Kuta Software - Infinite Algebra 1
Name___________________________________
Factoring Trinomials (a = 1)
Date________________ Period____
Factor each completely.
1) b 2 + 8b + 7
2) n 2 − 11n + 10
3) m 2 + m − 90
4) n 2 + 4n − 12
5) n 2 − 10n + 9
6) b 2 + 16b + 64
7) m 2 + 2m − 24
8) x 2 − 4 x + 24
9) k 2 − 13k + 40
10) a 2 + 11a + 18
11) n 2 − n − 56
12) n 2 − 5n + 6
13) b 2 − 6b + 8
14) n 2 + 6n + 8
15) 2n 2 + 6n − 108
16) 5n 2 + 10n + 20
17) 2k 2 + 22k + 60
18) a 2 − a − 90
19) p 2 + 11 p + 10
20) 5v 2 − 30v + 40
21) 2 p 2 + 2 p − 4
22) 4v 2 − 4v − 8
23) x 2 − 15 x + 50
24) v 2 − 7v + 10
25) p 2 + 3 p − 18
26) 6v 2 + 66v + 60
Kuta Software - Infinite Algebra 1
Name___________________________________
Factoring Trinomials (a = 1)
Date________________ Period____
Factor each completely.
1) b 2 + 8b + 7
(b + 7)(b + 1)
3) m 2 + m − 90
(m − 9)(m + 10)
5) n 2 − 10n + 9
(n − 1)(n − 9)
7) m 2 + 2m − 24
(m + 6)(m − 4)
9) k 2 − 13k + 40
(k − 5)(k − 8)
11) n 2 − n − 56
(n + 7)(n − 8)
13) b 2 − 6b + 8
(b − 4)(b − 2)
2) n 2 − 11n + 10
(n − 10)(n − 1)
4) n 2 + 4n − 12
(n − 2)(n + 6)
6) b 2 + 16b + 64
(b + 8) 2
8) x 2 − 4 x + 24
Not factorable
10) a 2 + 11a + 18
(a + 2)(a + 9)
12) n 2 − 5n + 6
(n − 2)(n − 3)
14) n 2 + 6n + 8
(n + 2)(n + 4)
15) 2n 2 + 6n − 108
16) 5n 2 + 10n + 20
2(n + 9)(n − 6)
5(n 2 + 2n + 4)
17) 2k 2 + 22k + 60
18) a 2 − a − 90
2(k + 5)(k + 6)
(a − 10)(a + 9)
19) p 2 + 11 p + 10
20) 5v 2 − 30v + 40
( p + 10)( p + 1)
21) 2 p 2 + 2 p − 4
2( p − 1)( p + 2)
23) x 2 − 15 x + 50
( x − 10)( x − 5)
25) p 2 + 3 p − 18
( p − 3)( p + 6)
5(v − 2)(v − 4)
22) 4v 2 − 4v − 8
4(v + 1)(v − 2)
24) v 2 − 7v + 10
(v − 5)(v − 2)
26) 6v 2 + 66v + 60
6(v + 10)(v + 1)
Kuta Software - Infinite Algebra 1
Name___________________________________
Factoring Trinomials (a > 1)
Date________________ Period____
Factor each completely.
1) 3 p 2 − 2 p − 5
2) 2n 2 + 3n − 9
3) 3n 2 − 8n + 4
4) 5n 2 + 19n + 12
5) 2v 2 + 11v + 5
6) 2n 2 + 5n + 2
7) 7a 2 + 53a + 28
8) 9k 2 + 66k + 21
9) 15n 2 − 27n − 6
10) 5 x 2 − 18 x + 9
11) 4n 2 − 15n − 25
12) 4 x 2 − 35 x + 49
13) 4n 2 − 17n + 4
14) 6 x 2 + 7 x − 49
15) 6 x 2 + 37 x + 6
16) −6a 2 − 25a − 25
17) 6n 2 + 5n − 6
18) 16b 2 + 60b − 100
Kuta Software - Infinite Algebra 1
Name___________________________________
Factoring Trinomials (a > 1)
Date________________ Period____
Factor each completely.
