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FINAL EXAM REVIEW: Chapter 8
Required Skills:
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
Date: _________________
Per.: _______
Polynomials
Multiply monomials.
Simplify expressions involving powers of monomials.
Simplify expressions involving quotients of monomials.
Simplify expressions containing negative exponents.
Express numbers in scientific notation.
Express numbers in standard notation.
Find the degree of a monomial.
Classify a polynomial.
Write a polynomial in ascending and descending order.
Find the degree of a polynomial.
Add and subtract polynomials.
Find the product of a monomial and a polynomial.
Multiply two polynomials.
Evaluate each of the following.
1)
46
2)
(-3)4
3)
(12.1)3
6)
3.7 x 103
9)
0.00791
Express each of the following in standard notation
4)
8.12 x 104
5)
1.105 x 10-6
Express each of the following numbers in scientific notation.
7)
0.00137
8)
587020000
Classify each of the following using the most appropriate term: binomial, monomial,
polynomial, or trinomial.
10)
12)
-3x3 + 8x
7m11n9
11)
4x8 – 7x5 + 9
13)
-3x6 – 4x5 + 9x - 1
1
Determine the degree of each monomial.
15)
14x2y7z
17)
27m23n14 – 9m11n31
19)
5x + x7 – 14x11
20) (3x2 - 4x + 1) + (-8x2 + 7x - 3)
21)
(7x2 + 3x - 9) + (-5x2 - x + 1)
22) (5x2 - x + 8) - (2x2 + 3x - 1)
23) (-7x2 + x - 3) - (-5x2 - x + 4)
14)
7m11n9
Determine the degree of each polynomial.
16)
7x3 – 9x + 11
Write each polynomial in descending order.
18)
3x3 – 11x5 + 4x4 – 7
Perform the indicated operation.
Simplify each of the following expressions.
24) (3x2y)(-2x5y2)
25) (x2y3)4
27) (-4x3y)(2x2y3)
28)
30x5
5x3
26) (3x2y)2
29)
21y8
28y11
2
30) (4x2y3)0
33)
x5z 3
xz
7
11
31)
(-7y3x0)(2x4)
32)
34) -(3x2 - 8)
a 5
b7
35) 11a2 - 4a + a - 16a2
Find each product.
36) 2x (3x2 - 4x + 1)
37) 6y3 (3y4 – 11y2 – 7y)
38) (x + 3)(x - 7)
39) (x - 9)(x + 9)
40) (y + 7)2
41)
42) (2y + 5)(3y + 1)
43) (7y – 4)(4y + 6)
44) (3x - 4)2
45) (2x + 7)(3x2 – 4x + 2)
(3y + 1)(y - 2)
3
FINAL EXAM REVIEW: Chapter 9
Required Skills:
1)
2)
3)
4)
5)
6)
7)
8)
Factoring
Write the prime factorization of a number.
Identify the factors of a number.
Determine the greatest common factor of two monomials.
Factor a polynomial using the greatest common factor.
Factor a trinomial with a leading coefficient of 1.
Factor a trinomial with a leading coefficient other than 1.
Factor the difference of perfect squares.
Identify the sum of perfect squares as prime.
Write each of the following numbers as a product of primes.
1)
40
2)
56
3)
250
4)
345
7)
100
8)
225
Identify all the factors of each number.
5)
28
6)
80
Factor completely (if possible).
19)
3x2 + 27x + 9
20) b4 – 3b3 + 7b2
21)
4y3 + 40y2 + 24y
22) 14a5w6 – 49a4w5 + 28a2w7
4
23) x2 + 5x + 6
24) x2 – 25
25) y2 + y – 12
26) a2 – 7a – 18
27) w2 + 36
28) n2 – 16n + 28
29) 2x2 + 23x + 45
30) 4x2 - 4x – 3
5x2 - 17x + 6
32) 3x2 - 13x + 12
33) 4y2 + 4y – 35
34) 6u2 – 13u - 15
31)
35)
2x2 + 16x + 30
36)
2x2 - 32x
37)
5x2 - 10x + 5
38)
4x3y - 2x2y - 2xy
5
FINAL EXAM REVIEW: Chapter 10
Required Skills:
1)
2)
3)
Quadratic Equations
Solving a quadratic equation by taking the square root.
Solving a quadratic equation by factoring.
Solving a quadratic equation using the Quadratic Formula.
Solve each of the following by taking the square root where appropriate.
1)
5x2 – 6 = 26
2)
3 – 7(x + 2)2 = 66
Solve each of the following. by factoring (if possible) or the Quadratic Formula. Round
your answers to the nearest tenth if necessary.
1)
x2 – 8x = 20
2)
r2 + 10r + 9 = 0
3)
4p2 + 4p = 15
4)
21a2 + 5a – 7 = 0
5)
2d2 + 8d + 3 = 3
6)
4y2 + 3 = 2y2 – 8y
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