Alg.II Honors
CHAPTER 2 REVIEW
1.
Do these points represent a function? ( −4, 6 ) , ( 7, 1 ) , ( 2, −9 ) , ( 7, 7 ) , ( 4, 5 )
2.
Solve
2
1
( 14 + 21x ) −
( 10x − 15 ) = 2 + x
7
5
for x.
3.
Solve
r + 8 − 2( r + 2 ) = 7( 3 − r ) − (−1)
for r.
4.
Solve
−4( 5 − a ) + 3( a − 2 ) = −3( 14a − 50 ) − 29
5.
Solve 8 −
6.
Determine k so that ( 3 + k ) x − ( 1 − y ) = 1 − y has slope
7.
⎞
⎛ 2
Determine k so that the point ⎜ , − 3 ⎟ lies on the line 2kx − ( 1 − k ) y = 5 .
⎠
⎝ 5
8.
Determine k so that the line through ( − k , k − 1 ) , ( 3 − k , 1 ) has slope 1 − k .
9.
2 ⎞
⎛ 1
Find an equation in standard form of the line containing the points ( − 5 , 2 ) , ⎜ , − ⎟
3 ⎠
⎝ 2
10.
11.
9
3
p > p−1
4
4
for a.
for p.
1
.
3
Find an equation in standard form of the line ⊥ to the line y = − 6 , with x-intercept 5 .
1 ⎞
⎛
Find an equation in std. form of the line through ⎜ 3 ,
⎟ and parallel to the line containing
5 ⎠
⎝
(−2, 0), (8, 1) .
12.
Lance covered a horizontal distance of 3 km while riding up a 12% slope. How much altitude did
he gain?
13.
Find an equation in standard form of the line with slope 0 that passes through point ( − 13 , −
14.
Find an equation in slope-intercept form of the line through point ( 5 , − 1 ) that is perpendicular
⎛ 7
4 ⎞
1
⎟⎟ with slope
, −
.
to a line that passes through point ⎜⎜
13 ⎠
3
⎝ 20
15.
⎛ 13
⎛ 1 3 11
5 ⎞
, − ⎟⎟ and ⎜⎜
,
Find an equation in standard form for the line passing through ⎜⎜
8 ⎠
⎝ 17
⎝ 17 9
16.
If r is a linear function and r(−8) = 7 and r(9) = −2 , what is r(5) ?
17.
Find the value of k for the line through points ( 3k − 2 , k2 − 1 ), ( 1 − k , 5 − k2 ) with slope
18.
If n is a linear function and n(5) = −3 and n(−2) =
19.
Find the solution set of 4x = 61 − 3y if each variable represents a whole number.
3
, what is n(x) ?
7
⎞
⎟⎟ .
⎠
k
.
2
12
).
17
2
−3( 7x + 2x ) + x −
(
39
) 2 < 2( x − 1 ) − 18 − 6( x
2
− 4 ) + ( −1 )
4
20.
Solve
for x .
21.
Simplify
22.
The points ( x , 2 ) , ( −7 , y ) , ( 4 , −1 ) , ( 5 , 5 ) are collinear. Find the value of x and y.
23.
Translate into words the expression:
5 x − 6 < 35
24.
Translate into words the expression:
3 − 4 x > 32
25.
If h is a linear function and
26.
Solve for m and n.
−12 + 12 ÷ 3 • 5
h( −1 ) = 2 and h( 3 ) = − 1 , find h( 10 ) .
2
( 5 n − m ) = − 1 ( 2 m − 9n )
4
3
1
(5 − 2m ) = − 3 ( n − 2m )
4
3
If g( x ) = mx + b
28.
1 ⎞
⎛ 1
Is the point ⎜ , − ⎟ on the graph of
3 ⎠
⎝ 3
29.
Find x if the perimeter of the figure is 108.
30.
Determine the lines that make up the graph of the function
each line.
31.
Multiple Choice.
a) −
1
3
<p<−
5
5
d) p < −
3
1
or p > −
5
5
find
3m h
g( x + h ) − g( x )
27.
Solve
3p −
f( x ) =
3
6
>
5
5
b) −
2x2
?
5x −1
y = − 3 x − 7 + 9 . Give the domain of
for p .
1
3
<p<
5
5
e) none of these
c) p >
3
1
or p < −
5
5
32. Solve for x if the perimeter of the figure shown is 44 .
(Please do not write on the test!)
a) x = 2
b) x = 3
c) x = 4
d) x = 5
e) none of these
33.
Multiple Choice.
r ( x ) = x − 2 − 6 and f( x ) is the reflection of r( x ) across the
y-axis.
Given:
What is f( x )?
a)
f(x)= x + 2 + 6
b)
f(x)= x + 2 − 6
d)
f( x) = − x + 2 + 6
e)
f( x) = − x − 2 − 6
34.
Consider the functions h( x ) = 2 x − 3
is common to both functions?
a) ( 2.25 , 1.5 )
b) ( 2 , 2 )
c)
f( x) = − x + 2 − 6
and r ( x ) = 2 x − 3 . Which one of the following points
c) ( 1.5 , 2.25 )
d) ( −1 , 8 )
35. Describe the transformations on
f( x)= x
by the function
g( x ) = 4 − x − 5
36. Describe the transformations on
f( x)= x
by the function
g( x ) = − x − 1 + 2
37. What is/are the x-intercept(s) of the function g( x ) = 2 x − 6 − 3 ?
38. What is/are the x-intercept(s) of the function g( x ) = − x + 2 ?
39. What is/are the x-intercept(s) of the function g( x ) = x − 4 + 1 ?
40. Solve
r − 3 w ( 1 − r ) + 2 wr = w − w ( 2r + 1 ) + 1
for r.
e) ( −3 , 9 )
ANSWER KEY
1.
NO
5.
p<3
9.
2.
x=3
6.
k= −
11
3
3.
r=3
7.
k= −
10
11
10.
x=5
11.
x − 10y = 1
14.
y = −3x + 14
15.
17x = 13
19.
4.
a=3
8.
k=
1
2
12.
3 53 km
16.
y=
(13, 3), (10, 7),
(7, 11), (4, 15),
(1, 19)
20.
x > −2
23.
the solution is
the set of points
a distance less than
6
7 units from
.
5
24.
27.
3
28.
16x + 33y = −14
13.
y= −
17.
k=4
12
17
18.
24
27
n( x ) = −
x −
49
49
21.
8
25.
22.
x=
9
, y = −67
2
26.
h(10) = -6.25
29.
m=
30.
31.
33.
b
34.
a
C
32.
7
x≤
3
y = −3x + 16 , x ≥
NO.
⎛ 1⎞ 1
f⎜ ⎟=
⎝ 3⎠ 3
13
1
, n=
16
8
y = 3x + 2 ,
2
17
7
3
35.
36.
37.
1.5 and 4.5
38.
39.
40.
r=
1 + 3w
1 + 7w