1) 3 p 2 − 2 p − 5
(3 p − 5)( p + 1)
3) 3n 2 − 8n + 4
(3n − 2)(n − 2)
5) 2v 2 + 11v + 5
(2v + 1)(v + 5)
7) 7a 2 + 53a + 28
(7a + 4)(a + 7)
9) 15n 2 − 27n − 6
3(5n + 1)(n − 2)
2) 2n 2 + 3n − 9
(2n − 3)(n + 3)
4) 5n 2 + 19n + 12
(5n + 4)(n + 3)
6) 2n 2 + 5n + 2
(2n + 1)(n + 2)
8) 9k 2 + 66k + 21
3(3k + 1)(k + 7)
10) 5 x 2 − 18 x + 9
(5 x − 3)( x − 3)
11) 4n 2 − 15n − 25
12) 4 x 2 − 35 x + 49
(n − 5)(4n + 5)
( x − 7)(4 x − 7)
13) 4n 2 − 17n + 4
(n − 4)(4n − 1)
15) 6 x 2 + 37 x + 6
( x + 6)(6 x + 1)
17) 6n 2 + 5n − 6
(2n + 3)(3n − 2)
14) 6 x 2 + 7 x − 49
(3 x − 7)(2 x + 7)
16) −6a 2 − 25a − 25
−(2a + 5)(3a + 5)
18) 16b 2 + 60b − 100
4(b + 5)(4b − 5)
Kuta Software - Infinite Algebra 1
Mixture Word Problems
Name___________________________________
Date________________ Period____
1) 2 m³ of soil containing 35% sand was mixed
into 6 m³ of soil containing 15% sand. What
is the sand content of the mixture?
2) 9 lbs. of mixed nuts containing 55% peanuts
were mixed with 6 lbs. of another kind of
mixed nuts that contain 40% peanuts. What
percent of the new mixture is peanuts?
3) 5 fl. oz. of a 2% alcohol solution was mixed
with 11 fl. oz. of a 66% alcohol solution.
Find the concentration of the new mixture.
4) 16 lb of Brand M Cinnamon was made by
combining 12 lb of Indonesian cinnamon
which costs $19/lb with 4 lb of Thai
cinnamon which costs $11/lb. Find the cost
per lb of the mixture.
5) Emily mixed together 9 gal. of Brand A fruit
drink and 8 gal. of Brand B fruit drink
which contains 48% fruit juice. Find the
percent of fruit juice in Brand A if the
mixture contained 30% fruit juice.
6) How many mg of a metal containing 45%
nickel must be combined with 6 mg of pure
nickel to form an alloy containing 78%
nickel?
7) How much soil containing 45% sand do you need
to add to 1 ft³ of soil containing 15% sand in order
to make a soil containing 35% sand?
8) 9 gal. of a sugar solution was mixed with 6
gal. of a 90% sugar solution to make a 84%
sugar solution. Find the percent
concentration of the first solution.
9) A metallurgist needs to make 12.4 lb. of an
alloy containing 50% gold. He is going to
melt and combine one metal that is 60%
gold with another metal that is 40% gold.
How much of each should he use?
10) Brand X sells 21 oz. bags of mixed nuts that
contain 29% peanuts. To make their
product they combine Brand A mixed nuts
which contain 35% peanuts and Brand B
mixed nuts which contain 25% peanuts.
How much of each do they need to use?
Kuta Software - Infinite Algebra 1
Name___________________________________
Mixture Word Problems
1) 2 m³ of soil containing 35% sand was mixed
into 6 m³ of soil containing 15% sand. What
is the sand content of the mixture?
20%
Date________________ Period____
2) 9 lbs. of mixed nuts containing 55% peanuts
were mixed with 6 lbs. of another kind of
mixed nuts that contain 40% peanuts. What
percent of the new mixture is peanuts?
49%
3) 5 fl. oz. of a 2% alcohol solution was mixed
with 11 fl. oz. of a 66% alcohol solution.
Find the concentration of the new mixture.
46%
4) 16 lb of Brand M Cinnamon was made by
combining 12 lb of Indonesian cinnamon
which costs $19/lb with 4 lb of Thai
cinnamon which costs $11/lb. Find the cost
per lb of the mixture.
$17/lb
5) Emily mixed together 9 gal. of Brand A fruit
drink and 8 gal. of Brand B fruit drink
which contains 48% fruit juice. Find the
percent of fruit juice in Brand A if the
mixture contained 30% fruit juice.
6) How many mg of a metal containing 45%
nickel must be combined with 6 mg of pure
nickel to form an alloy containing 78%
nickel?
4 mg
14%
7) How much soil containing 45% sand do you need
to add to 1 ft³ of soil containing 15% sand in order
to make a soil containing 35% sand?
2 ft³
8) 9 gal. of a sugar solution was mixed with 6
gal. of a 90% sugar solution to make a 84%
sugar solution. Find the percent
concentration of the first solution.
80%
9) A metallurgist needs to make 12.4 lb. of an
alloy containing 50% gold. He is going to
melt and combine one metal that is 60%
gold with another metal that is 40% gold.
How much of each should he use?
6.2 lb. of 60% gold, 6.2 lb. of 40% gold
10) Brand X sells 21 oz. bags of mixed nuts that
contain 29% peanuts. To make their
product they combine Brand A mixed nuts
which contain 35% peanuts and Brand B
mixed nuts which contain 25% peanuts.
How much of each do they need to use?
