Download Honors Algebra Review WS for Midterm I. Number Systems Name

Honors Algebra Review WS for Midterm
I. Number Systems
Name all of the number systems that the following numbers belong.
5
̅̅̅̅
̅̅̅̅ 8) 6.21… 9) pi 10) √17
1) 5
2) – 4 3) 0
4) ½ 5) – 6 6)2.15
7) – 5.06215
II. Order of Operations...Evaluate the following Problems
11) 5 – 8 + 2 – 3
9∗4+2∗6
12) 29 – 3(9 – 4)
2
3
2
14) [8(5 – 2) + 3 ∗ 2]
13) 288 ÷ [3(9 + 3)]
1
15) 7∗7
16) 25 – 3(18+9)
III. Solve for the indicated variable
1
2
1
3
𝑥
5
17) 3 𝑥 = 12 18) 3 𝑥 + 4 𝑥 = 11 19) 5 – 2x = 13
20) 2 + 14 = 7 21) 6x – 5 – 3x = 13
22) 17x – 15 = 10 + 12x
IV. Solve and graph the following inequalities on a number line.
23) 6 – 2x > 12 24) 4x + 6 < 10 + 12x
25) 8x + 3 < 9x – 14 26) 2x + 8 – 10x > –16
V. Solve and graph the compound inequalities below
27) 12 < 2x – 4 < 16 28) – 15 > –2x + 3 > – 31 29) 5x + 1 < 6 or 2x – 12 > 8
VI. Simplify the following expressions.
30) (5xy3)(3x3y)
31) (–2x3y9z8)3
−2
15𝑥 2 𝑦 −2 𝑧 8
)
25𝑥 6 𝑦 −3 𝑧 −2
32) (
−1
24𝑥 6 𝑦 −2 𝑧 −5
)
12𝑥 6 𝑦 5 𝑧 −3
33) (
0
2,000𝑧 198
)
25𝑥 −166 𝑦 −3 𝑧 −211
34) (
VII. Scientific Notation: Convert the given numbers to Scientific Notation or to Standard Notation.
35) 3,125,000 36) 126,000
37) 0.00007
38) 0.0000000847 39) 3.12 * 105 40) – 6.45 * 10–2
Perform the indicated Operations on the numbers in scientific notation.
41) (3.14 * 103) + (1.2 * 102) 42) (9.89 * 105) – (2.2 * 104)
43) (5.1 * 106)(3 * 104)
12
9
44) (144 * 10 ) ÷ (12 * 10 )
VIII. Polynomial Expressions: Perform the indicated Operations
45) (5x4 + 2x2 – 4) + (3x4 – 6x3 – 2x2 + 7x) 46) (8x2 – 6x + 7) – (10x2 – 5x + 7) 47) 5x3y6(4xy2 – 7x3)
48) (3x – 2)(2x + 4) 49) (x – 6)(x + 8) 50) (x + 4)2
IX. Factor
51) x2 – 25 52) x2 + 6x + 9 53) 9x2 – 30x + 25 54) 25x3 – 4x 55) 8x2 – 10x – 3 56) 7x2 – 33x – 10
SOLVE BY FACTORING
57) x3 – x = 0 58) – 9x2 + 64 = 0 59) 8x2 +18x – 5 = 0
X. Translating & Story Problems
Translate the following sentences into mathematical expressions or equations.
60) five more than twice a number 61) seven less than a number tripled 62) six less than twice a number
Translate and solve
63) eight less than twice a number is 12 64) four more than a number tripled is at least 37
65) the sum of two consecutive odd integers is 76
66) when the square of the first of three consecutive odd integers is is added to twice the third of the three
consecutive odd integers, the result is fourteen less than the square of the 2nd of the three consecutive
integers. What are the three integers?
ANSWER KEY
1) natural, whole, integer, rational, real 2) Integer, rational, real 3) whole, integer, rational real 4) rational (terminating) whole
5) rational (repeating), real 6) rational (repeating), real 7) rational (repeating), real 8) irrational, real 9) irrational, real
𝟒𝟖
10) irrational, real 11) – 4
12) 14
13) 8
14) 52
15)
16) 16
17) x = 36 18) x = 12 19) x = – 4 20) x = – 11
𝟒𝟗
1
21) x = 6
22) x = 5
23) x < – 3 24) x > –
25) x > 17 26) x < 3 27) 8< x < 10 28) 9 < x < 17 29) x < 1 or x > 10
2
𝟐𝟓𝒙𝟖𝒚𝟐
𝒚 𝟕 𝒛𝟐
4 4
9 27 24
30) 15x y 31) – 8x y z
32)
33)
34) 1 35) 3.125 * 106 36) 1.26 * 105
37) 7 * 10–5 38) 8.47 * 10–8 39) 312,000
𝟗𝒛𝟐𝟎
𝟐
3
5
11
4
4
3
40) –0.0645 41) 3.26 * 10 42) 9.67 * 10 43) 1.53 * 10 44) 1.2 * 10 45) 8x – 6x + 7x – 4 46) – 2x2 – x 47) 20x4y8 – 35x6y6
48) 6x2 + 8x – 8 49) x2 + 2x – 48 50) x2 + 8x + 16 51) (x + 5)(x – 5) 52) (x + 3)2 53) (3x – 5)2 54) x(5x +2)(5x – 2)
𝟖
𝟓
𝟏
55) (2x – 3)(4x + 1) 56) (7x + 2)(x – 5) 57) x(x + 1)(x – 1); x = 0, + 1 58) (-3x + 8)(3x + 8); x = + 59) (2x + 5)(4x – 1); x = − 𝒐𝒓
𝟑
𝟐
𝟒
60) 2n + 5 61) 3n – 7 62) 2n – 6 63) 2n – 8 = 12; n = 10 64) 3n + 4 > 37; n > 11 65) n +n+2 = 76; n = 38
2
2
66) N + 2(n + 4) = (n+2) – 14; 9, 11, 13