Name
Alg1 Q3 Quarter Exam
Test: 3/26/14
PRACTICE 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) -.25
d) none
D
4) Which number is whole, but not natural?
a) 0
b) 4
c) .75
d) 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.
acceptable
answers
½ (many
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)
J2)
H3)
D4)
B5)
F6)
6-9=6-9
4(5 + 2) = 4(5) + 4(2)
17 · 8 = 8 · 17
a) Reflexive
b) Additive Identity
c) Multiplicative identity
6 · (2 · 12) = (6 · 2) · 12
d) Associative Property of Mult.
32 + 0 = 32
e) Transitive
11 + (3 + 18) = (11 +3) + 18
f) Associative Property of Add.
Name
Alg1 Q3 Quarter Exam
E7)
I8)
G9)
C10)
Test: 3/26/14
PRACTICE PROBLEMS
If 40 + 4 = 44 and 44 = 4 · 11, then 40 + 4 = 4 · 11
g) Symmetric
22 · 0 = 0
h) Commutative Property of Mult.
If 30 = 5 · 6, then 5 · 6 = 30
i) Multiplicative property of zero
26 · 1 = 26
j) Distributive
Section 3: Order of Operations:
1) 256 – 13 ÷ ⅓ + 11= 228
5) Substitute and Evaluate:
3y3 - 2y2 ÷ 10 + 379 = -1
y = -5
2) 24 ÷ (6 – 3 · 4) · 13 = -52
6) Substitute and Evaluate:
2
3) (-7)2 - 122 · ¼ + (6)(-2) = 1
b = 7 and c = -
bc2 ÷ (42 – 4b) – 11c = 24
7) Evaluate when a = -8, b = -3, and c = 9
4b3 + ac – ab + 1
c2 – 16b ÷ a + 8a + 2b
numerator: -95
FINAL ANSWER = -19
denominator: 5
Section 4: Simplifying:
1) (6x - 5) + (7x + 7)
3)
13x+ 2
2) (6x2 – 5x + 7) + (9x2 – 4x + 8)
15x2 – 9x + 15
3) 4(3x – 5) + 6(4x +
36x – 2
4) 5(6x – 9) – 7(4x – 8)
2x + 11
5)8(3x2 – 4x + 9) + 6(4x2 + 5x – 12)
48x2 – 2x
6) 9(4x2 + 3x – 8) – 7(6x2 – 4x + 10)
-6x2 + 55x – 142
7) 6(2x – 5) + 3(3x + 2)
21x – 24
8) 4(8x + 5) – 10(5x + 2)
-18x
9) 6(4x2 – x + 7) + 8(3x2 – 2x – 6)
48x2 -22x – 6
10) 10(3x2 – 5x + 3) + 6(5x2 – 4)
12)
60x2 – 50x + 6
11) 12(3x2 – 6x + 9) – 9(4x2 – 8x +
0
Section 5: Solving Equations:
1) ½ x + 39 = 31
-16
7) 42 - ¾ x = 21
28
2) 8x – 5 = 3x + 50
11
8) (5x – 2) + (7x + 5) = -81
3) 12x – 14 = -74
-5
9) 100- 9x = -154
254/9
-7
Name
Alg1 Q3 Quarter Exam
Test: 3/26/14
PRACTICE PROBLEMS
4) 7(4x – 5) + 6(2x + 1) = 171
5) 8(3x – 10) = 10(2x – 6)
5
6) 6(4x -7) – 5(3x – 5) = 55 8
5
10) 10(6x – 4) – 7(8x – 3) = -17
½
11) 7(4x – 10) = 6(8x – 10)
-½
12) 9(2x + 3) – 4 = 5(3x – 2)
-11
Name
Alg1 Q3 Quarter Exam
Test: 3/26/14
PRACTICE PROBLEMS
Q1 Test 2 Review
Solving Equations:
1) (6x - 5) - (10x - 11) = 34
2) 4(3x – 7) + 6(3x + 4) = -49
3) 6(5x – 4) – 4(7x – 9) = 36
4) 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 .
11
=7
8) 4(3x + 3) .
6
+ 8 = -8
9) 6(4x - 3) + 3 .
7
= 15
10) 5(2x - 6) .
12
- 15 = -10
11) 8(6x – 7) .
5
+ 40 = 72
12) 2(8x - 5) + 2 .
-5
13) 5(6x + 3) .
9
+ 3 = -22
14) 7(5x + 4) + 22 .