8.4 oz. of Brand A, 12.6 oz. of Brand B
Kuta Software - Infinite Algebra 1
Name___________________________________
Distance - Rate - Time Word Problems
Date________________ Period____
1) An aircraft carrier made a trip to Guam and
back. The trip there took three hours and
the trip back took four hours. It averaged 6
km/h on the return trip. Find the average
speed of the trip there.
2) A passenger plane made a trip to Las Vegas
and back. On the trip there it flew 432 mph
and on the return trip it went 480 mph. How
long did the trip there take if the return trip
took nine hours?
3) A cattle train left Miami and traveled toward
New York. 14 hours later a diesel train left
traveling at 45 km/h in an effort to catch up
to the cattle train. After traveling for four
hours the diesel train finally caught up.
What was the cattle train's average speed?
4) Jose left the White House and drove toward
the recycling plant at an average speed of 40
km/h. Rob left some time later driving in
the same direction at an average speed of 48
km/h. After driving for five hours Rob
caught up with Jose. How long did Jose
drive before Rob caught up?
5) A cargo plane flew to the maintenance
facility and back. It took one hour less time
to get there than it did to get back. The
average speed on the trip there was 220
mph. The average speed on the way back
was 200 mph. How many hours did the trip
there take?
6) Kali left school and traveled toward her
friend's house at an average speed of 40
km/h. Matt left one hour later and traveled
in the opposite direction with an average
speed of 50 km/h. Find the number of hours
Matt needs to travel before they are 400 km
apart.
-1-
7) Ryan left the science museum and drove
south. Gabriella left three hours later
driving 42 km/h faster in an effort to catch
up to him. After two hours Gabriella finally
caught up. Find Ryan's average speed.
8) A submarine left Hawaii two hours before
an aircraft carrier. The vessels traveled in
opposite directions. The aircraft carrier
traveled at 25 mph for nine hours. After this
time the vessels were 280 mi. apart. Find
the submarine's speed.
9) Chelsea left the White House and traveled
toward the capital at an average speed of 34
km/h. Jasmine left at the same time and
traveled in the opposite direction with an
average speed of 65 km/h. Find the number
of hours Jasmine needs to travel before they
are 59.4 km apart.
10) Jose left the airport and traveled toward the
mountains. Kayla left 2.1 hours later
traveling 35 mph faster in an effort to catch
up to him. After 1.2 hours Kayla finally
caught up. Find Jose's average speed.
-2-
Kuta Software - Infinite Algebra 1
Name___________________________________
Distance - Rate - Time Word Problems
1) An aircraft carrier made a trip to Guam and
back. The trip there took three hours and
the trip back took four hours. It averaged 6
km/h on the return trip. Find the average
speed of the trip there.
Date________________ Period____
2) A passenger plane made a trip to Las Vegas
and back. On the trip there it flew 432 mph
and on the return trip it went 480 mph. How
long did the trip there take if the return trip
took nine hours?
8 km/h
3) A cattle train left Miami and traveled toward
New York. 14 hours later a diesel train left
traveling at 45 km/h in an effort to catch up
to the cattle train. After traveling for four
hours the diesel train finally caught up.
What was the cattle train's average speed?
10 km/h
10 hours
4) Jose left the White House and drove toward
the recycling plant at an average speed of 40
km/h. Rob left some time later driving in
the same direction at an average speed of 48
km/h. After driving for five hours Rob
caught up with Jose. How long did Jose
drive before Rob caught up?
6 hours
5) A cargo plane flew to the maintenance
facility and back. It took one hour less time
to get there than it did to get back. The
average speed on the trip there was 220
mph. The average speed on the way back
was 200 mph. How many hours did the trip
there take?
6) Kali left school and traveled toward her
friend's house at an average speed of 40
km/h. Matt left one hour later and traveled
in the opposite direction with an average
speed of 50 km/h. Find the number of hours
Matt needs to travel before they are 400 km
apart.
10 hours
4 hours
-1-
7) Ryan left the science museum and drove
south. Gabriella left three hours later
driving 42 km/h faster in an effort to catch
up to him. After two hours Gabriella finally
caught up. Find Ryan's average speed.
28 km/h
8) A submarine left Hawaii two hours before
an aircraft carrier. The vessels traveled in
opposite directions. The aircraft carrier
traveled at 25 mph for nine hours. After this
time the vessels were 280 mi. apart. Find
the submarine's speed.
5 mph
9) Chelsea left the White House and traveled
toward the capital at an average speed of 34
km/h. Jasmine left at the same time and
traveled in the opposite direction with an
average speed of 65 km/h. Find the number
of hours Jasmine needs to travel before they
are 59.4 km apart.
10) Jose left the airport and traveled toward the
mountains. Kayla left 2.1 hours later
traveling 35 mph faster in an effort to catch
up to him. After 1.2 hours Kayla finally
caught up. Find Jose's average speed.
