Mth 65
1)
Practice Exam
Franz Helfenstein
Name
True or False. Circle T if always true otherwise circle F.
a)
T
F
x + y = x1/2 + y1/2
b)
T
F
c)
T
F
x+7=
d)
T
F
e)
T
F
f)
T
F
x+
7
(a + b + c)2 = a2 + b2 + c2
x1/2 + x1/2 = x1
x3 = x x
A parabola must cross the x-axis.
b2 – 4ac
determine x (nearest hundredth) for: 3.58 x2 – 4.26 x – 27.4 = 0
2a
Simplify by removing to all positive exponents:
x4 (x–3 y2 )3
3)
(a3 b2)3 a3 b5 =
4)
=
y–3 x3
Factor: If the expression does not factor, write DNF or Prime.
5)
2x2 – 3x3 =
6)
6xy + 3x2 y =
–b ±
2)
Using: x =
7)
4x2 – 25y2 =
8)
21xy – 10y + 35y2 – 6x =
9)
6x2 + x – 2 =
10)
x2 – 7x + 12 =
In problems 11 – 17 simplify and write any polynomials in standard form.
11)
P(x) = x2 – 9x + 6
12)
9x5 – 4x3 (2x2 – 3x) =
13)
14)
(3x2 – 3x + 2) + ( 11x2 – 7x – 5) =
15)
16)
(2x + 3)(4x – 5) =
17)
(a) P(t) =
(c) P(2) + 2x2 + 8 =
(b) P(–2) =
6xy(x + 2x2) + 3(2x2 y – 3x3 y) =
(7x2 – 5x + 2) – (11x2 – 7x + 5) =
(x + 1)(x2 – x + 1) =
In problems 18 – 23 simplify and write any polynomials in standard form.
1
x
=
1
1–
x
1+
18)
x
y
+ =
y
x
19)
20)
27x + 18
x–3
·
=
x–2
18x + 12
21)
x2 x2 – 1
·
=
x+1
x3
22)
2x
x–1
–
=
1
x+1
23)
7
5
+
=
x x+4
Solve the equations in problems 24 – 31. If there is no solution write 'no solution'.
2
2x2 + 7x = 15
24)
x + 24 = 11x
25)
26)
x(x + 4) – 5(x + 3) + 3 = 0
27)
28)
3
–5
– 2=
x+5
x+5
29)
2x + 2 2x – 2
–
=3
x–1
x+1
30)
2x + 5 + x = 5
31)
Solve for y:
32)
Find the missing side, z,
when: x = 24, y = 7
33)
(x + 4)(x – 3) = (2x – 1)(3 – x)
x
y+x 1
+
=
2
3
4
Find the area, A, when:
x = 8, z = 17
x
A
y
z
y
z
x
34)
2
V(t) = – t + t + 90 represents the amount of a nasty cold virus in the bloodstream. t=0 is the
moment you notice the cold symptoms.
(a) Find the 4 critical points for V(t):
roots:
root1 t =
y-intercept: y =
root2 t =
vertex: (t, y) =
(b)
Sketch V(t) and label the critical points.
(c)
According to your graph, when did you catch the cold?
(d)
According to your graph, when will it be the worst?
(e)
According to your graph, when will it be completely over?
(x – 9)(x + 5)
7
Sketch the parabola, Include with labels:
All roots, y-intercepts, the (x,y)-vertex:
37)
The Falling Body Model, H(t) = -16 t2 + v0 t + h0 , gives the height, H (ft), as a function of time, t (sec).
v0 represents the initial velocity and h0 represents the initial height.
(a) How long until the arrow hits the ground?
(b) An arrow is shot upward from ground level with initial velocity of 384 ft/sec. What is the
maximum height attained?
38)
C(t) = t2 – 8t + 15 represents the coyote population in a test plot where t=0
corresponds to the year 2000. In what year will the population become
extinct if this trend continues?
40)
41)
Given y =
Coyotes
Given y =
C(t)
t=0
2000
t=10
2010
m ax cap acit y
C(t) = 0.1t2 + 0.1t + 199.4 represents the coyote population in a test plot
where t=0 corresponds to the year 2000. In what year will the population
reach 200 if this trend continues?
Co yo tes
39)
36)
(x + 10)(2 – x)
4
Sketch the parabola, Include with labels:
All roots, y-intercepts, the (x,y)-vertex:
35)
C(t )
t=0
2000
t=10
2010
C(t) = -t2 + 10t + 75 represents the concentration of cold virus in the bloodstream. t=0 is the moment
you notice the cold symptoms. What does C = 0 represent? When did you catch the cold? When will
it be the worst? When will it be completely over? When will the symptoms go away?
100 (t + 5)
Suppose P(t) =
represents a population at time t, t ≥ 0.
t + 20
(a) Is there any time for which the population is undefined?
(b) Create a T-table for 0 ≤ t ≤ 50 and graph the population.
(c) How do we interpret P(0)?
t
0
5
10
15
P
(d) Estimate P(∞). How do we interpret this?
(e) Estimate the maximum population.
20
25
…