11
= -8
= -5
Solving and Graphing Simple Inequalities:
1) 8x – 17 > -5
2) 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)
Name
Alg1 Q3 Quarter Exam
Test: 3/26/14
PRACTICE PROBLEMS
Absolute Value Equations
1) 3|7x + 35|_ + 22 = 64
2
2) 6|4x - 24| -10
-5
3) 3|15x + 30| - 112 = 113
4) -½ | 8x – 24 | + 12 = -4
5) ¾ |5x + 1| - 39 = -12
6) 7|4x -12| + 129 = 17
7) 6| 7x – 21 | + 25 = 319
8) 7|5x – 10| - 11 = 59
9)
5 | 12x – 8 | - 8 .
4
= 33
11) ¾ |12x – 12| + 20 = -16
= -22
10) 3|4x – 5| - 14 = -11
7
12) -3 |40 - ⅔x| = -114
Absolute Value Inequalities
1) 4| 9x – 18 | - 32 > 76
2) ⅔ | 6x – 12 | + 5 < 13
3) 3 | 5x – 15 | + 6 .
4
4) 3| 4x + 12 |
8
5)
5 | 4x + 2 | .
-6
<9
– 3 < -18
7) 3| 5x – 20 | - 7 > 23
+ 14 > 23
6) 3| 6x – 18 | + 5 .
11
<7
8) ¾ | 9x – 27 | - 15 < 12
Name
Alg1 Q3 Quarter Exam
Test: 3/26/14
PRACTICE PROBLEMS
Q2 Test 1 Review
Solve and graph the solution ste for each compound inequality:
1) 19 - 4x < -1  6x -29 > -41
2) 18x – 31 > 41  23 – 5x < 28
3) 17 - 3x > 26  7x – 13 > 15
4) 7 < ⅖x + 11 < 13
5) 28 – ¾ x > 31  ½ x + 19 < 22
6) -39 < 4x - 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?
Name
Alg1 Q3 Quarter Exam
Test: 3/26/14
PRACTICE PROBLEMS
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)
Name
Alg1 Q3 Quarter Exam
4) m = - ¾ (-8, 7)
5) m = 2 (5, 6)
6) m = undefined (3,8)
Test: 3/26/14
PRACTICE PROBLEMS
Name
Alg1 Q3 Quarter Exam
7) y - 5 = ¼(x - 4)
8) 48x - 12y = 72
9) y + 2 = (-3/5)(x - 10)
Test: 3/26/14
PRACTICE PROBLEMS
Name
Alg1 Q3 Quarter Exam
10) 54x + 18y = 36
11) 55x - 22y = 66
12) y - 4 = (-1/3)(x + 3)
Test: 3/26/14
PRACTICE PROBLEMS
Name
Alg1 Q3 Quarter Exam
Part II: Solve each system graphically
1) y = 2x - 5
y = - ½x + 5
2) 15x + 15y = 30
y - 6 = -1(x + 4)
Test: 3/26/14
PRACTICE PROBLEMS
Name
Alg1 Q3 Quarter Exam
3) y - 3 = ¾ (x - 8)
34x – 17y = -34
4) 24x - 18y = -18
y = -7
Test: 3/26/14
PRACTICE PROBLEMS
Name
Alg1 Q3 Quarter Exam
5) y - 2 = ⅓(x - 9)
9x – 27y = -135
6) x = -6
y + 15 = (-5/3)(x - 9)
Test: 3/26/14
PRACTICE PROBLEMS
Name
Alg1 Q3 Quarter Exam
Part I:
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
Y = -2x
Y = ⅔x + 3
Y = -6
Y=-¾x+1
Y = 2x – 4
X = -3
Y=¼x+4
Y = 4x – 6
Y = (-3/5)x + 4
Y = -3x + 2
Y = (5/2)x – 3
Y = -⅓x + 3
Part II:
1)
2)
3)
4)
5)
6)
(4,3)
Dependent
(-4,-6)
(-6,-7)
Inconsistent
(-6,10)
Test: 3/26/14
PRACTICE PROBLEMS
Name
Alg1 Q3 Quarter Exam
Test: 3/26/14
PRACTICE PROBLEMS
Q2 Test 3 Review
Part I:
Solve each system GRAPHICALLY and check!
