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Algebra 1.1 Final Review
HW45
Name: _______________________
Do your work on this sheet but write your answers on the answer sheet.
1.
Simplify: (9x2 + 2x −10) + (6x2 − 8x − 3)
a) 3x2 – 6x – 13
2.
b) 15x2 – 6x - 13
c) 15x2 + 10x – 7
d) 15x2 – 6x – 7
Simplify: (7x2 − 2x +1) − (4x2 + 7x − 8)
a) 3x2 + 5x – 7
b) 3x2 + 5x + 9
c) 3x2 – 9x + 9
d) 3x2 – 9 x –7
Match the polynomial with its correct name. One name will not be used.
3.
5x3 + 4x
4.
7x2 – 6x + 1
4
a) Quartic Polynomial
b) Quadratic Trinomial
c) Linear Monomial
3
5.
2x + x – 9x + 5
d) Cubic Binomial
6.
13x
e) Constant Monomial
7.
Rewrite the expression without parenthesis: -7(3x - 5)
a) – 21x + 35
8.
d) 21x – 35
b) 6x9y8 - 12x9y2
c) 6x9y6 - 12x9y2
d) 6x10y6 - 12x9y2
Multiply: (x + 4)(x + 9)
a)
10.
c) 21x + 35
Rewrite the expression without parenthesis: 3x9y2 (2xy4 - 4)
a) 6x10y6 - 12
9.
b) – 21x – 35
x2 + 13x + 36
b)
x2 + 13x + 13
c)
2x + 36
d)
15x + 36
b)
10x - 10
c)
3x2 – 13x - 10
d)
3x2 + 17x – 10
Multiply: (3x + 2)(x - 5)
a)
3x2 – 13x - 3
11. Multiply: (x + 3)(2x2 - 5x + 10)
12.
13.
14.
a)
2x3 + 11x2 - 5x + 30
b)
2x3 + 6x2 + 15x + 30
c)
3x2 - 5x + 30
d)
2x3 + x2 - 5x + 30
Factor the difference of two squares: m2 – 16
a)
(m + 16)(m – 16)
b)
(m + 4)(m – 4)
c)
(m – 4)(m – 4)
d)
(4m + 1)(4m – 1)
Factor the difference of two squares: 9y2 – 49
a)
(9y + 49)(9y – 49)
b)
(3y – 7)(y – 7)
c)
(3y + 49)(3y – 49)
d)
(3y + 7)(3y – 7)
Factor the GCF: 5w7x – 15w4x2 – 25w6x3
a)
5w7x(x – 3w3 – 5wx2)
b)
wx(5w6 – 15w3x – 25w5x2)
c)
5w4x(w3 – 3x – 5w2x2)
d)
w4x(5w6 – 15x – 25w2x2)
a)
(p – 9)(p – 14)
b)
(p + 7)(p – 2)
c)
(p + 2)(p + 7)
d)
(p + 1)(p + 14)
Factor. Remember to use a BIG X.
15.
p2 + 9p + 14
____________________________________________________________________________
16.
a2 – 10a + 9
a)
(a – 1)(a – 9)
b)
(a – 3)(a – 3)
c)
(a + 1)(a – 9)
d)
(a + 3)(a – 3)
_____________________________________________________________________________
17.
b2 + 7b – 30
a)
(b + 5)(b – 6)
b)
(b – 10)(b + 3)
c)
(b – 5)(b + 6)
d)
(b + 10)(b – 3)
18.
2d2 + 12d – 32 (Hint: Factor the GCF 1st)
a)
(2d – 8)(d + 2)
b)
2(d – 8)(d + 2)
c)
(2d + 8)(d – 2)
d)
2(d + 8)(d – 2)
___________________________________________________________________________
19.
2x2 + 7x + 5 (Hint: Use the “long way”)
a)
(2x + 5)(x + 1)
b)
(2x + 3)(x + 2)
c)
(2x + 1)(x + 5)
d)
(2x + 7)(x + 5)
_____________________________________________________________________________
Factor by grouping:
20.
8w – 8p + xw – xp
a)
(8 + x)(w – p)
b)
(8x – 8p)(xw – xp)
c)
(8 - x)(w + p)
d)
(8x + 8p)(xw + xp)
a)
x = – 7 or x = 17
b)
x = 7 or x = –17
c)
x = 17
d)
no solution
a)
x = –12 or x = 12
b)
x = 2 or x = –2
c)
x = –2 or x = 12
d)
no solution
a)
x = –3 or x = 2
b)
x = 2 or x = –3
c)
x = -3
d)
no solution
a)
x = 1.5 or x = –1
b)
x = -1.5 or x = 1
c)
x = 1.5
d)
x=1
a)
x < -3 or x > 11
b)
-3 < x < 11
c)
x < –11 or x > 3
d)
–11 < x < 3
Solve.
21.
x ! 5 = 12
22.
23.
24.
25.
!5+ x = 7
2x +1 = !5
5 4x !1 = 25
x+4 >7
26.
2x ! 3 " 1
a)
x ≤ 1 or x ≥ 2
b)
1≤x≤2
c)
x ≤ –2 or x ≥ -1
d)
-2 ≤ x ≤ -1
Solve and graph.
27.
x!6 "5
a)
b)
1 11 c
11 -­‐11 1 -­‐5 5 -­‐5 5 d)
-­‐11 28.
1 1 6x < 30
a)
b)
-­‐5 5 c)
d)
-­‐5 5 Use this information to answer #29 and #30:
The dog, Marley, ran at an average speed of 15 mph. One hour later, Bingo left from the same place going 10
mph. How long will it take for Bingo to catch up with Marley if they continue at the same speeds?
Fill in the table below:
Who?
X
=
Marley
Bingo
29.
30.
What is the correct equation to use to solve this problem?
a)
10t = 15
b)
10t = 15(t – 1)
c)
10t = 15
d)
15t = 10(t – 1)
Solve the equation. How long it will take for Bingo to catch up with Marley?
a) 1 hours
b) 2 hours
c) 3 hours
d) 4 hours