20 mph
0.6 hours
-2-
Kuta Software - Infinite Algebra 1
Name___________________________________
Finding Slope From an Equation
Date________________ Period____
Find the slope of each line.
5
1) y = − x − 5
2
4
2) y = − x − 1
3
3) y = − x + 3
4) y = −4 x − 1
5) 2 x − y = 1
6) x + 2 y = −8
7) 8 x + 3 y = −9
8) 4 x + 5 y = −10
9) x − y = −2
10) 4 x − 3 y = 9
11) 3 x + 2 y = 6
12) 4 x − 5 y = 0
13) y = −1
14) x + 5 y = −15
15) −2 y − 10 + 2 x = 0
16) x + 5 + y = 0
17) 3 x + 20 = −4 y
18) −15 − x = −5 y
19) −1 = −2 x + y
20) − x − 1 = y
21) 0 = 5 y − x
22) −30 + 10 y = −2 x
Kuta Software - Infinite Algebra 1
Name___________________________________
Finding Slope From an Equation
Date________________ Period____
Find the slope of each line.
5
5
1) y = − x − 5 −
2
2
4
4
2) y = − x − 1 −
3
3
3) y = − x + 3 −1
4) y = −4 x − 1 −4
5) 2 x − y = 1
6) x + 2 y = −8
2
−
7) 8 x + 3 y = −9
−
8
3
9) x − y = −2
8) 4 x + 5 y = −10
−
4
5
10) 4 x − 3 y = 9
4
3
1
11) 3 x + 2 y = 6
−
1
2
3
2
13) y = −1
0
15) −2 y − 10 + 2 x = 0
1
12) 4 x − 5 y = 0
4
5
14) x + 5 y = −15
−
1
5
16) x + 5 + y = 0
−1
17) 3 x + 20 = −4 y
3
−
4
18) −15 − x = −5 y
1
5
19) −1 = −2 x + y
20) − x − 1 = y
2
21) 0 = 5 y − x
1
5
−1
22) −30 + 10 y = −2 x
1
−
5
Kuta Software - Infinite Algebra 1
Name___________________________________
Finding Slope From a Graph
Date________________ Period____
Find the slope of each line.
1)
2)
3)
4)
5)
6)
7)
8)
-1-
9)
10)
11)
12)
13)
14)
15)
16)
-2-
Kuta Software - Infinite Algebra 1
Name___________________________________
Finding Slope From a Graph
Date________________ Period____
Find the slope of each line.
1)
−
7
9
2)
2
3
3)
−
4
5
4)
−
1
4
5)
2
5
6)
−
3
2
7)
8)
Undefined
−5
-1-
9)
10)
3
8
3
11)
12)
3
2
5
4
13)
14)
2
0
15)
16)
−
2
3
−3
-2-
Kuta Software - Infinite Algebra 1
Name___________________________________
Writing Linear Equations
Date________________ Period____
Write the slope-intercept form of the equation of each line.
1) 3 x − 2 y = −16
2) 13 x − 11 y = −12
3) 9 x − 7 y = −7
4) x − 3 y = 6
5) 6 x + 5 y = −15
6) 4 x − y = 1
7) 11 x − 4 y = 32
8) 11 x − 8 y = −48
Write the standard form of the equation of the line through the given point with the given slope.
9) through: (1, 2), slope = 7
11) through: (−2, 5), slope = −4
10) through: (3, −1), slope = −1
12) through: (3, 5), slope =
5
3
13) through: (2, −4), slope = −1
15) through: (3, 1), slope =
14) through: (2, 5), slope = undefined
16) through: (−1, 2), slope = 2
1
2
Write the point-slope form of the equation of the line described.
3
17) through: (4, 2), parallel to y = − x − 5
4
19) through: (−4, 0), parallel to y =
21) through: (2, 0), parallel to y =
3
x−2
4
1
x+3
3
5
23) through: (−2, 4), parallel to y = − x + 5
2
18) through: (−3, −3), parallel to y =
7
x+3
3
20) through: (−1, 4), parallel to y = −5 x + 2
22) through: (4, −4), parallel to y = − x − 4
1
24) through: (−4, −1), parallel to y = − x − 1
2
Kuta Software - Infinite Algebra 1
Name___________________________________
Writing Linear Equations
Date________________ Period____
Write the slope-intercept form of the equation of each line.
1) 3 x − 2 y = −16
y=
3
x+8
2
3) 9 x − 7 y = −7
y=
9
x+1
7
5) 6 x + 5 y = −15
6
y=− x−3
5
7) 11 x − 4 y = 32
y=
11
x−8
4
2) 13 x − 11 y = −12
y=
13
12
x+
11
11
4) x − 3 y = 6
y=
1
x−2
3
6) 4 x − y = 1
y = 4x − 1
8) 11 x − 8 y = −48
y=
11
x+6
8
Write the standard form of the equation of the line through the given point with the given slope.
