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# math for ACT

Question | Answer |
---|---|

IMAGINARY NUMBERS | NUMBERS THAT INVOLVE SQUARE ROOTS OF NEGATIVE NUMBERS |

EVEN NUMBER ARE DIVISIBLE BY | 2 |

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 |