Pre-Calculus
Summer Assignment
Name_____________________________
 This assignment will be due the first day of class.
 Late assignments will have ten points deducted for each day late.
 Show ALL WORK for ALL PROBLEMS. Credit will not be given to those
answers lacking written work.
Pre-Calculus Summer Assignment
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Solve the system by the method of substitution.
____
1.
a. (0, –5)
b. (–5, 0)
c. (5, 1)
d. (1, 5)
Use the elimination method to solve the system.
____
2.
a. (3, 5)
b. (5, 3)
Solve the system of inequalities by graphing.
c. (–3, –5)
d. (–5, –3)
____
3.
a.
c.
y
–4
–2
4
4
2
2
O
2
4
–2
O
–2
–4
–4
d.
y
–2
–4
x
–2
b.
–4
y
4
2
2
2
4
x
4
x
2
4
x
y
4
O
2
–4
–2
O
–2
–2
–4
–4
Identify the vertex and the axis of symmetry of the parabola. Identify points corresponding to P and Q.
____
y
4.
8
4
Q
–8
–4
O
P
4
8
x
–4
–8
a. (–1, –2), x = –1
P'(0, –1), Q'(–3, 2)
c. (–1, –2), x = –1
P'(–2, –1), Q'(–1, 2)
b. (–2, –1), x = –2
P'(–2, –1), Q'(–1, 2)
d. (–2, –1), x = –2
P'(0, –1), Q'(–3, 2)
Find a quadratic model for the set of values.
____
5. (–2, 8), (0, –4), (4, 68)
a.
b.
____
c.
d.
6. Use vertex form to write the equation of the parabola.
y
8
6
4
2
–8 –6 –4 –2 O
–2
2
4
6
8
x
–4
–6
–8
a.
c.
b.
d.
Factor the expression.
____
____
____
7.
a.
c.
b.
d.
a.
c.
b.
d.
a.
c.
b.
d.
8.
9.
____ 10.
a.
c.
b.
d.
Solve the equation.
____ 11.
a. 14, 4
c. 14, –14
b. –4, –14
d. –4, 4
____ 12.
a. –5, 11
b. 5
c. 11
Solve the quadratic equation by completing the square.
d. –11
____ 13.
a.
c.
6
b.
6
d.
____ 14. Find the zeros of
. Then graph the equation.
a. 3, 2, –3
c. 3, 2
y
–6
–4
y
6
6
4
4
2
2
–2
2
4
6
x
–6
–4
–2
–2
–2
–4
–4
–6
–6
b. 0, –3, –2
4
6
x
2
4
6
x
d. 0, 3, 2
y
–6
2
–4
y
6
6
4
4
2
2
–2
2
4
6
x
–6
–4
–2
–2
–2
–4
–4
–6
–6
Divide using synthetic division.
____ 15.
a.
c.
b.
d.
Use Pascal’s Triangle to expand the binomial.
____ 16.
a.
b.
c.
d.
Multiply and simplify if possible.
____ 17.
a.
c.
b.
d.
____ 18. Simplify
. Assume that all variables are positive.
a.
c.
b.
d. none of these
a.
c.
b.
d. none of these
____ 19.
Multiply.
____ 20.
a.
b. –3
c. 17
d.
____ 21.
a.
7
6
b.
2
3
c.

1
4
____ 22. Use a graphing calculator to find the point(s) of intersection of
nearest hundredth.
a. (5, 1), (–5, 1)
c. (0.45, 1), (–0.45, 1)
b. (2.24, 1), (–2.24, 1)
d. (0.2, 1), (–0.2, 1)
Add or subtract. Simplify if possible.
____ 23.
a.
c.
d.
6
7
and y = 1. If necessary, round to the
b.
d.
Simplify the complex fraction.
____ 24.
a.
c.
b.
d. not here
Solve the equation. Check the solution.
____ 25.
a. –9
____ 26. Find
a. –9
b. –6
c. –9 and –6
d. 6
b. 9
c.
d.
.
41
Graph the equation. Describe the graph and its lines of symmetry.
____ 27.
a.
c.
y
y
8
8
6
6
4
4
2
2
–8 –6 –4 –2
–2
2
4
6
8
–8 –6 –4 –2
–2
x
–4
–4
–6
–6
–8
–8
The graph is an ellipse. The center is at the
origin. It has two lines of symmetry, the
x-axis and the y-axis.
b.
8
6
6
4
4
2
2
2
4
6
8
x
–8 –6 –4 –2
–2
–4
–4
–6
–6
–8
–8
The graph is an ellipse. The center is at the
origin. It has two lines of symmetry, the
x-axis and the y-axis.
6
8
x
y
8
–8 –6 –4 –2
–2
4
The graph is a circle. The center is at the
origin. Every line through the origin is a
line of symmetry.
d.
y
2
2
4
6
8
x
The graph is a circle. The center is at the
origin. Every line through the origin is a
line of symmetry.
Identify the center and intercepts of the conic section. Then find the domain and range.
