algebra 1 200 final exam review packet name · 2017-05-30 · algebra 1 200 final exam review...

Algebra 1 200

Final Exam Review Packet Name

UNIT 1 – EXPONENTS / RADICALS

Exponents

Degree of a monomial: Add the degrees of all the _______________ in the monomial together.

o Example - Find the degree of 3 527x yz

Degree of a polynomial: Is equal to the _________________ with the highest degree.

o Example – Find the degree of the polynomial: 3 43 7 5x xy xy

Adding / Subtracting Monomials: You can only add or subtract monomials that have the ________

bases AND ________ exponents.

o You add / subtract the _________________, the bases & exponents stay the _______!

o Example – Simplify -3x2 + 7x2y2 - 2x2 + 6x2y2 + 5y2

Multiplying Monomials: When you multiply like bases, _______ the exponents!

o Example - 2 3 5 4(4 )( 3 )x y z xy z

Powers of Monomials: When you raise a monomial to a power ____________ the exponents!

o Example 2 7 4(2 )x y z

Dividing Monomials: When you divide like bases, ______________ the exponents!

o Example 5 9

4 3

12

6

x y z

y xz

Distributing Monomials: Example 3 2 5 43 (5 3 )xy x xy y

Multiplying Polynomials: Double - Distribute or ____________!

o Example 2( 5)( 3)x x

Algebra 1 200


Exponents Practice:

Write each expression in exponential form.

1. 72 pppp 2. mnnmn 324

Find the degree of the monomial.

3. dbca 27125

Find the degree of the polynomial.

4. abbaabba 243 22543

Simplify the following expressions.

5. 4228361226 2223 xxxxxx

6. 242892 232 xxxx

7. 932634125x 344 xxxxx

Simplify and show your work. All fractions must be simplified.

8. xyx 23 y-36x- 9. 323242 234 baababba

Algebra 1 200


10. 223 36

5yxyx

11. 3223 3542 xxxx

12.

5

6

3

10 232 yxyx 13. 126 22 xxx

14. 4232 yx 15. yxxy 232 2

16. 2aam 17. 44 xx

18. 237 xx 19. 264 p

20. )3)(4( 2232 yxyx + )2)(3( 432 yxxy 21. 64

37

3

9

ba

ba

22. 085 23. 0( 9 )x

24. 3(5 )x 25. 23m

Algebra 1 200


Radicals

Simplifying Radicals: Always look for the ________________ perfect square.

o Example 216

Multiplying Radicals: You can multiply the coefficients in front of the radicals and everything under

the radicals together.

o Example 1

802

Dividing Radicals: You can not have a radical in the denominator so you must “rationalize” it by

multiplying the whole fraction by the radical in the denominator.

o Example 2

3

Adding and Subtracting Radicals: After simplifying, you can combine “like radicals" which means

that the expressions have the same number under the radical.

o Example 27 2 48

Distributing Radicals: Use the distributive property with all of the rules of radicals.

o Example 4 3 3 6

Solving Radical Equations: Follow these 4 steps

o 1. Isolate the square root quantity.

o 2. ____________ both sides of the equation.

o 3. Simplify and solve.

o 4. ___________!

Example 2 7 28x

Algebra 1 200


Radicals Practice:

Simplify the following radicals:

1.) 2.)

4.) 5.)

6.) 7.)

9.) 10.)

11.) 12.)

13.) 14.)

15.) 16.)

Algebra 1 200


17.) 18.) 2

12 5 2

19.) 20.) (3 3)(4 5)

21.) 4 5 2 3 2 3 22.) 4 6 3 2

Solve for x:

23.) 24.)

25.) 26.)

27.) 28.)

Algebra 1 200


UNIT 2 – QUADRATICS

Methods for solving quadratics:

1. Factoring – factor then solve using Zero Product Property

Methods of factoring:

a. Difference of Two Squares – Binomials only ( A )2 – ( B )2 = ( A – B ) ( A + B )

Must Have :

1. Binomial

2. Subtraction

3. Perfect Squares

4. Even Exponents

b. “Sum Product” Factoring ( when 1a so that x2 + bx + c) - Trinomials

What two numbers multiply to give you c and also add up to give you b?

(x + ?)(x + ?) or (x - ?)(x - ?) , c > 0

(x + ?)(x + ?) , c > 0

c. Splitting the Middle Term ( when 1a so that cbxax 2) - Trinomials

1. Find product of ac

2. Find factors of ac that add up to b

3. Rewrite the trinomial with new factors

4. Group and factor!

2. Solve by Taking Square Root of both sides

1. Isolate the squared quantity

2. Square root each side

3. “T” it off and make one side positive and one side negative

4. Check your solutions in the original equation

3. Solve by Quadratic Formula -

.2

4 then ,0

22

a

acbbxcbxax

If

1. Arrange the terms into the standard form.

2. State the value of a, b, c

3. Use the quadratic formula to solve for x

Algebra 1 200


Graphing Quadratics (Parabolas)

Direction it faces - depends on sign of a, +a = upward, - a = downward

Axis of Symmetry (AOS) - If the symmetrical sides of a parabola graph are folded, this is the line on

which the fold occurs – formula 2

b

a

Vertex – the maximum or minimum point of the parabola (AOS determines x, plug x into original

equations to determine y coordinate

y-intercept – The point where the parabola crosses the y-axis (set x =0)

x-intercepts – the point(s) where the parabola crosses the x-axis (set y =0)

Factor the following polynomials (you do NOT have to find solutions for x). GCF FIRST!

1. 22 412 xyyx 2. 40182 2 xx

3. 143 2 xx 4. xx 123 3

Algebra 1 200


Solve the following equations by factoring. Solve by factoring (difference of perfect squares, sum

product, or splitting the middle term.) Be sure to pull out GCF if possible!

5. 3x2 – 15x + 12 = 0 6. x2 + 9 = 6x

7. (4x2 + 3x + 20) + (x2 + 2x + 10) = 180 8. 2x2 + 3x = 5

Solve by taking the square root of both sides. No decimals (i.e., simplify all radicals).

9. 723 2 x 10. 3(x – 2)2 – 6 = 42

11. ¼(x + 5)2 + 9 = 19 12. 49x2 +36 = 0

Algebra 1 200


Solve by the quadratic formula. No decimals (i.e., simplify all radicals).

13. 263 2 xx 14. 54 2 xx

15. 3x2 + 1 – 8x = 0 16. 3x2 + 15x = 0

Solve by any method you choose. No decimals (i.e., simplify all radicals). You do not need to check

your answers.

17. 3083 xx 18. xx 12 2

19. (y +6) (2y - 7) = 0 20. 9862x

Algebra 1 200


For the following word problems, use any method of solving that is applicable.

21. The length of a rectangle is 5 cm greater than its width. Find the dimensions of the rectangle if its area is

126 cm2.

22. Find three consecutive odd integers such that the sums of the squares of the first and third is eight more

than two times the second. Find the set of integers.

Algebra 1 200


23. 2 2 3y x x

a.) Vertex______________

b.) Axis of Symmetry________________

c.) x-intercept(s) _______________________

d.) y-intercept______________

Algebra 1 200


24. 2 4 4y x x

a.) Vertex______________


c.) x-intercept(s) _______________________

d.) y-intercept______________

Algebra 1 200


25. 24 16y x

a.) Vertex______________


c.) x-intercept(s) _______________________

d.) y-intercept______________

algebra 1 200 final exam review packet name · 2017-05-30 · algebra 1 200 final exam review...

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