CSET 2: Math Summary

• Prime number: 2 positive integer factors
• 2,3,5,7...
• Composite number: other numbers
• 4,6,8...

1 is neither

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

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

any base raised to the power of 1 is itself

2¹ = 2

look at the inverse operation of multiplication, which is division:

2^-4 =  =

when multiplying exponents w/ the same base, add the exponents and keep the same base

2⁴ x 2³ = 2 ⁽⁴⁺³⁾ = 2⁷ = 128

when dividing exponents w/ the same base, subtract the exponents and keep the same base

= 2 ^(4-3) = 2^-1

When an exponent is raised to another power,multiply the exponents and keep the same base

(2⁴)^-3 = 2 ^(4x-3) = 2 ^-12

a number is multiplied by 1 equals itself

365 x 1 = 365

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

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)

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)

• 1) write in fraction form
• 2) multiply first term by the reciprocal of the second term
• 3) write in simplest form

divide =  x = =

• left to right:
• Parentheses
• Exponents
• Roots
• Division
• Multiplication
• Addition
• Subtraction

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

makes lines

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)

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

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

• Isosceles - 2 sides of the same length
• Scalene - no equal sides

• A=bxh
• A=lxw

• mass - amt of matter an object has
• weight - measure of how much gravitational pull is acting on it

proportional to each other

C = 5/9 (F-32)

F = 9/5C + 32

• Metric Prefix     Mathematical Value
• Mega-              Million
• Kilo-                Thousand
• Hecto-             Hundred
• Deka-              Ten
• Deci-               One-tenth
• Centi-              One-hundredth
• Milli-                One-thousandth
• Micro-              One-millionth

• Length
• 1 in = 2.54 cm
• 1 ft = 30 cm
• 1 yd = .9 m
• 1 mile = 1.6 km

• 1 oz = 28 g
• 1 lb = 45 kg
• 1 T = .9 metric tonne (t)

• 1 in² = 6.5 sq cm
• 1 ft² = .09 sq m
• 1 m² = 2.6 sq km

• 1 fl oz = 30 mL
• 1 qt = .95 L
• 1 gal = 3.8 L
• 1 ft³ =.03 m³
• 1 yd³ =.76 m³

• 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

• 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

• Perimeter (P)          Area (A)
• Triangle    = a+b+c           =1/2bh

Trapezoid  =s₁+s₂+b₁+b₂    =1/2h(b₁+b₂)

Parallelogram =2(a+b)         =bh

Rectangle      =2(l+w)          =lw

Square          =4s                 =s²

Circle            =d or 2r         =r²

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

Prism     =Bh (area of the base x height)

Pyramid =Bh (area of the base x height)

Cylinder =r²h

Cone =r²h

Sphere =r³

d = rt

• Line - show change over time
• Circle - part to whole relationships
• Bar - compare amts between grps
• Tally tables - record amts in general way

• mean - avg
• median - middle number
• mode - occurs frequently
• range - difference between high and low number

Probability of an event =