8th Grade Annual Review

1
8th Grade Annual Review

• CRCT Final Benchmark

2
Pythagorean Theorem

• a2 b2 c2
• Key words diagonals right triangle area
• In word problems, reference to trees, buildings,
  etc. (make right angles from the ground) are
  hints to use Pythagorean Theorem.

hypotenuse
leg
leg
3
Radicals

• Perfect squares 1, 4, 9, 16, 25, 36, 49, 64, 81,
  100, 121, 144,
• is the radical sign. Asks what
  times itself radicand ( inside).
• For squares. Side length
• To approximate square root find the 2 perfect
  squares that are smaller and larger than the
  you have. Your answer is between those s.

4
Radical Computation

• Simplifying radicals Find any perfect square
  factors (ex 50 25 x 2 25 is a perfect square)
  in the radicand. Take the square root of the
  perfect square (5) and place it on the outside of
  the radical sign (multiply it if a is already
  outside) leave non-perfect square factor (2)
  under radical sign.
• Add/Sub must have LIKE s or variables under
  radical sign add/sub the coefficients.
• Mult/Div use the coefficients then the
  radicand. If there are perfect square factors
  created by multiplying/dividing, simplify (see
  above!).

5
Exponent Computation

• Bases must be the same to use rules.
• When MULT s with exponents, ADD the exponents if
  bases are the same.
• When DIV s with exponents, SUBTRACT the
  exponents if bases are the same.
• When raising to a power (usually has
  parentheses), MULT exponents (similar to
  distributive property).
• If no variables are involved, follow order of
  operations.

6
Sequences

• Arithmetic increasing or decreasing by add/sub
  same number
• Geometric increasing or decreasing by mult/div
  same number
• Sequence-- s that follow a pattern
• Functions are sequences!!

7
Functions

• Shows relationship between input (x) and output
  (y)
• Use function tables substitution to create
  ordered pairs for graphing
• The rule is whatever you do to x to end up with
  y.
• Ordered pairs are solutions to the equation or
  function.
• Graphs will be LINEAR if the variables have an
  exponent of 1.

8
Equations

• Use inverses to move terms across the sign.
• Check for distributive property 1st.
• Move variables to one side 2nd.
• Undo add/sub from the side where the variable is
  3rd.
• Undo mult/div from the side where the variable is
  4th.
• Check your solution by substituting into original
  equation.

9
Graphing Equations

• Slope y2 -y1
• x2 -x1
• Get equations into slope-int form to graph!
• Slope-intercept y mx b
• M slope b y-int (0, b)
• Graph y-int 1st
• Use slope to find 2nd point
• Connect dots to form line

10
Parallel Perpendicular

• Parallel means SAME slope (m) and DIFFERENT y-int
  (b)
• Perpendicular means NEGATIVE RECIPROCAL slope.
  (ex ½ -2)
• If asked to find an equation parallel/perpendicula
  r to given equation, find the slope of the
  original 1st.
• Determine what the slope should be for the new
  line using above rules.
• Use point-slope form to find new equation

11
Writing Equations

• Point-slope form y y1 m (x x1)
• Substitute m and (x1, y1)
• Solve to get in slope-int form
• Standard form Ax By C
• x y on same side No decimals or fractions

12
Systems of Equations

• Graph Check graph lines using slop-int rules
  point of intersection is solution.
• Substitution get one variable by itself
  substitute into other equation to get 2nd
  variable isolated determine ordered pair
• Elimination use addition or multiplication to
  cancel out one variable solve for 2nd variable
  determine ordered pair
• ORDERED PAIR MUST WORK IN ALL EQUATIONS!

13
Inequalities

• lt less than gt greater than
• Solve inequalities just like equations
• Remember to reverse inequality when MULT/DIV by a
  NEGATIVE. This does NOT mean reverse if the
  answer is negative only if the you use to
  mult/div is negative!!

14
Graphing Inequalities

• Open dot for less/ greater than
• Closed dot for less/greater OR equal to
• Test 0 for single variable inequalities test
  (0,0) for linear inequalities.
• If using 0 or (0,0) made a true statement, draw
  arrow or shade toward zero. If not, go away from
  zero.

15
Systems of Inequalities

• Graph each linear inequality on the same
  coordinate plane.
• Shade each inequality separately.
• Identify the area where shading overlaps this is
  the solution!

16
Set Theory

• Venn Diagrams show sets
• Subset member of the set
• Universal set numbers/symbols that can be used
• Complement universal set minus the set!
  Everything thats left!
• Union combine sets
• Intersection items that are in common
  overlapping

17
Probability

• Sample space-- possible outcomes
• Probability of an event
• of times event can occur
• of possible total events
• AND statements multiply the probabilities
• OR statements add the probabilities

18
Parallel Lines/ Transversals

• Alternate Interior- between parallel lines
  opposite sides of transversal
• Alternate Exterior- outside parallel lines
  opposite sides of transversal
• Corresponding same position
• Vertical diagonal from each other
• Supplementary 180 Complementary 90
• Adjacent next to touching
• Use ZIG ZAG method to find congruent angles