/2bh
square formulas perimeter=4s area=sxs or s2
rectangle formulas perimeter=2(b+h),or 2b+2h Area=bh or lw
parallelogram formulas perimeter = 2(l+w), or 2l +2w Area =bh
Trapezoid formulas perimeter = b1 + b2 + s1 + s2 Area = 1/2h(b1 + b2) or h(b1 + b2) -------- 2
circle formulas circumference = 2pieR or pieD area = pieR2
cube formulas Volume = s~s~s=s3 Surface area = s~s~6
rectangular prism Volume = l~w~h Surface area = 2(lw) + 2(lh) +(wh)
1/100 .01 1%
1/10 .1 10%
1/5 = 2/10 .2 .20 20%
3/10 .3 .30 30%
2/5 = 4/10 .4 .40 40%
1/2 = 5/10 = .5 .50 50%
3/5 = 6/10 = .6 .60 60%
7/10 = .7 .70 70%
4/5 = 8/10 = .8 .80 80%
9/10 = .9 .90 90%
1/4 = 25/100 = .25 25%
3/4 75/100 = .75 75%
1/3 = .33 1/3 = 33 1/3%
2/3 = .66 2/3 = 66 2/3%
1/8 = .125 .12 1/2 = 12 1/2%
3/8 = .375 = .37 1/2 = 37 1/2%
5/8 = .625 = .62 1/2 = 62 1/2%
7/8 = .875 = .87 1/2 = 87 1/2%
1/6 = .16 2/3 = 16 2/3%
5/6 = .83 1/3 = 83 1/3%
1 = 1.00 = 100%
2 = 2.00 = 200%
3 1/2 = 3.5 = 3.50 = 350%
3ft = yard
36 inches = 1 yard
1760 yards = 1 mile
5280 ft = 1 mile
5 1/2 yards = 1 rod
144 sq in = 1 sq ft
16 oz = 1 lb
2000 lbs = 1 ton
8 ounces 1 cup
2 cups 1 pint
2 pints 1 quart
4 quarts 1 gallon
8 dry quarts 1 peck
4 pecks 1 bushel
10 yrs 1 decade
100 yrs 1 century
kilometer = 1000 meters
hectometer (hm) 100 meters
dekameter(dam) 10 meters
10 decimeters 1 meter
1000 millimeters(mm) 1 meter
1000 milliliters 1 liter
1000 liters 1 kiloliter (kl)
terms of division quotient divisor dividend ratio parts
vertical angles formed by two intersecting lines,across from each other,always equal
adjacent angles next to each other, share a common side and vertex
right angle 90 degrees
straight angle, or line measures 180 degrees
angle bisector divides an angle into two equal angles
supplementary angles two angles whose total is 180 degrees
complementary angles two angles whose total is 90 degrees
what determines a line two points
parallel lines never meet; slopes are the same
perpendicular lines meet at right angles; slopes are opposite reciprocals(ex: 1/3 and -3)
polygon many sided (more that two) closed figure
regular polygon a polygon with all sides and all angles equal
triangle three sided polygon; interior is 180 degrees
equilateral all sides are equal
isosceles triangle two sides are equal
scalene triangle all sides are different
in a triangle- angles opposite equal sides are equal
in a triangle - an exterior angle is equal to the sum of the remote two angles
median of a triangle a line segment that connects the vertex and the midpoint of the opposite side
quadrilateral four-sided polygon interior angles total 360 degrees
parallelogram a quadrilateral with opposite sides parallel
rhombus a parallelogram with equal sides
trapezoid a quadrilateral with two parallel sides
pentagon five sided polygon
hexagon SIX sided polygon
radius of a circle a line segment from the center of the circle to the circle itself
diameter of a circle a line segment that starts and ends on the circle and goes through the center
chord a line segment that starts and ends on the circle
arc a part of the circle
to reduce a fraction find the common denominator
to multiply fractions line them up and multiply straight across
to divide fractions invert the second and multiply
to change a fraction to a decimal divide denominator into numerator
order of operation p.e.m.a.s
every fraction implies another fraction
a decimal is just another way to express a fraction
in an average question you should think total divided by #of things times average
3x + 7 = 28 first step is do the opposite of addition and subtract 7
3x + 7 = 28 the second step 3x = 28 get rid of the 3 do the opposite and divide both x=7
Act English, is (any form of the word be) IS THE SAME AS =
Act English, of product times x(multiply)
Act English, what a certain number x,y,z(your favorite variable
Act English, what percent x/100
Act English,more than, is added to the sum of increased by add
one equation and two variables can not be solved
working backwards on math questions is often easier
when you solve an inequality, remember if you multiply or divide by a negative number the sign flips
degrees in a circle 360
degrees in a quadrilateral 360
degrees in a line 180
degrees in a perpendicular angle 90
degrees in a triangle 180
in geometry, because the problems are always drawn to scale it will be possible to get very close approximation of the correct answers before you even do the problem
if you have no diagram draw one
Transitive axiom If a = b and b = c, then a = c. 1+3=4 and 4=2+2 then 1+3=2+2
cross multiplying notes Cross multiplying can be used only when the format is two fractions separated by an equal sign.