1) y - 10 = -4(x + 4)
18x – 27y = -216
2) y – 2 = - ¾(x – 4)
28x – 14y = 84
3) x = -5
8x + 20y = 40
4) 27x + 9y = 27
y + 7 = -2(x - 6)
5) y = 6
y + 9 = (3/2)(x + 6)
6) 11x + 11y = 44
12x – 36y = 144
Answers:
1) (-3,6)
2) (4,2)
Part II:
Graph each inequality:
3) (-5,4)
4) (-2,9)
5) (4,6)
1) 28x + 7y > 21
2) y – 4 = ⅔(x – 6)
3) x > 3
4) y < - 4
Part III: Graph each system of inequalities:
1) 28x – 14y > 56
y – 3 > - ¼ (x + 12)
2) y – 7 > - ⅓(x + 15)
12x – 60y > -60
3) y > 6
16x + 4y < 20
4) x < -4
y – 3 > ½ (x + 2)
5) 27x -18y < -18
y + 3 > -2(x – 2)
6) y – 4 < (4/3)(x – 3)
33x + 44y < 126
6) (6,-2)
Name
Alg1 Q3 Quarter Exam
Test: 3/26/14
PRACTICE PROBLEMS
Q3 Test 1 Review
Part I: Monomials and Multiplying Polynomials:
1) (4x4y-3z6)3
2) (2x8y10z-5)(5x-5y3z2)3
3) 48x7y6z8 _
32x5y-6z8
4) (4x10y8z5 )2
(2x4y-4z-2)5
5) (7x7y4z3)2(4x-5y3z)3
6)
7) 6x(9x2 – 4x + 8) + 4x(6x2 + 12x – 9)
9) (x + 8)(x – 7)
(8x2y5z3)2 _
(4x-3y2z2)3
8) 8x2(7x2 – 3x – 12) – 6x(4x2 – 16x – 3)
10) (x – 9)(x – 12)
12) (x – 4)(x + 7)
13) (x – 11)2
14) (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
7
6
1) 24x - 72x + 40x
5
4 3
6
5
4
11
10
9
5 2
3) 60x - 105x - 90x
8
4 2
4 4 4
4 3
2 4
7 2
6 3
6 5
6) 240a b + 96a b - 144a b
3
5
4
8) 75x + 150x -25x3
7) 12x y + 24x y - 44x y
5 4 3
2 5
2
5
4) 64x y - 160x y + 288x y - 96xy
5) 84b + 96b -18b + 6b
5 3
3 4
2) 42x y - 70x y + 56x y - 14xy
3 4 5
9) 135a b c - 90a b c + 180a b c
5
2 2
5
10) 12x + 11x y – 10xy
Name
Alg1 Q3 Quarter Exam
Test: 3/26/14
PRACTICE PROBLEMS
Q3 Test 2 Review:
For 1-36 Factor each quadratic:
1) 8x2 + 2x - 3
2) 49x2 – 64
3) 9x2 - 36
4) x2 – 16x + 64
5) x2 + 15x + 54
6) 3x3 + 21x2 – 132x
7) 36x2 – 1
8) 100x2 – 25
9) x2 + 22x - 48
10) x2 + 2x – 1,443
11) x2 – 50x + 504
12) x2 – 10x - 24
13) x2 – 13x + 36
14) x2 - 34x + 64
15) 169x2 - 196
16) 4x2 – 26x + 12
17) 4x2 + 24x - 13
18) 4x2 - 32x – 192
19) 64x2 – 121
20) 64x2 – 4
21) 64x2 - 144
22) 5x2 – 60x + 180
23) x7 + 44x6 + 84x5
24) 12x4 – 60x3 – 288x2
25) 8x2 + 14x + 5
26) 8x2 – 112x - 120
27) 8x2 + 14x - 4
28) x2 – 12x - 45
29) x2 + 26x + 25
30) x2 + 6x – 16
31) x2 – 3x - 88
32) x2 – x - 30
33) x2 + 11x - 42
34) 8x2 - 200
35) 12x2 - 27
36) 12x2 + 61x + 5
For #’s 37- 42 write the reason WHY each quadratic is PRIME:
37) x2 + 2x + 35
40) x2 – 17x – 72
38) x2 – x + 42
41) x2 + 64
For #’s 43 – 45 pick out which quadratic is prime:
43)
a) x2 + 89x – 90
c) x2 – 25x + 84
b) x2 – 17x – 38
d) x2 + 19x – 90
44)
a) x2 – 441
c) x2 – 30
b) 5x2 + 80
d) 9x2 + 81
45)
a) 3x2 + 24x - 45
c) x2 – 25x + 26
b) x2 – 20x – 44
d) x2 + x – 270
39) x2 + 14x – 48
42) x2 – 63
Name
Alg1 Q3 Quarter Exam
Test: 3/26/14
PRACTICE PROBLEMS
For #’s 43 – 45 pick out which quadratic IS NOT PRIME:
46)
a) x2 + 9x – 90
c) x2 – 19x - 84
b) x2 – x + 90
d) x2 + 5x + 84
47)
a) x2 – 44
c) 3x2 – 35
b) 289x2 - 1
d) 8x2 - 27
48)
a) 3x2 + 24x - 41
c) x2 – 29x + 28
b) x2 – 45x – 44
d) x2 + 6x – 27