Download 1. Write down the standard form of a linear equation Ax + By = C 2

1. Write down the standard form of a linear equation
Ax + By = C
2. Write down the functional form of a linear equation
y = mx + b
3. Let m1 and m2 be slopes of two parallel lines. What is the relation between m1 and
m2?
m1 = m2
4. Let m1 and m2 be slopes of two perpendicular lines. What is the relation between
m1 and m2?
1
m1 = −
m2
5.
a) Write an equation for a line parallel to 1 =
2
x+y
and through the point (1, −1).
y = −x
b) Is your line from part a perpendicular to y = x?
Yes.
6. Which of the following are always true or false?
F
a) 2ab = 2a +√
2b
√
√
F
b) x + y = x + y
a+b = 2a 2b
T
c) 2√
n
F
d) √
xn = |x|
n
F
e) √ xn = x
F
f) n√x = x−n
T
g) n x = x1/n
7. Simplify the following expressions. This includes multiplying out or dividing any polynomials when possible. Indicate if simplification is impossible.
p
p
a) 5 4(x − 3)4 5 16(x − 3)4
q
2(x − 3) 5 2(x − 3)3
b)
4x4 − 3x3 + 2x − 2
x2 − 2x + 3
c) (−2)4/3
Doesn’t simplify.
√
3
2 2
√
√
√
√
d) 3 18 + 2 12 + 2 + 7 3
e)
√
√
10 2 + 11 3
12x6 y−3
√ p
6 3 x 4 y3
2x6
√
√
y4 3 x 4 y
f) (x2 − 3)(2x3 − 4x2 + x)
2x5 − 4x4 − 5x3 + 12x2 − 3x
g) −24
−16
8. Factor the following
a) x6 + y6
(x2 + y2 )(x4 + x2 y2 + y4 )
b) x3 − 5x2 + 6x
x(x − 2)(x − 3)
c) x2 − 4x + 3
(x − 3)(x − 1)
9. How many x-intercepts do the following equations have?
a) y = x2 + 2x + 3
None.
b) y = x2 − 4x + 3
Two.
c) y = x2 − 2x + 4
None.
d) y =
1
x−2
One.
e) y = x4 + 2x2 + 1
None.
10. Solve the following equations for x (and y if applicable).
a) 210−(x+1) = 16
x=5
b)
√
3
x−7+4 = 2
x = −1
c)
2x + 3y = 5
3x − 4y = 3
x=
d) (x2 − 11)2 = 25
9
29
, y=
17
17
√
x = ± 6, ±4
e) 3x4 − 31x2 + 36 = 0
x = ±3, ±
f)
1
x+2
r
4
3
=3
x=−
5
3
11. Let E(t) = 2(256)t be a formula for the number of bacteria in a dish at time t given
in hours.
a) How many bacteria are initially in the plate?
2
b) How many bacteria are in the plate after 30 minutes?
32
c) How many bacteria are in the plate after 45 minutes?
128
12.
a) Write down inequalities that define the shaded area. Is the area a rectangle?
A
B
C
D
Not a rectangle.
b) Find the corner points.
A&B: (−1, 3)
B&C: (−4 − 32 )
C&D: (− 17 , − 75
14 )
D&E: (2, 0)
y ≤ −x + 2
3
9
y ≤
x+
2
2
11
y ≥ −x −
2
5
x −5
y ≥
2
13. On the back of the page, graph the solution set of the following inequalities: x >
2, y < 3, y > 32 x − 6.
y=3
4
4
x−
6
2
3
−2
−2
2
−4
−4
−6
y=
−6
x=2
2
6