C Challenge
Add or subtract.
-
1
1
−
5
+
1
1
+
5
fraction 1 , over 1 minus square root of 5 end fraction . plus . fraction 1 , over 1 plus square root of 5 end fraction
-
4
5
−
3
−
4
5
+
3
fraction 4 , over square root of 5 minus square root of 3 end fraction . minus . fraction 4 , over square root of 5 plus square root of 3 end fraction
- For what values of a and b does
a
+
b
=
a
+
b
?
square root of eh plus square root of b equals , square root of eh plus b end root , question mark
- In the expression
x
m
n
,
the th , root of x to the m end root , , comma m and n are positive integers and x is a real number. The expression can be simplified.
- If
x
>
0
,
x greater than 0 comma what are the possible values for m and n?
- If
x
<
0
,
x less than 0 comma what are the possible values for m and n?
- If
x
<
0
,
x less than 0 comma and an absolute value symbol is needed in the simplified expression, what are the possible values of m and n?
Standardized Test Prep
GRIDDED RESPONSE
SAT/ACT
- What is the value of the expression
(
5
−
2
3
)
(
5
+
2
3
)
?
open . 5 minus 2 square root of 3 . close . open . 5 plus 2 square root of 3 . close . question mark
- What is the value of z in the solution of the system of equations below?
{
2
x
−
3
y
+
z
=
6
−
x
+
y
−
2
z
=
−
5
3
x
−
y
−
3
z
=
−
7
left brace . table with 3 rows and 3 columns , row1 column 1 , 2 x minus , column 2 3 y plus z , column 3 equals 6 , row2 column 1 , negative x plus , column 2 y minus 2 z , column 3 equals negative 5 , row3 column 1 , 3 x minus , column 2 y minus 3 z , column 3 equals negative 7 , end table
- What is the y-value of the y-intercept of the line
5
x
−
7
y
=
−
15
?
5 x minus 7 y equals negative 15 question mark
- What is the slope of a line perpendicular to the line
2
x
+
5
y
=
10
?
2 x plus 5 y equals 10 question mark
- What is the value of p for which the equation
x
2
−
12
x
+
4
p
=
0
x squared , minus 12 x plus 4 p equals 0 has exactly one real root?
Mixed Review
See Lesson 6-2.
Simplify each expression. Rationalize all denominators.
-
3
3
⋅
18
3
cube root of 3 , , dot , cube root of 18 ,
-
4
0.5
x
3
cube root of fraction 4 , over 0.5 x end fraction end root ,
-
32
2
fraction square root of 32 , over square root of 2 end fraction
-
216
6
fraction square root of 216 , over square root of 6 end fraction
-
2
x
2
3
⋅
4
x
3
cube root of 2 , x squared end root , . dot , cube root of 4 x end root ,
-
7
x
⋅
14
x
3
square root of 7 x end root , dot . square root of 14 , x cubed end root
-
3
x
⋅
5
x
square root of 3 x end root , dot , square root of 5 x end root
-
9
x
2
⋅
25
x
2
square root of 9 , x squared end root , dot . square root of 25 , x squared end root
See Lesson 5-3.
Find the real and imaginary solutions of each equation.
-
2
x
3
−
16
=
0
2 x cubed , minus 16 equals 0
-
x
3
+
1000
=
0
x cubed , plus , 1000 , equals 0
-
125
x
3
−
1
=
0
125 x cubed . minus 1 equals 0
-
x
4
−
14
x
2
+
49
=
0
x to the fourth , minus , 14 x squared , plus 49 equals 0
-
25
x
4
−
40
x
2
+
16
=
0
25 x to the fourth , minus , 40 x squared , plus 16 equals 0
-
81
x
4
−
1
=
0
81 x to the fourth , minus 1 equals 0
Get Ready! To prepare for Lesson 6-4, do Exercises 88-91.
See p. 970.
Simplify.
-
(
x
2
)
3
open , x squared , close cubed
-
(
p
q
)
5
open p q close to the fifth
-
(
2
4
)
(
2
5
)
open , 2 to the fourth , close open , 2 to the fifth , close
-
(
3
−
2
)
(
3
5
)
open , 3 super negative 2 end super , close open , 3 to the fifth , close
