1. 8 th Grade Annual Review CRCT & Final Benchmark

2. Pythagorean Theorem a 2 + b 2 = c 2 a 2 + b 2 = c 2 Key words: diagonals; right triangle; area 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. In word problems, reference to trees, buildings, etc. (make right angles from the ground) are hints to use Pythagorean Theorem. hypotenuse leg

3. Radicals Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, … Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, … is the radical sign. Asks what # times itself = radicand (# inside). is the radical sign. Asks what # times itself = radicand (# inside). For squares…. Side length = 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. 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. 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. 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!). 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. Bases must be the same to use rules. When MULT #s with exponents, ADD the exponents if bases are the same. 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). When raising to a power (usually has parentheses), MULT exponents (similar to distributive property). If no variables are involved, follow order of operations. If no variables are involved, follow order of operations.

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

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

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

9. Graphing Equations Slope= y 2 -y 1 Slope= y 2 -y 1 x 2 -x 1 x 2 -x 1 Get equations into slope-int form to graph! Get equations into slope-int form to graph! Slope-intercept y = mx + b Slope-intercept y = mx + b M = slope; b = y-int (0, b) M = slope; b = y-int (0, b) Graph y-int 1 st Graph y-int 1 st Use slope to find 2 nd point Use slope to find 2 nd point Connect dots to form line Connect dots to form line

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

11. Writing Equations Point-slope form: y – y 1 = m (x – x 1 ) Point-slope form: y – y 1 = m (x – x 1 ) Substitute m and (x 1, y 1 ) Substitute m and (x 1, y 1 ) Solve to get in slope-int form Solve to get in slope-int form Standard form: Ax + By = C Standard form: Ax + By = C x & y on same side; No decimals or fractions 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. 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 2 nd variable isolated; determine ordered pair Substitution: get one variable by itself; substitute into other equation to get 2 nd variable isolated; determine ordered pair Elimination: use addition or multiplication to cancel out one variable; solve for 2 nd variable; determine ordered pair Elimination: use addition or multiplication to cancel out one variable; solve for 2 nd variable; determine ordered pair ORDERED PAIR MUST WORK IN ALL EQUATIONS! ORDERED PAIR MUST WORK IN ALL EQUATIONS!

13. Inequalities greater than greater than Solve inequalities just like equations 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!! 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 Open dot for less/ greater than Closed dot for less/greater OR equal to Closed dot for less/greater OR equal to Test 0 for single variable inequalities; test (0,0) for linear inequalities. 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. 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. Graph each linear inequality on the same coordinate plane. Shade each inequality separately. Shade each inequality separately. Identify the area where shading overlaps; this is the solution! Identify the area where shading overlaps; this is the solution!

16. Set Theory Venn Diagrams – show sets Venn Diagrams – show sets Subset– member of the set Subset– member of the set Universal set– numbers/symbols that can be used Universal set– numbers/symbols that can be used Complement– universal set minus the set! Everything that’s left! Complement– universal set minus the set! Everything that’s left! Union– combine sets Union– combine sets Intersection– items that are in common; overlapping Intersection– items that are in common; overlapping

17. Probability Sample space-- # possible outcomes Sample space-- # possible outcomes Probability of an event: 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 Interior- between parallel lines; opposite sides of transversal Alternate Exterior- outside parallel lines; opposite sides of transversal Alternate Exterior- outside parallel lines; opposite sides of transversal Corresponding– same position Corresponding– same position Vertical– diagonal from each other Vertical– diagonal from each other Supplementary = 180; Complementary = 90 Supplementary = 180; Complementary = 90 Adjacent– next to; touching Adjacent– next to; touching Use ZIG ZAG method to find congruent angles Use ZIG ZAG method to find congruent angles