Algebra 1
Name___________________________________ ID: 1
©a g2`0\1D5g mKZuctMaN ISAoWfFtYwmaQrvew aL_L[Cw.K d fAjlvlM yrci`ghhAtush vryeSsKeerxvdeVdU.
Assignment
Date________________ Period____
Evaluate each expression.
1) 18 ¸ -3 - (4)((2)(4 - 1))
2) (2)(-1 - ((3)(2)) ¸ (-3 - -2))
-30
1
4
3) 2 ¸
10
((( )( ))( ))
2 3
3
4
1
3
1
5
4) -3 ¸ -2 -
9
10
5)
( )( )
1 -7
5 4
39
20
(21)(3)
(14 - 11) 2
(
6) (3) 7 -
(25)(3)
15
)
6
7
Solve each inequality.
7) -2 x - 4( x + 3) > -12 - 6 x
8) 40 - 4n £ 2n + 4(6n - 5)
No solution. :
n³2:
10 12 14 16 18 20
9) -4 - 4r ³ -6(-r - 1)
-4
-2
0
2
4
6
10) -2n + 16 > -6 - 2(7 + 4n)
r £ -1 :
n > -6 :
-4
-2
0
2
4
-10
-8
-6
-4
-2
Simplify each expression.
11) -7(a + 10) - 3(1 + a)
12) 2(-12 + 4m) - 8m(-12m + 1)
-24 + 96m 2
-10a - 73
13) -10 x(3 - 5 x) + 12 x( x + 6)
14) -3( x + 9) - 5(5 + 9 x)
42 x + 62 x 2
-48 x - 52
Worksheet by Kuta Software LLC
-1-
©P X2C0W1X5t sKVuttmak KSloWfht_wzaErNeI wLpLACi.i _ \ArlElk frWi]gWhytVsX lreedsIeyrXvPeLdG.v l qMbaQdeeC gwGiKtYhn FIInBfci_nbidtWes ^AHllgGeebarKag l1l.
Write the slope-intercept form of the equation of the line through the given point with the given
slope.
15) through: (0, -4), slope = 0
16) through: (1, 4), slope = -1
y = -4
y = -x + 5
17) through: (4, 5), slope =
9
4
18) through: (-2, 0), slope =
9
4
4
7
y= x-4
y= x+
19) through: (4, -5), slope = -2
4
7
8
7
20) through: (2, 3), slope = -
y = -2 x + 3
1
2
1
2
y=- x+4
Sketch the graph of each line.
2
5
3
2
21) y = - x - 4
22) y = x - 2
y
y
6
5
4
3
2
1
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
6
5
4
3
2
1
1 2 3 4 5 6 x
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
1 2 3 4 5 6 x
Worksheet by Kuta Software LLC
-2-
©O t2t0H1y5L KKVuOtqaz \Spo\fstGwlagraef JLWLqCP.x j nAml^lq FrVicgghPtWsH RrheUsWeprpvJeKdt.u J MMdamdYep awBiXtshS SICnqfDifnVi_tqey SAjlZgheubirZat E1g.
24) x = -5
2
3
23) y = - x + 5
y
6
5
4
3
2
1
y
6
5
4
3
2
1
-6 -5 -4 -3 -2 -1
-6 -5 -4 -3 -2 -1
1 2 3 4 5 6 x
-1
-2
-3
-4
-5
-6
25) 9 x - y = 5
1 2 3 4 5 6 x
-1
-2
-3
-4
-5
-6
26) 7 x - 5 y = 10
y
y
6
5
4
3
2
1
6
5
4
3
2
1
-6 -5 -4 -3 -2 -1
1 2 3 4 5 6 x
-1
-2
-3
-4
-5
-6
27) 4 x + y = -1
-6 -5 -4 -3 -2 -1
1 2 3 4 5 6 x
-1
-2
-3
-4
-5
-6
28) 6 x + 5 y = -10
y
y
6
5
4
3
2
1
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
6
5
4
3
2
1
1 2 3 4 5 6 x
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
1 2 3 4 5 6 x
Worksheet by Kuta Software LLC
-3-
©\ D2\0y1u5A nKsuPtxaa RSmoVfutswqadrueq RL`LPCC.H t BAZlJlK irFitg[hstEss irdexsdeWr\vPeTdN.q X BMjavdjeh TwdiNtLhO NIUnOfPi_nRiDt[ec sA_lzgkeibCrVa[ C1G.
Solve each system by elimination.
29) 12 x + 6 y = 26
-4 x - 2 y = -8
30) x + 5 y = -2
-6 x + 10 y = -28
(3, -1)
No solution
31) 5 x + 4 y = 20
9 x + 3 y = -6
32) 9 x - 3 y = -24
8 x - 7 y = -30
(-4, 10)
(-2, 2)
Factor each completely.
