Name Test: 3/26/14
Alg1 Q3 Quarter ExamPRACTICE PROBLEMS
Q1 Test 1 Review
Sections 1 and 2 can be done on sheet.
Sections 3,4, and 5 MUST be done in NB
Section 1: Sets of Numbers
1) Which number is a rational number but not an integer?
a) – 6 b) 0 c) ⅝ d) none C
2) Which number is an integer but not a natural number?
a) π b) -¾ c) 0 d) none C
3) Which number is an integer, but not rational?
a) π b) 4 c) -.25d) none D
4) Which number is whole, but not natural?
a) 0 b) 4 c) .75d) none A
5) Which number is natural, but not whole?
a) ¼ b) 4 c) 0 d) none D
6) Give an example of a number that is rational, but not an integer.½ (many acceptable answers
7) Give an example of a number that is an integer, but not a whole number. -4 (many acceptable answers
8) Give an example of a number that is a whole number, but not a natural number.0(only answer)
9) Give an example of a number that is a whole number, but not an integer. None
10) Give an example of a number that is rational, but not a whole number. ½ (many acceptable answers
Section 2: Properties
A. Complete the Matching Column (put the corresponding letter next to the number
A1) 6 - 9 = 6 - 9 a) Reflexive
J2)4(5 + 2) = 4(5) + 4(2) b) Additive Identity
H3)17 · 8 = 8 · 17 c) Multiplicative identity
D4)6 · (2 · 12) = (6 · 2) · 12 d) Associative Property of Mult.
B5) 32 + 0 = 32 e) Transitive
F6)11 + (3 + 18) = (11 +3) + 18 f) Associative Property of Add.
E7) If 40 + 4 = 44 and 44 = 4 · 11, then 40 + 4 = 4 · 11 g) Symmetric
I8)22 · 0 = 0 h) CommutativeProperty of Mult.
G9)If 30 = 5 · 6, then 5 · 6 = 30 i) Multiplicative property of zero
C10) 26 · 1 = 26 j)Distributive
Section 3: Order of Operations:
1) 256 – 13 ÷ ⅓ + 11= 2285) Substitute and Evaluate:y = -5
3y3 - 2y2 ÷ 10 + 379 = -1
2) 24 ÷ (6 – 3 · 4) · 13 = -52
6) Substitute and Evaluate:b = 7 and c = -2
3) (-7)2- 122· ¼ + (6)(-2) =1bc2 ÷ (42 – 4b) – 11c = 24
7) Evaluate when a = -8, b = -3, and c = 9
4b3 + ac – ab + 1 numerator: -95 FINAL ANSWER = -19
c2 – 16b ÷ a + 8a + 2bdenominator: 5
Section 4: Simplifying:
1)(6x - 5) + (7x + 7)2) (6x2 – 5x + 7) + (9x2 – 4x + 8)3) 4(3x – 5) + 6(4x + 3)
13x+ 215x2 – 9x + 1536x – 2
4) 5(6x – 9) – 7(4x – 8)5)8(3x2 – 4x + 9) + 6(4x2 + 5x – 12)
2x + 1148x2 – 2x
6) 9(4x2 + 3x – 8) – 7(6x2 – 4x + 10)7) 6(2x – 5) + 3(3x + 2)
-6x2 + 55x – 14221x – 24
8) 4(8x + 5) – 10(5x + 2)9) 6(4x2 – x + 7) + 8(3x2 – 2x – 6)
-18x48x2 -22x – 6
10) 10(3x2 – 5x + 3) + 6(5x2 – 4)11) 12(3x2 – 6x + 9) – 9(4x2 – 8x + 12)
60x2 – 50x + 60
Section 5: Solving Equations:
1) ½ x + 39 = 31-167) 42 - ¾ x = 2128
2) 8x – 5 = 3x + 50118) (5x – 2) + (7x + 5) = -81-7
3) 12x – 14 = -74-59) 100- 9x = -154254/9
4) 7(4x – 5) + 6(2x + 1) = 171510) 10(6x – 4) – 7(8x – 3) = -17½
5) 8(3x – 10) = 10(2x – 6)511) 7(4x – 10) = 6(8x – 10)- ½
6) 6(4x -7) – 5(3x – 5) = 55812) 9(2x + 3) – 4 = 5(3x – 2)-11
Q1 Test 2 Review
Solving Equations:
1) (6x - 5) - (10x - 11) = 342) 4(3x – 7) + 6(3x + 4) = -49
3) 6(5x – 4) – 4(7x – 9) = 364) 6(4x – 5) - 5(7x - 6) = -110
5) 5(3x – 2) = 4(6x + 11) 6) 8(5x – 3) = 6(5x + 1)
7) 4(6x - 4) - 3 . = 78) 4(3x + 3) . + 8 = -8
11 6
9) 6(4x - 3) + 3 . = 1510) 5(2x - 6) . - 15 = -10
7 12
11) 8(6x – 7) . + 40 =7212) 2(8x - 5) + 2 . = -8
5 -5
13) 5(6x + 3) . + 3 = -2214) 7(5x + 4) + 22 . = -5
9 11
Solving and Graphing Simple Inequalities:
1) 8x – 17 > -52) 50 – ¾ x 68
3) 12x - 2 17x + 18 4) 8(5x – 4) – 6(7x + 4) -64
5) 38 < 26 - ⅜ x 6) 6(4x -1) 7(4x - 2)
7) 9(4x + 4) > 4(4x - 1)8) -4 5(4x + 6) + 6(4x – 2)