reflexive noting a relation in which each element is in relation to itself, as the relation “less than or equal to
axiom (a=a) a proposition that is assumed without proof for the sake of studying the consequences that follow from it.
Symmetric axiom if a=b then b=a
solving equations
cross multiplying in algebra Be aware that cross multiplying is most effective only when the letter you are solving for is on the bottom of a fraction.
Addition/Subtraction Method Combine equations to eliminate one variable. The equations may need to be multiplied by a common multiple first.
substitution method Solve one equation for one variable and substitute that variable into other equations.
grafting method Graph each equation on the same graph. The coordinates of the intersection are the solution.
to multiply Monomials add the exponents of the same bases: x4(x3) = x7. 9882.html#ixzz0knPnlwRf
to divide monomials subtract the exponent of the divisor from the exponent of the dividend of the same base: x8/x3 = x5.
add/subtract equations Combine equations to eliminate one variable. The equations may need to be multiplied by a common multiple first.
add/subtract polynomials add/subtract like terms only
multiply two polynomials multiply each term in one polynomial by each term in the other polynomial.
the f.o.i.l method first-outer-inner-last is often used when multiply binomial
binomial an expression that is a sum or difference of two terms, as 3x + 2y and x2 − 4x.
To divide a polynomial by a monomial divide each term by the monomial
to divide a polynomial by another polynomial make sure both are in descending order, then use long division (divide by first term, multiply, subtract, bring down).
distance is rate x time
interest is principal x rate x time
work accomplished rate of work x time worked
How many irrational numbers are between 1 and 6 there are an infinite number of irrational numbers between any two real numbers.
A number is divisible by 2 if its last digit is 0,2,4,6,8
A number is divisible by 3 if the sum of its digits is divisible by 3. 168 is divisible by 3 since the sum of its digits is 15 (1+6+8=15), and 15 is divisible by 3.
A number is divisible by 4 if the number formed by its last two digits is divisible by 4. 316 is divisible by 4 since its last two digits are 16 and 16 is divisible by 4.
A number is divisible by 5 if its last digit is either 0 or 5. 195
A number is divisible by 6 if it is divisible by 2 AND it is divisible by 3. 168 is divisible by 6 since it is divisible by 2 AND it is divisible by 3.
A number is divisible by 8 if the number formed by its last three digits is divisible by 8. 7,120 is divisible by 8 since its last three digits are 120 and 120 is divisible by 8.
A number is divisible by 9 if the sum of its digits is divisible by 9. 549 is divisible by 9 since the sum of its digits is 18 (5+4+9=18), and 18 is divisible by 9.
any number raised to the 0 power is 1 eg 1490 to the zero power = 1
any number raised sto the 1st power is itself 81 =8 raised to the first power
a negative sign applied to a group changes the sign of each term in the group -(a+b)= -a + -b -(a + -b) = -a + b
Rules for subtracting integers: # Change the problem to an addition problem. * Subtracting a negative becomes adding a positive. * Subtracting a positive becomes adding a negative.
Rules for adding integers: neg+neg=neg pos+pos=pos poa+neg subtract keep the sign of the larger number
Rules for multiplying integers: * A positive times a positive equals a positive. * A negative times a negative equals a positive. * A positive times a negative equals a negative. * A negative times a positive equals a negative.
Rules for dividing integers: # positive divided by a positive equals a positive. # A negative divided by a negative equals a positive. # A positive divided by a negative equals a negative. # A negative divided by a positive equals a negative.
To cube a number raise it to the third power
a root is the opposite of an exponent spuare root of 81 is 9..16 is 4
order of operations parentheses-exponents and roots-do all multiplication and division left to right -do what comes first do not do all multi than division do what comes first
Created by: carolyn495
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