33) r 2 + 5r + 6
34) x 2 + 4 x - 32
(r + 2)(r + 3)
( x - 4)( x + 8)
35) x 2 - 6 x + 8
36) n 2 + 11n + 24
( x - 4)( x - 2)
(n + 3)(n + 8)
37) 6n 2 - 31n - 30
38) 4 x 2 + 11 x - 20
(n - 6)(6n + 5)
( x + 4)(4 x - 5)
39) 4n 2 + 20n + 21
40) 6n 2 + n - 2
(2n + 3)(2n + 7)
41) 16 x 2 - 1
(2n - 1)(3n + 2)
42) 25r 2 - 16
(4 x + 1)(4 x - 1)
(5r + 4)(5r - 4)
Simplify. Your answer should contain only positive exponents.
(
m3
43)
2nm 0 × nm -3
)
-3
44)
(u 2v -3) 3 × 2vu 2
u -4v 3
8n 6
2u 12
m 18
v 11
Worksheet by Kuta Software LLC
-4-
©n U2G0j1s5B nKZuQtjaW fSqoefZtiwUaDrveS ]L\LKCd.i G fAQlDlS _rFicgAhgtUsI NrCensyeCrXvqepdk.O P WMta[dHeN twKistKhg KIPnhfXipnqivtUeb _AklLgwehbirBaM W1e.
45)
mn 3 × 2m 0n 4
(n 3) -4
46)
2n 19 m
m 4n -2
m 3n 3 × (mn 2)
2
1
9
nm
Simplify.
47) - 45 + 2 5 + 3 20
48) - 54 - 3 6 + 2 24
5 5
-2 6
49) - 5 + 3 5 - 2 2
2 5-2 2
Solve each equation. Remember to check for extraneous solutions.
50)
6k + 10 = k - 1
51) k - 5 =
{9 }
k+1
{8}
Simplify.
52)
4 4x4
3x2
53)
8x 3
3
2ab
5ab 2
10b
5b
Solve each equation with the quadratic formula.
54) x 2 - 56 = - x
55) 5m 2 - 6m = 11
{7, -8}
{ }
1
2 , -1
5
Write the slope-intercept form of the equation of the line through the given points.
56) through: (0, 3) and (-3, -2)
57) through: (-4, -2) and (0, 1)
5
3
3
4
y= x+3
y= x+1
58) through: (1, 2) and (2, -2)
y = -4 x + 6
Worksheet by Kuta Software LLC
-5-
©j f2`0t1a5] WKYugtaac aSVoffRtkwdabrsec zLOLQCA.D Q yAWlJlb NrniNgwhrtFsn UrJeEsMeTryvdeOdO.w p WMnaZdMec Bwqi_t]hO IIbnyfKi_nxiWtqeS pAIlSgoeRb^rsax i1R.
Find each product.
59) (3 x + 1)(2 x 2 + 8 x + 5)
60) (7v - 6)(7v 2 + 7v - 8)
6 x 3 + 26 x 2 + 23 x + 5
49v 3 + 7v 2 - 98v + 48
Simplify.
61) (-3 - 4 2 )(-5 +
2)
62) (5 2 +
7 + 17 2
63)
(
5 )( 2 + 2 )
20 + 2 10
3 + 1)( 3 - 2)
64) (-5 3 + 2)(3 3 - 5)
1- 3
-55 + 31 3
Find the vertex of the following quadratics.
65) f ( x) = 2 x 2 - 12 x + 20
66) f ( x) = x 2 - 8 x + 18
y
y
7
10
67) f ( x) = -2 x 2 + 16 x - 35
6
8
5
6
4
4
68) f ( x) = -2 x 2 + 8 x - 7 2
3
y
2
-4 -2
-4
-2
-2
2
4
2
6
4
y
2
1
x
1 -22
x
3
4 2 5 46
76 x x
-4
-2
-6
-4
-8
Simplify. Write each answer in scientific
notation.
69) (4.7 ´ 10 -1)(5.64 ´ 10 0)
2.651 ´ 10
-10
-12
70) (2.9 ´ 10 -1)(6.1 ´ 10 -3)
0
1.769 ´ 10
-6
-8
-3
Write each number in scientific notation.
71) 15000000
72) 0.000028
1.5 ´ 10 7
73) 164000000
2.8 ´ 10 -5
74) 0.000000037
1.64 ´ 10 8
3.7 ´ 10 -8
Worksheet by Kuta Software LLC
-6-
©J x2j0d1p5] tKquKtjat hS`oaf`tyweajrzey ZLsLeCT.e A QAylFlP wrhi\g\hTtosa traeVspegrCvWeJdU.I q XMdawdMeR LwiiEtShl ]IgnNf[iynTiCtwem xALlMghevbCrsat s1f.