9) through: (1, 2), slope = 7
7x − y = 5
11) through: (−2, 5), slope = −4
10) through: (3, −1), slope = −1
x+ y=2
12) through: (3, 5), slope =
4 x + y = −3
5x − 3 y = 0
5
3
13) through: (2, −4), slope = −1
14) through: (2, 5), slope = undefined
x + y = −2
15) through: (3, 1), slope =
x=2
16) through: (−1, 2), slope = 2
1
2
2 x − y = −4
x − 2y = 1
Write the point-slope form of the equation of the line described.
3
17) through: (4, 2), parallel to y = − x − 5
4
18) through: (−3, −3), parallel to y =
7
x+3
3
7
y + 3 = ( x + 3)
3
3
y − 2 = − ( x − 4)
4
19) through: (−4, 0), parallel to y =
3
x−2
4
20) through: (−1, 4), parallel to y = −5 x + 2
y − 4 = −5( x + 1)
3
y = ( x + 4)
4
21) through: (2, 0), parallel to y =
1
x+3
3
22) through: (4, −4), parallel to y = − x − 4
y + 4 = − ( x − 4)
1
y = ( x − 2)
3
5
23) through: (−2, 4), parallel to y = − x + 5
2
5
y − 4 = − ( x + 2)
2
1
24) through: (−4, −1), parallel to y = − x − 1
2
1
y + 1 = − ( x + 4)
2
Kuta Software - Infinite Algebra 1
Name___________________________________
Solving Rational Equations 1
Date________________ Period____
Solve each equation. Remember to check for extraneous solutions.
1)
3
m−4
2
=
+
2
2
m
3m
3m 2
2)
1
1
n−1
=
−
n 5n
5n
3)
1
x+3
1
=
−
2
2
3x
2x
6x2
4)
4 5
1
= − 2
2
n
n
n
5)
3n + 15 1
n−3
= 2 −
2
4n
n
4n 2
6)
1
5
n−2
+
= 2
2
2n
2n
n
7)
x−6 x+4
=
+1
x
x
8)
1
1
1
+ 2 =
2n 4n
4n
9)
6b + 18 1 3
+ =
b2
b b
10)
-1-
1
x−1 3
−
=
2x
2x2
x
11)
1
1
2
+
= 2
b − 7b + 10 b − 2 b − 7b + 10
12)
1
1
3
+
= 2
x − 3x
x − 3 x − 3x
13)
6
1
p+4
=
− 2
p p−5
p − 5p
14)
5 x − 20
1
x−4
+
= 2
x − 9 x + 18
x − 6 x − 9 x + 18
15)
1
6
6
−
= 2
5k + 2k
5k + 2 5k + 2k
16)
6
1
1
= 2
−
n − 6n + 8 n − 6n + 8
n−4
17)
4
1
a+3
= 2
− 2
a a + 4a
a + 4a
18)
3
k−6
1
− 2
=
k + 5k + 6
k + 5k + 6 k + 3
19)
v−3
1
v−5
=
− 2
2
v + 3v v + 3
v + 3v
20) 1 =
2
2
-2-
2
2
2
2
3
3m
+
m+3 m+3
Kuta Software - Infinite Algebra 1
Name___________________________________
Solving Rational Equations 1
Date________________ Period____
Solve each equation. Remember to check for extraneous solutions.
1)
3
m−4
2
=
+
2
2
m
3m
3m 2
2)
{11}
3)
1
x+3
1
=
−
2
2
3x
2x
6x2
{−3}
4)
{−2}
5)
3n + 15 1
n−3
= 2 −
2
4n
n
4n 2
x−6 x+4
=
+1
x
x
6)
6b + 18 1 3
+ =
b2
b b
1
5
n−2
+
= 2
2
2n
2n
n
5
{− }
3
8)
{−10}
9)
4 5
1
= − 2
2
n
n
n
{1}
{−2}
7)
1
1
n−1
=
−
n 5n
5n
1
1
1
+ 2 =
2n 4n
4n
{−1}
10)
9
{− }
2
1
x−1 3
−
=
2x
2x2
x
1
{ }
6
-1-
11)
1
1
2
+
= 2
b − 7b + 10 b − 2 b − 7b + 10
2
12)
{6}
13)
6
1
p+4
=
− 2
p p−5
p − 5p
{
15)
{2}
14)
13
}
3
1
6
6
−
= 2
5k + 2k
5k + 2 5k + 2k
2
4
1
a+3
= 2
− 2
a a + 4a
a + 4a
{−
19)
16)
19
}
5
6
1
1
= 2
−
n − 6n + 8 n − 6n + 8
n−4
2
{−3}
18)
18
}
5
v−3
1
v−5
=
− 2
2
v + 3v v + 3
v + 3v
5 x − 20
1
x−4
+
= 2
x − 9 x + 18
x − 6 x − 9 x + 18
2
{
5
{− }
6
17)
1
1
3
+
= 2
x − 3x
x − 3 x − 3x
2
3
k−6
1
− 2
=
k + 5k + 6
k + 5k + 6 k + 3
2
7
{ }
2
20) 1 =
{8}
3
3m
+
m+3 m+3
{0}
-2-
Kuta Software - Infinite Algebra 1
Name___________________________________
Solving Rational Equations 2
Date________________ Period____
Solve each equation. Remember to check for extraneous solutions.
