Transcript 8th Grade Annual Review

th
8
Grade Annual
Review
CRCT & Final Benchmark
Pythagorean Theorem
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a2 + b2 = c2
hypotenuse
leg
leg
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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.
Radicals
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Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100,
121, 144, …
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is the radical sign. Asks what # times itself
= radicand (# inside).
For squares…. Side length =
area
To approximate square root: find the 2 perfect
squares that are smaller and larger than the # you
have. Your answer is between those #s.
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Radical Computation
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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.
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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!).
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Exponent Computation
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Bases must be the same to use rules.
When MULT #s with exponents, ADD 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.
Sequences
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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!!
Functions
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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.
Equations
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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.
Graphing Equations
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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
Parallel & Perpendicular
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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/perpendicular 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
Writing Equations
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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
Systems of Equations
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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!
Inequalities
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< less than; > 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!!
Graphing Inequalities
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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.
Systems of Inequalities
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Graph each linear inequality on the same
coordinate plane.
Shade each inequality separately.
Identify the area where shading overlaps; this is
the solution!
Set Theory
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Venn Diagrams – show sets
Subset– member of the set
Universal set– numbers/symbols that can be
used
Complement– universal set minus the set!
Everything that’s left!
Union– combine sets
Intersection– items that are in common;
overlapping
Probability
Sample space-- # possible outcomes
 Probability of an event:
# of times event can occur
# of possible total events
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AND statements– multiply the probabilities
 OR statements– add the probabilities
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Parallel Lines/ Transversals
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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