Name:_______________________
Final/Regents Review Packet
Date:_____ Period:____
Mr. Woods
Final/Regents Review Packet
The following topics are those we covered this year. Refer back to all of the
handouts you received this year for detailed descriptions on how to handle
problems; rework the problems on those sheets. The Finals Review packet should
be the FIRST place you start in reviewing for the final. The Regents Review
packet is the best source of problems while reviewing for the Regents on the 16th.
Where appropriate, I have indicated where to look for information in your Regents
Review "blue" book. Another good source is regentsprep.org.
1. Real Numbers and Properties – you have several packets on this.
a. Sets – – blue page 8 – 9
i. intersection of sets ("and", symbol )
ii. union of sets ("or", symbol U)
b. Set notation – blue page 10, problems on page 11
c. Real numbers and their subsets – diagram, blue page 7
d. Properties of real numbers – blue page 16 - 17
2. Operations with Signed Numbers – see handouts and blue page 12 through 17
a. PEMDAS – blue page 27-28 (problems on Finals review packet)
b. Blue Section 1.8 – Translating English and Algebra – this will help with word
problems – problems on page 32 and 33.
3. Monomials/Polynomials and Simplifying / Equations
a. One Step Equations – blue page 34
b. Multistep Equations – problems on blue 41
c. Combining Like Terms – page 42 to 44
d. Formulas on page 58 – important! Also:
i. volume of a cube: V = s3
ii. volume of a cylinder: V = Bh, where B is the area of the base

Since the base is a circle, that’s A =
π r2
4. Inequalities (Simple and Compound)
a. Graphing simple inequalities on a line – blue page 62 – 64; problems 65 - 66
b. Remember - when graphing on the number line, if the sign is < or >, the
circle is NOT colored in; if the symbol is < or >, the circle IS colored in.
c. When solving inequalities, if you multiply or divide by a negative number,
FLIP THE SIGN!
5. Absolute Value Equations / Inequalities
a. Simplify the equation/inequality until you isolate the absolute value
statement on one side.
b. Then take what is inside the absolute value statement and set it equal to the
value and the negative of the value and solve for both.
6. Solving Systems of Equations Algebraically (substitution/elimination)
a. Substitution
i. Identify equation with variable having coefficient of 1
ii. Solve for that variable
iii. Replace that value into the other equation; you can now solve as you
only have one variable
iv. Once you have solved for one variable, replace it in either equation to
solve for the other variable.
v. ALWAYS DO CHECKS!
b. Elimination
i. Line up the equations, one under the other
ii. Multiply the top equation by the coefficient of the bottom equation;
multiply the bottom equation by the NEGATIVE of the top equation
(if you do this right the first terms cancel out and are eliminated.
iii. Add the two equations.
iv. Solve for the remaining variable.
v. Substitute the solved variable back into either of the original
equations, and solve for the second variable
vi. ALWAYS DO CHECKS!
7. Word Problems – review the vocabulary handout we did. Also the best practice for
word problems is the sheet of 65 problems (with answer keys) that you had during
the year. Practice them!
8. Graphing
a. Slope = m = y2 – y1
x2 – x1
b. Remember when graphing an equation, you need to get it in the following
format: y = mx + b, where m is the slope and b is the y-intercept.
9. Systems Graphically
a. Get both equations into y – mx + b format
b. Then graph each
c. Where they intersect is the solution.
10. Graphing Inequalities
a. Graph the inequalities as if they were equations
b. If the inequality is either < or >, the line will be dashed; if the inequality is <
or >, the line will be solid.
c. Once you graph the line, pick a point either below or above the line and plug
it into the inequality; if the point makes the inequality TRUE, than it is part
of the solution; that is the side you shade towards. If it is FALSE, it is not
part of the solution.
11. Factoring
a. ALWAYS start with GCF – look for multiples of the coefficients; then look
to see if variables exist in all the terms; if so, use the one with the lowest
exponent.
b. CASE 1 factoring (when the coefficient of the x2 term is 1) –
i. Factor into two binomials
ii. The numbers must result in a product of the last term and the sum of
the "x" term.
iii. Example: x2 – 5x - 14
 (x – 7)(x + 2)  -7 x 2 = - 14 and -7 + 2 = -5
 Remember, when looking at the original expression:
a. If the second sign is positive, the signs of the binomials
are the same, and their sign is the sign as the first sign
of the expression.
b. If the second sign is negative, the signs of the
binomials are different, and the larger of the two
numbers will have the sign of the first sign of the
expression.
c. CASE II Factoring (when the coefficient of the x2 term is not 1)
i. Look for a GCF
ii. Take off coefficient of the x2 term and multiply the last term by it.
iii. Do CASE 1 Factoring.
iv. Bring back the term you removed and add it to the front of each
binomial.
v. Check to see if there are any GCFs that can be eliminated from
either binomial; if so take them out and throw them away
vi. The remaining pair of binomials is the proper factoring
vii. KEEP any GCF from the first step!
viii. CHECK TO SEE IF IT WORKS by multiplying it all out!
d. DOTS – difference of two squares
i. If you have two perfect squares and a subtraction sign, you can do
DOTS. Remember the binomials are plus and minus!
e. ALWAYS FACTOR COMPLETELY!
12. Solving Quadratics by Factoring
a. Take the quadratic and set it equal to zero
b. Factor as normal
c. Set each binomial to zero and solve
13. Pythagorean Theorem
a2 + b2 = c2