1)
k+4 k−1 k+4
+
=
4
4
4k
2)
1
1
1
=
−
2
2m
m
2
3)
n2 − n − 6
2n + 12 n − 6
−
=
2
n
n
2n
4)
3 x 2 + 24 x + 48
x−6
1
+
= 2
2
2
x
2x
x
5)
k 2 + 2k − 8
1
1
= 2 + 2
3
3k
3k
k
6)
k
1
1
−
=
3
3k k
7)
x−4
x 2 − 3 x − 10 x − 1
+
=
6x
6x
6
8)
1
x−1 1
=
+
2
x
x
x
-1-
9)
1
r+4
6
=
+
r+3 r−2 r−2
1
n 2 + 6n + 5
11)
+
=n−3
n+3
n+3
13)
1
1
=5+ 2
k
k +k
5
6
n 2 + 5n − 6
15)
− 3
= 3
n
n − 2n 2
n − 2n 2
10)
2x + 2
4 x 2 − 16
5x − 5
−
= 2
2
3 x − 12
3 x − 24 x + 48 3 x − 24 x + 48
1 x 2 − 7 x + 10
1
12) =
−
2
4x
2x
14)
1
p−6
+1=
p − 4p
p
16)
x+2 x−1
4x + 2
=
− 2
x
x
x − 3x
-2-
2
Kuta Software - Infinite Algebra 1
Name___________________________________
Solving Rational Equations 2
Date________________ Period____
Solve each equation. Remember to check for extraneous solutions.
1)
k+4 k−1 k+4
+
=
4
4
4k
2)
{−2, 1}
3)
n2 − n − 6
2n + 12 n − 6
−
=
2
n
n
2n
{1}
4)
2
{− , −6}
3
5)
k 2 + 2k − 8
1
1
= 2 + 2
3
3k
3k
k
x−4
x 2 − 3 x − 10 x − 1
+
=
6x
6x
6
3 x 2 + 24 x + 48
x−6
1
+
= 2
2
2
x
2x
x
8 11
{− , − }
3
2
6)
{−2, 4}
7)
1
1
1
=
−
2
2m
m
2
k
1
1
−
=
3
3k k
{−2, 2}
8)
1
x−1 1
=
+
2
x
x
x
{1, −1}
{−14}
-1-
9)
1
r+4
6
=
+
r+3 r−2 r−2
10)
{−8, −4}
1
n 2 + 6n + 5
11)
+
=n−3
n+3
n+3
{1, −
1
1
=5+ 2
k
k +k
{1, 8}
14)
4
{− }
5
5
6
n 2 + 5n − 6
15)
− 3
= 3
n
n − 2n 2
n − 2n 2
{
13
}
2
1 x 2 − 7 x + 10
1
12) =
−
2
4x
2x
5
{− }
2
13)
2x + 2
4 x 2 − 16
5x − 5
−
= 2
2
3 x − 12
3 x − 24 x + 48 3 x − 24 x + 48
1
p−6
+1=
p − 4p
p
2
{
16)
23
}
6
x+2 x−1
4x + 2
=
− 2
x
x
x − 3x
{1}
15
}
4
-2-
Kuta Software - Infinite Algebra 1
Name___________________________________
Solving Quadratic Equations with Square Roots
Solve each equation by taking square roots.
1) k 2 = 76
2) k 2 = 16
3) x 2 = 21
4) a 2 = 4
5) x 2 + 8 = 28
6) 2n 2 = −144
7) −6m 2 = −414
8) 7 x 2 = −21
9) m 2 + 7 = 88
10) −5 x 2 = −500
11) −7n 2 = −448
12) −2k 2 = −162
13) x 2 − 5 = 73
14) 16n 2 = 49
-1-
Date________________ Period____
15) n 2 − 5 = −4
16) n 2 + 8 = 80
17) 7v 2 + 1 = 29
18) 10n 2 + 2 = 292
19) 2m 2 + 10 = 210
20) 9n 2 + 10 = 91
21) 5n 2 − 7 = 488
22) 8n 2 − 6 = 306
23) 10n 2 − 10 = 470
24) 8n 2 − 4 = 532
25) 4r 2 + 1 = 325
26) 8b 2 − 7 = 193
27) 2k 2 − 2 = 144
28) 3 − 4 x 2 = −85
-2-
Kuta Software - Infinite Algebra 1
Name___________________________________
Solving Quadratic Equations with Square Roots
Solve each equation by taking square roots.
