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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 |
Created by:
carolyn495
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