Absolute Value Equations
1) 3|7x + 35|_ + 22 = 642) 6|4x - 24| -10 = -22
2 -5
3) 3|15x + 30| - 112 = 1134) -½ | 8x – 24 | + 12 = -4
5) ¾ |5x + 1| - 39 = -126) 7|4x -12| + 129 = 17
7) 6| 7x –21 | +25 =319 8) 7|5x – 10| - 11 = 59
9)5 | 12x – 8 | - 8 .= 33 10) 3|4x – 5|- 14 = -11
4 7
11) ¾ |12x – 12|+ 20 = -16 12) -3 |40 - ⅔x| =-114
Absolute Value Inequalities
1) 4| 9x – 18 | - 32 > 762) ⅔ | 6x – 12 | + 5 < 13
3) 3 | 5x – 15 | + 6 . 94) 3| 4x + 12 | + 14 23
4 8
5) 5 | 4x+ 2| .– 3 <-18 6)3| 6x – 18 | +5 . 7
-611
7) 3| 5x – 20 | - 7 > 238) ¾ | 9x – 27 | - 15 < 12
Q2 Test 1 Review
Solve and graph the solution ste for each compound inequality:
1)19 - 4x < -1 6x -29 -412) 18x – 31 > 41 23 – 5x 28
3) 17 - 3x > 26 7x – 13 15 4) 7⅖x + 11< 13
5) 28–¾ x > 31 ½ x + 19 22 6) -394x - 15< 5
7) A snack stand at Yankee Stadium sells sodas for $4.25 and hot dogs for $6.50. During one game the stand sold 3 more hot dogs than 4 times the amount of sodas. If the total sales for sodas and hot dogs were $4,254.50; how many of each item were sold?
8) A phone call cost $7.67. Introductory minutes cost $.20/min and additional minutes are $.13/min. If there were 7 less additional minutes than triple the introductory minutes, how many minutes were billed at each rate?
9) A store sold Seminole t-shirts for $27 and Gator t-shirts for $22. The store sold 38 more Seminole shirts than 11 times the amount of Gator shirts and made $1,664. How many of each T-shirt were sold?
10) A jar of change has $81.25 in it. There are 4 dimes more than 3 times the amount of nickels and 3 quarters less than double the amount of nickels. How many nickels, dimes, and quarters are in the jar? (There are no pennies.)
11) A jar of change has $67.75 in it. There are 5 less nickels than 3 times the amount of dimes and 8 quarters more than double the amount of dimes. How many nickels, dimes, and quarters are in the jar? (There are no pennies.)
12) A jar of change has $74.15 in it. There are 7 nickels less than twice the amount of dimes and 6 less quarters than triple the amount of dimes. How many nickels, dimes, and quarters are in the jar?
13)The perimeter of a rectangular garden is 172 feet. If the length is 10 feet less than 3 times the width, what are the length and width of the garden?
14)The perimeter of a rectangle is 134 inches. If the width is 7 inches more than ½ the length, what are the dimensions of the rectangle?
15)The perimeter of a rectangle is 234 inches. If the width is 12 inches less than ¼ the length, what are the dimensions of the rectangle?
Q2 Test 2 Review
Part I: Find the equation in slope intercept form and graph: (1 on each set of axis)
1) (-3, 6)(4, -8)
2) (3, 5)(-6, -1)
3) (4, -6)(-4, -6)
4) m = - ¾ (-8, 7)
5) m = 2 (5, 6)
6) m = undefined (3,8)
7) y - 5 = ¼(x - 4)
8) 48x - 12y = 72
9) y + 2 = (-3/5)(x - 10)
10) 54x + 18y = 36
11) 55x - 22y = 66
12) y - 4 = (-1/3)(x + 3)
Part II: Solve each system graphically
1) y = 2x - 5
y = - ½x + 5
2) 15x + 15y = 30
y - 6 = -1(x + 4)
3) y - 3 = ¾ (x - 8)
34x – 17y = -34
4) 24x - 18y = -18
y = -7
5) y - 2 = ⅓(x - 9)
9x – 27y = -135
6) x = -6
y + 15 = (-5/3)(x - 9)
Part I:
1)Y = -2x
2)Y = ⅔x + 3
3)Y = -6
4)Y = - ¾ x + 1
5)Y = 2x – 4
6)X = -3
7)Y = ¼ x + 4
8)Y = 4x – 6
9)Y = (-3/5)x + 4
10)Y = -3x + 2
11)Y = (5/2)x – 3
12)Y = -⅓x + 3
Part II:
1)(4,3)
2)Dependent
3)(-4,-6)
4)(-6,-7)
5)Inconsistent
6)(-6,10)
Q2 Test 3 Review
Part I:Solve each system GRAPHICALLY and check!