1) k 2 = 76
2) k 2 = 16
{8.717, −8.717}
3) x 2 = 21
{4, −4}
4) a 2 = 4
{4.582, −4.582}
5) x 2 + 8 = 28
{2, −2}
6) 2n 2 = −144
No solution.
{4.472, −4.472}
7) −6m 2 = −414
8) 7 x 2 = −21
No solution.
{8.306, −8.306}
9) m 2 + 7 = 88
10) −5 x 2 = −500
{9, −9}
{10, −10}
11) −7n 2 = −448
12) −2k 2 = −162
{8, −8}
{9, −9}
13) x 2 − 5 = 73
14) 16n 2 = 49
{8.831, −8.831}
{1.75, −1.75}
-1-
Date________________ Period____
15) n 2 − 5 = −4
16) n 2 + 8 = 80
{1, −1}
17) 7v 2 + 1 = 29
{8.485, −8.485}
18) 10n 2 + 2 = 292
{2, −2}
{5.385, −5.385}
19) 2m 2 + 10 = 210
20) 9n 2 + 10 = 91
{10, −10}
{3, −3}
21) 5n 2 − 7 = 488
22) 8n 2 − 6 = 306
{9.949, −9.949}
23) 10n 2 − 10 = 470
{6.244, −6.244}
24) 8n 2 − 4 = 532
{6.928, −6.928}
{8.185, −8.185}
25) 4r 2 + 1 = 325
26) 8b 2 − 7 = 193
{9, −9}
{5, −5}
27) 2k 2 − 2 = 144
28) 3 − 4 x 2 = −85
{8.544, −8.544}
{4.69, −4.69}
-2-
Kuta Software - Infinite Algebra 1
Name___________________________________
Using the Quadratic Formula
Date________________ Period____
Solve each equation with the quadratic formula.
1) m 2 − 5m − 14 = 0
2) b 2 − 4b + 4 = 0
3) 2m 2 + 2m − 12 = 0
4) 2 x 2 − 3 x − 5 = 0
5) x 2 + 4 x + 3 = 0
6) 2 x 2 + 3 x − 20 = 0
7) 4b 2 + 8b + 7 = 4
8) 2m 2 − 7m − 13 = −10
-1-
9) 2 x 2 − 3 x − 15 = 5
10) x 2 + 2 x − 1 = 2
11) 2k 2 + 9k = −7
12) 5r 2 = 80
13) 2 x 2 − 36 = x
14) 5 x 2 + 9 x = −4
15) k 2 − 31 − 2k = −6 − 3k 2 − 2k
16) 9n 2 = 4 + 7n
17) 8n 2 + 4n − 16 = −n 2
18) 8n 2 + 7n − 15 = −7
-2-
Kuta Software - Infinite Algebra 1
Name___________________________________
Using the Quadratic Formula
Date________________ Period____
Solve each equation with the quadratic formula.
1) m 2 − 5m − 14 = 0
2) b 2 − 4b + 4 = 0
{7, −2}
3) 2m 2 + 2m − 12 = 0
{2}
4) 2 x 2 − 3 x − 5 = 0
{2, −3}
5) x 2 + 4 x + 3 = 0
5
{ , −1}
2
6) 2 x 2 + 3 x − 20 = 0
{−1, −3}
7) 4b 2 + 8b + 7 = 4
5
{ , −4}
2
8) 2m 2 − 7m − 13 = −10
1 3
{− , − }
2 2
{
7+
4
-1-
73 7 −
,
73
4
}
9) 2 x 2 − 3 x − 15 = 5
10) x 2 + 2 x − 1 = 2
{1, −3}
5
{4, − }
2
11) 2k 2 + 9k = −7
12) 5r 2 = 80
{4, −4}
7
{−1, − }
2
13) 2 x 2 − 36 = x
14) 5 x 2 + 9 x = −4
9
{ , −4}
2
15) k 2 − 31 − 2k = −6 − 3k 2 − 2k
4
{− , −1}
5
16) 9n 2 = 4 + 7n
5 5
{ ,− }
2 2
17) 8n 2 + 4n − 16 = −n 2
{
{
7+
193 7 − 193
,
}
18
18
18) 8n 2 + 7n − 15 = −7
−2 + 2 37 −2 − 2 37
,
}
9
9
{
-2-
−7 + 305 −7 − 305
,
}
16
16
Kuta Software - Infinite Algebra 1
Name___________________________________
Systems of Equations Word Problems
Date________________ Period____
1) Find the value of two numbers if their sum is 12 and their difference is 4.