Only works on right triangles
The hypotenuse is always across from the right angle
Be careful identifying which sides are which; you are not
always solving for c
14. Right Triangle Trigonometry – SOH CAH TOA
a. Solving for a side (the "x" is a side)
i. Label the diagram
ii. Determine which function to use
iii. Write the equation
iv. Fill in the values (example: SIN 35 = 12/x)
v. Cross multiply (unless you are solving for an angle).
b. Solving for an angle (the "x" is an angle)
i. Label the diagram
ii. Determine which function to use
iii. Write the equation
iv. Fill in the values
 use the "2nd" key…
 example: SIN x = 7/14..
 7/14 = .5
 2nd SIN .5 = …. That's your angle
15. Radicals
Adding and subtracting:
You can only add and subtract radicals with like numbers under the
radicand. You add the numbers OUTSIDE not the ones INSIDE.
Example: 3√2 + 4√2 = 7√2 – Note: you may have to simplify
Multiplying:
You multiply the OUTSIDE numbers and the INSIDE numbers.
Example: 3√4 x 2√5 = 6√20


Dividing:
You divide the outside and divide the inside.

Example: 21√8 = 7√4 = 7 x 2 = 14 (always remember to reduce
3√2
Simplifying:
Look for the LARGEST PERFECT SQUARE in the radical, and factor.
Example: √128 = √64 x √2 = 8 x √2 = 8√2
16. Probability and Statistics
a. Multiply the number of possibilities of each item to get the TOTAL number
of possibilities
b. Develop a tree diagram to show it (the right side should equal the total
number of possibilities
c. Remember: when you see the word AND, both things must be true; when you
see the word OR, either one being true means you count it.
17. Proportions –
a. A proportion is a statement that two ratios are equal. When trying to solve
proportions we use the Cross Products Property of Proportions (ie you cross
multiply!)
A
B
=
C
D
b. Percents:
18. Rational Expressions
A(D) = B(C)
Is
Of
=
%___
100
a. Factor everything in the numerator and denominator fully; then cross out
any common term that appear in the top and the bottom (must be a "one for
one" cancelling
b. If you are dividing fractions, you must flip the second fraction and make it
multiplication.
i. Example: x2 – 16 ÷ x2 - 2x + 8 becomes x2 – 16 x x2 + x - 6
x2 – 9
x2 + x – 6
x2 – 9
x2 -2x + 8
19. Scientific Notation
a. If the original number is greater than 10, the number of places the decimal
point needs to be moved to the left becomes the power of 10. If necessary,
insert the decimal point in the original number.
b. If the original number is between 0 and 1, make the power of 10 negative
followed by the number of places the decimal point needs to be moved to the
right
20. Midpoint - Midpoint formula = x1 + x2 , y1 + y2
2
2
Where the two endpoints are (x1, y1) and (x2, y2)
21. Venn Diagrams –
a. The intersection of the circles is the place where the both things are true.
b. Problems starting on page 403.
22. Scatter Plot –
a. Scatter plots are plots of points having two coordinates. Look to see what
the trend is and determine if is positive or negative, strong or weak.
b. Look at page 299 and problems there.
23. Graphing a Parabola – The instructions for this can be found out at the website.
Please Note: This packet just acts as a guide for what to study. Please review any
other packets that I give you. In addition, you will still need to go over your Final
Review Packet and your Green Book. If you have any questions throughout the course
of your studying, please feel free to e-mail me. I will be posting additional review
hours at the website as I find out my availability and the availability of classrooms, so
check every day! Good luck on your Final and your Regents Exam!!! 