# CSET 2: Math Summary

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 Author: hunnie_bebe ID: 199601 Filename: CSET 2: Math Summary Updated: 2013-02-13 17:17:18 Tags: CSET Math Summary Folders: Description: CSET 2: Math Summary Show Answers:

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1. Natural Number
Whole Number
Integer
Rational Number
Irrational Number
2. Prime Number
Composite Number
• Prime number: 2 positive integer factors
• 2,3,5,7...
• Composite number: other numbers
• 4,6,8...

1 is neither
3. Rules of Divisibility
4. Which expression below is incorrectly written in scientific notation?
A. 58x105
B. 5.333x10-9
C. 1.8x10-6
D. 4.92x1010
Scientific notation is the product of a number between 1 and 10 multiplied by a power of 10.

(a) should be 5.8x106

• 5.8 is a number between 1 and 10 and 58 is not
5. Zero Rule
Any number to the zero power equals 1 and not zero. This is so because the base is multiplied the exponent number of times so you are left with is 1

20 = 1
6. Rule of 1
any base raised to the power of 1 is itself

21 = 2
7. Negative exponents
look at the inverse operation of multiplication, which is division:

2-4 =
8. Product rules for exponents
when multiplying exponents w/ the same base, add the exponents and keep the same base

24 x 23 = 2 (4+3) = 27 = 128
9. Quotient rules for exponents
when dividing exponents w/ the same base, subtract the exponents and keep the same base

= 2 (4-3) = 2-1
10. Power rules for exponents
When an exponent is raised to another power,multiply the exponents and keep the same base

(24)-3 = 2 (4x-3) = 2 -12
11. multiplicative identity
a number is multiplied by 1 equals itself

365 x 1 = 365
12. commutative property
addition n multiplication stating the order in which 2 numbers are added or multiplied does not change their sum or product

• a + b = b + a
• 44 + 55 = 55 + 44

• a x b = b x a
• 25 x 5 = 5 x 25
13. associate property
addition n multiplication stating the grp of 3 numbers does not change their sum or product

• (a + b) + c = a + (b+c)
• (a x b) x c = a x (b x c)
14. distributive property
addition n multiplication stating that when multiplying a number by a sum or difference, you may either add/subtract first and then multiply, or multiply first then add/subtract

• a x (b+c) =a(b) + a(c)
• a x (b-c) =a(b) - a(c)
15. diving fractions w/ mixed numbers
• 1) write in fraction form
• 2) multiply first term by the reciprocal of the second term
• 3) write in simplest form

divide x = =
16. PERDMAS

please excuse my dear aunt sally PEMDAS
• left to right:
• Parentheses
• Exponents
• Roots
• Division
• Multiplication
• Subtraction
17. Flipping the inequality sign
occurs only when multiplying or dividing each side by a negative number; add/subtraction of terms from each side of an inequality does not change the direction of the inequality sign.

• -3x + 3 ≥ 12
• -3x ≥ 9
• x ≥ -3 change to x ≤3
18. Linear equations and their properties pg 274
19. System of equations pge 276
20. Linear equation y=mx+b pg 274
makes lines
21. quadratic equation ax2+bx+c=0 pg 280
finds a parabola that opens up and down (never sideways)

• x2 > 0 up
• x2 < 0 down

• x = -b/2a axis of symmetry of a parabola
• input "x" into the equation to find "y" to get
• coordinates (x,y)
23. Steps to graphing quadratic equation

y=ax2 + bx + c
1. Determine where the parabola opens upward/downward

a > 0 (up) or a < 0 (down)

2. Use the axis of symmetry formula to find "x"

x = -b/2a

3. Vertex of the parabola: substitute the x-coordinate into the equation to find the y-coordinate (x,y)

4. Determine the y-intercept: substitute x=0 into the standard form of the quadratic equation (0,y)

5. Determine the x-intercept: substitute y=0 into the standard form of the quadratic equation (x,0),(x,0) [zero property]

6. Draw the graph w/ the coordinates. Symmetric to the vertical axis
24. Pythagorean Theorem (right triangles only)
a2+b2=c2

the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse
25. Isosceles Triangle
Scalene Triangle
• Isosceles - 2 sides of the same length
• Scalene - no equal sides
26. Area: Parallogram = rectangle
• A=bxh
• A=lxw
27. mass and weight
• mass - amt of matter an object has
• weight - measure of how much gravitational pull is acting on it

proportional to each other
28. Temperature
C = 5/9 (F-32)

F = 9/5C + 32
29. Metric system
• Metric Prefix     Mathematical Value
• Mega-              Million
• Kilo-                Thousand
• Hecto-             Hundred
• Deka-              Ten
• Deci-               One-tenth
• Centi-              One-hundredth
• Milli-                One-thousandth
• Micro-              One-millionth
30. Length (US to metric)
• Length
• 1 in = 2.54 cm
• 1 ft = 30 cm
• 1 yd = .9 m
• 1 mile = 1.6 km
31. Weight (US to metric)
• 1 oz = 28 g
• 1 lb = 45 kg
• 1 T = .9 metric tonne (t)
32. Area (US to metric)
• 1 in2 = 6.5 sq cm
• 1 ft2 = .09 sq m
• 1 m2 = 2.6 sq km
33. Volume (US to metric)
• 1 fl oz = 30 mL
• 1 qt = .95 L
• 1 gal = 3.8 L
• 1 ft3 =.03 m3
• 1 yd3 =.76 m3
34. Metric Units
• Volume
• 1000 mL = 1 L
• 250 mL = 1 metric cup
• 4 metric cups = 1 L
• 1000 L = 1 kL

• Mass
• 1000 mg = 1 g
• 1000 g = 1 kg

• Linear Units
• 10 mm = 1 cm
• 100 cm = 1 m
• 1000 m = 1 km
35. US Units
• Volume
• 8 fl oz = 1 c
• 2 c = 1 pt
• 2 pt = 1 qt
• 4 c = 1 qt
• 4 qt = 1 gal

• Weight
• 16 oz = 1 lb
• 2000 lb = 1 T

• Linear Units
• 12 in = 1 ft
• 3 ft = 1 yd
• 5280 ft = 1 mi
• 1760 yd = 1 mi
36. Formulas
Perimeter
Area
• Perimeter (P)          Area (A)
• Triangle    = a+b+c           =1/2bh

Trapezoid  =s1+s2+b1+b   =1/2h(b1+b2)

Parallelogram =2(a+b)         =bh

Rectangle      =2(l+w)          =lw

Square          =4s                 =s2

Circle            =d or 2r         =r2
37. Formulas
Surface Area
Prism     =+ areas of each face

• Pyramid =+ areas of the base + each face

• Cylinder =
• (1) area of the 2 bases  r2
• (2) length (circumference value r) x height (width)
• (3) add the two values
38. Formulas
Volume
Prism     =Bh (area of the base x height)

Pyramid =Bh (area of the base x height)

Cylinder =r2h

Cone =r2h

Sphere =r3
39. Distance
d = rt
40. Graphs
• Line - show change over time
• Circle - part to whole relationships
• Bar - compare amts between grps
• Tally tables - record amts in general way
41. Mean, median, mode, range
• mean - avg
• median - middle number
• mode - occurs frequently
• range - difference between high and low number
42. Probability
Probability of an event =

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