2) The difference of two numbers is 3. Their sum is 13. Find the numbers.
3) Flying to Kampala with a tailwind a plane averaged 158 km/h. On the return trip the plane only
averaged 112 km/h while flying back into the same wind. Find the speed of the wind and the speed of
the plane in still air.
4) The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales
the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on
the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen
ticket and the price of a child ticket.
5) The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9.
What is the number?
6) A boat traveled 210 miles downstream and back. The trip downstream took 10 hours. The trip back
took 70 hours. What is the speed of the boat in still water? What is the speed of the current?
-1-
7) The state fair is a popular field trip destination. This year the senior class at High School A and the
senior class at High School B both planned trips there. The senior class at High School A rented and
filled 8 vans and 8 buses with 240 students. High School B rented and filled 4 vans and 1 bus with 54
students. Every van had the same number of students in it as did the buses. Find the number of students
in each van and in each bus.
8) The senior classes at High School A and High School B planned separate trips to New York City. The
senior class at High School A rented and filled 1 van and 6 buses with 372 students. High School B
rented and filled 4 vans and 12 buses with 780 students. Each van and each bus carried the same
number of students. How many students can a van carry? How many students can a bus carry?
9) Brenda's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3
senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day by
selling 8 senior citizen tickets and 5 child tickets. What is the price each of one senior citizen ticket and
one child ticket?
10) Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and
large boxes of oranges. Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of
$203. Ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the
cost each of one small box of oranges and one large box of oranges.
11) A boat traveled 336 miles downstream and back. The trip downstream took 12 hours. The trip back
took 14 hours. What is the speed of the boat in still water? What is the speed of the current?
12) DeShawn and Shayna are selling flower bulbs for a school fundraiser. Customers can buy bags of
windflower bulbs and bags of daffodil bulbs. DeShawn sold 10 bags of windflower bulbs and 12 bags
of daffodil bulbs for a total of $380. Shayna sold 6 bags of windflower bulbs and 8 bags of daffodil
bulbs for a total of $244. What is the cost each of one bag of windflower bulbs and one bag of daffodil
bulbs?
-2-
Kuta Software - Infinite Algebra 1
Name___________________________________
Systems of Equations Word Problems
Date________________ Period____
1) Find the value of two numbers if their sum is 12 and their difference is 4.
4 and 8
2) The difference of two numbers is 3. Their sum is 13. Find the numbers.
5 and 8
3) Flying to Kampala with a tailwind a plane averaged 158 km/h. On the return trip the plane only
averaged 112 km/h while flying back into the same wind. Find the speed of the wind and the speed of
the plane in still air.
Plane: 135 km/h, Wind: 23 km/h
4) The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales
the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on
the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen
ticket and the price of a child ticket.
senior citizen ticket: $8, child ticket: $14
5) The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9.
What is the number?
34
6) A boat traveled 210 miles downstream and back. The trip downstream took 10 hours. The trip back
took 70 hours. What is the speed of the boat in still water? What is the speed of the current?
boat: 12 mph, current: 9 mph
-1-
7) The state fair is a popular field trip destination. This year the senior class at High School A and the
senior class at High School B both planned trips there. The senior class at High School A rented and
filled 8 vans and 8 buses with 240 students. High School B rented and filled 4 vans and 1 bus with 54
students. Every van had the same number of students in it as did the buses. Find the number of students
in each van and in each bus.
Van: 8, Bus: 22
8) The senior classes at High School A and High School B planned separate trips to New York City. The
senior class at High School A rented and filled 1 van and 6 buses with 372 students. High School B
rented and filled 4 vans and 12 buses with 780 students. Each van and each bus carried the same
number of students. How many students can a van carry? How many students can a bus carry?
Van: 18, Bus: 59
9) Brenda's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3
senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day by
selling 8 senior citizen tickets and 5 child tickets. What is the price each of one senior citizen ticket and
one child ticket?
senior citizen ticket: $4, child ticket: $7
10) Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and
large boxes of oranges. Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of
$203. Ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the
cost each of one small box of oranges and one large box of oranges.
small box of oranges: $7, large box of oranges: $13
11) A boat traveled 336 miles downstream and back. The trip downstream took 12 hours. The trip back
took 14 hours. What is the speed of the boat in still water? What is the speed of the current?
boat: 26 mph, current: 2 mph
12) DeShawn and Shayna are selling flower bulbs for a school fundraiser. Customers can buy bags of
windflower bulbs and bags of daffodil bulbs. DeShawn sold 10 bags of windflower bulbs and 12 bags
of daffodil bulbs for a total of $380. Shayna sold 6 bags of windflower bulbs and 8 bags of daffodil
bulbs for a total of $244. What is the cost each of one bag of windflower bulbs and one bag of daffodil
bulbs?
bag of windflower bulbs: $14, bag of daffodil bulbs: $20
-2-