____ 28.
y
8
6
4
2
–8 –6 –4 –2
–2
2
4
6
8
x
–4
–6
–8
a. The center of the hyperbola is (0, 0). The y-intercepts are (0, 5) and (0, –5). The domain is all
real numbers. The range is {y | y  –5 or y  5}.
b. The center of the hyperbola is (0, 0). The x-intercepts are (0, 5) and (0, –5). The domain is all
real numbers. The range is {y | y  –5 or y  5}.
c. The center of the hyperbola is (0, 0). The y-intercepts are (0, 5) and (0, –5). The domain is all
real numbers. The range is {y | y  –5 or y  5}.
d. The center of the hyperbola is (0, 0). The x-intercepts are (0, 5) and (0, –5). The domain is all
real numbers. The range is {x | x  –5 or x  5}.
____ 29. The point
the graph.
is on the graph of
. Use symmetry to find at least one more point on
a.
c.
b.
d.
____ 30. In a factory, a parabolic mirror to be used in a searchlight was placed on the floor. It measured 50 centimeters
tall and 90 centimeters wide. Find the equation of the parabola.
y
80
60
40
20
–40
–20
20
40
x
a.
c.
b.
d. none of these
____ 31. Graph
.
a.
c.
y
–4
4
4
2
2
–2
2
4
–4
x
–2
–2
–2
–4
–4
b.
d.
y
–4
y
4
2
2
2
4
–4
x
4
x
2
4
x
y
4
–2
2
–2
–2
–2
–4
–4
____ 32. A satellite is launched in a circular orbit around Earth at an altitude of 120 miles above the surface. The
diameter of Earth is 7920 miles. Write an equation for the orbit of the satellite if the center of the orbit is the
center of the Earth labeled (0, 0).
a.
c.
b.
d.
Graph the exponential function.
____ 33.
a.
c.
y
y
4
16
–6
–4
–2
2
4
6
x
12
–4
8
–8
4
–12
–6
–16
–4
–2
2
4
6
x
2
4
6
x
–4
–20
b.
d.
y
y
20
16
16
12
12
8
8
4
4
–6
–4
–2
2
4
6
x
–6
–4
–4
–2
–4
____ 34. An initial population of 895 quail increases at an annual rate of 7%. Write an exponential function to model the
quail population.
a.
c.
b.
d.
Graph the function. Identify the horizontal asymptote.
____ 35.
a.
c.
y
y
14
14
12
12
10
10
8
8
6
6
4
4
2
2
–4 –3 –2 –1
–2
1
2
3
4
–4 –3 –2 –1
–2
x
asymptote: x = 0
2
3
4
x
1
2
3
4
x
asymptote: x = 7
b.
d.
y
y
1
–8 –6 –4 –2
–1
14
12
2
4
6
8
x
10
–2
8
–3
6
–4
4
–5
2
–6
–4 –3 –2 –1
–2
–7
asymptote: x = –4
asymptote: x = 0
____ 36. Use a graphing calculator. Use the graph of
a. 5.4739
1
b. 4.6211
to evaluate
c. 2.7183
to four decimal places.
d. 0.1827
____ 37. How much money invested at 5% compounded continuously for 3 years will yield $820?
a. $952.70
b. $818.84
c. $780.01
d. $705.78
Write the equation in logarithmic form.
____ 38.
a.
c.
b.
d.
Evaluate the logarithm.
____ 39.
a. –3
b. 5
____ 40. Write the equation
a.
c. –4
d. 4
in exponential form.
b.
c.
d.
Graph the logarithmic equation.
____ 41.
a.
c.
y
–12
–8
12
8
8
4
4
–4
4
8
–4
–8
–8
–12
–12
d.
12
8
8
4
4
–4
4
8
12 x
4
8
12 x
4
8
12 x
y
12
–12
–8
–4
–4
–4
–8
–8
–12
–12
Write the expression as a single logarithm.
____ 42.
–8
–4
y
–8
–12
12 x
–4
b.
–12
y
12
a.
c.
b.
d.
a.
c.
b.
d. none of these
____ 43.
Expand the logarithmic expression.
____ 44.
a.
c.
b.
d.
____ 45. Solve
a. 0.6616
. Round to the nearest ten-thousandth.
b. 2.6466
c. 1.7509
d. 1.9091
____ 46. Use the Change of Base Formula to solve
a. 7.6133
____ 47. Solve
a.

b. 9.3658
. Round to the nearest ten-thousandth.
c. 3.2459
d. 12.9837
c.
d.
.
7
4
b.
495
2
____ 48. Solve
a. 12.3308
250
.
b. 43.3013
c. 86.6025
Write the expression as a single natural logarithm.
____ 49.
990
d. 1875
a.
b.
c.
____ 50. Describe the vertical asymptote(s) and hole(s) for the graph of
a. asymptote: x = –4 and hole: x = 2
b. asymptotes: x = –4 and x = 2
c. asymptote: x = –5 and hole: x = –4
d. asymptote: x = 4 and hole: x = –2
d.
.