1) y - 10 = -4(x + 4)2) y – 2 = - ¾(x – 4)
18x – 27y = -216 28x – 14y = 84
3) x = -54) 27x + 9y = 27
8x + 20y = 40 y + 7 = -2(x - 6)
5) y = 6 6) 11x + 11y = 44
y + 9 = (3/2)(x + 6) 12x – 36y = 144
Answers:
1) (-3,6)2) (4,2)3) (-5,4)4) (-2,9)5) (4,6)6) (6,-2)
Part II:Graph each inequality:
1)28x + 7y > 212) y – 4 = ⅔(x – 6)
3) x 34) y - 4
Part III: Graph each system of inequalities:
1) 28x – 14y 562) y – 7 > - ⅓(x + 15)
y – 3 > - ¼ (x + 12) 12x – 60y -60
3) y 64) x < -4
16x + 4y < 20 y – 3 ½ (x + 2)
5) 27x -18y < -186) y – 4 (4/3)(x – 3)
y + 3 > -2(x – 2) 33x + 44y < 126
Q3 Test 1 Review
Part I: Monomials and Multiplying Polynomials:
1) (4x4y-3z6)32) (2x8y10z-5)(5x-5y3z2)33) 48x7y6z8 _ 32x5y-6z8
4) (4x10y8z5 )2 5) (7x7y4z3)2(4x-5y3z)36) (8x2y5z3)2 _
(2x4y-4z-2)5 (4x-3y2z2)3
7) 6x(9x2 – 4x + 8) + 4x(6x2 + 12x – 9)8) 8x2(7x2 – 3x – 12) – 6x(4x2 – 16x – 3)
9) (x + 8)(x – 7)10) (x – 9)(x – 12)12) (x – 4)(x + 7)
13) (x – 11)214) (5x – 4)(12x + 9)
15) (3x + 4)(8x + 3)16) (7x2 – 4x + 3)(5x – 4)
17) (4x2 – 7x + 2)(10x2 – 3x – 5)18) (6x2 + 8x – 3)(5x2 + 10x – 2)
19) (5x3 – 9x + 3x – 7)(11x3 + 5x2 – 4x + 8)20) (3x2 – 5x - 2)2
Part II: Factoring with the GCF
1) 24x7 - 72x6 + 40x52) 42x4y3 - 70x3y4 + 56x2y5 - 14xy2
3) 60x6 - 105x5 - 90x44) 64x5y2 - 160x4y3 + 288x2y4 - 96xy5
5) 84b11 + 96b10 -18b9 + 6b86) 240a7b2 + 96a6b3 - 144a6b5
7) 12x5y3 + 24x4y2 - 44x3y8) 75x5 + 150x4 -25x3
9) 135a5b4c3 - 90a4b4c4 + 180a3b4c510) 12x5+ 11x2y2 – 10xy5
Q3 Test 2 Review:
For 1-36 Factor each quadratic:
1) 8x2 + 2x - 32) 49x2 – 643) 9x2 - 36
4) x2 – 16x + 645) x2 + 15x + 54 6) 3x3 + 21x2 – 132x
7) 36x2 – 18) 100x2 – 25 9) x2 + 22x - 48
10) x2 + 2x – 1,44311) x2 – 50x + 50412) x2 – 10x - 24
13) x2 – 13x + 3614) x2 - 34x + 6415) 169x2 - 196
16) 4x2 – 26x + 1217) 4x2 + 24x - 13 18) 4x2 - 32x – 192
19) 64x2 – 12120) 64x2 – 4 21) 64x2 - 144
22) 5x2 – 60x + 18023) x7 + 44x6 + 84x524) 12x4 – 60x3 – 288x2
25) 8x2 + 14x + 526) 8x2 – 112x- 12027) 8x2 + 14x - 4
28) x2 – 12x - 4529) x2 + 26x + 25 30) x2 + 6x – 16
31) x2 – 3x - 8832) x2 – x - 30 33) x2 + 11x - 42
34) 8x2 - 20035) 12x2 - 27 36) 12x2 + 61x + 5
For #’s 37- 42 write the reason WHY each quadratic is PRIME:
37) x2 + 2x + 3538) x2 – x + 4239) x2 + 14x – 48
40) x2 – 17x – 7241) x2 + 6442) x2 – 63
For #’s 43 – 45 pick out which quadratic is prime:
43) a) x2 + 89x – 90b) x2 – 17x – 38
c) x2 – 25x + 84d) x2 + 19x – 90
44) a) x2 – 441b) 5x2 + 80
c) x2 – 30d) 9x2 + 81
45)a) 3x2 + 24x - 45b) x2 – 20x – 44
c) x2 – 25x + 26d) x2 + x – 270
For #’s 43 – 45 pick out which quadratic IS NOT PRIME:
46) a) x2 + 9x – 90b) x2 – x + 90
c) x2 – 19x - 84d) x2 + 5x + 84
47) a) x2 – 44b) 289x2 - 1
c) 3x2 – 35d) 8x2 - 27
48)a) 3x2 + 24x - 41b) x2 – 45x – 44
c) x2 – 29x + 28d) x2 + 6x – 27