Download Summer Packet Honors PreCalculus Pre

Summer Packet
Honors PreCalculus
Pre-Calculus is a demanding course that relies heavily upon a student’s algebra, geometry, and trigonometry skills. You
are expected to know these topics before entering Honors Pre-Calc. You should be able to do 95% of this packet without
a calculator!
DUE: 1st day of school
We will briefly review this in class and you will be assessed on the contents of the packet before starting the new
material. The packet will be collected and graded.
1. Graph the line using x- and y- intercepts.
4x – y = 8
2. Are the points (3, 4) and (-2, 6) solutions to 4x – y = 8? Justify.
3. Find the slope of each line and graph.
a) y = -4
4. If the point
b) x = 2
lies on the graph of the equation
, find the value of k.
1
5. Put 7x + 13y = 26 into slope intercept form and graph.
6.
Find the slope of the line Ax + By = C
7. A line has equation x + 2y = 5. Find the slope of a line that is
a) parallel
b) perpendicular
8. Find an equation in Standard Form of the line with x – intercept 5 and y-intercept 3.
9. Find an equation in Slope-Intercept Form of the line that goes through (8, 3) and (2, -1).
10. Find an equation in Standard Form of the line through (1, -4) that is perpendicular to the line 2x – y = 4.
11. Find an equation in Standard Form for the perpendicular bisector of the segment joining (0, 3) and (-4, 5).
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12. Use substitution to find all points of intersection of the graphs of
13. Use elimination to find all points of intersection of the graphs of
14. Find all points of intersection of the system of
2 x  y  2
x y 2
3 x  2 y  10
and
6 x  5 y  16 .
and
and
4 x  y  6
2x  5 y  3 .
by graphing.
15. The dollar value of a product in 2011 is $1430. The value of the product is expected to increase $83 per year for the
next five years. Write a linear equation that gives the dollar value V of the product in terms of the year t.
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16. During the first and second quarters of a year a business has sales of $150,000 and $185,000, respectively. If the
growth follows a linear pattern, what will sales be during the fourth quarter?
17. For the points (1, 4) and (-5, -1) find the distance and midpoint.
18. If A(2, 0), B(0, 8), C(-4, 7), and D(-2, -1) are points,
a) Show AC and BD bisect each other.
b) Show AC = BD.
c) What kind of quadrilateral is ABCD?
19. If 3 pencils and 2 pads cost $1.30 while 5 pencils and 1 pad cost $1.00, what would be the
cost of each pencil and each pad? Model the situation with equations, define variables, and solve.
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20. The table shows the years of experience for eight technicians and the hourly pay each earns.
Experience
9
4
3
1
10
6
12
8
$17
$10
$10
$7
$19
$12
$20
$15
(Years)
Hourly Pay
a) Make a scatter plot of the data.
b) Draw a line of best fit.
c) Determine an equation for your line.
d) According to your model, what is the expected hourly
pay of a technician with 15 years experience?
21. Find the intercepts, zeros, axis of symmetry and vertex of the graph of
Graph the parabola.
5
y  x 2  3x  10 .
22. Without putting the parabola in vertex form, identify the vertex. Is the vertex a maximum or minimum?
a)
b)
23. Find the domain and range of each:
a)
b)
y  x 2
c)
y  2x2  6x  7
24. Let
,
and
. Find:
a)
b)
c)
d)
f ( x  b)
e)
( f  g )( x)
f)
h
  x 
g
g)
( f  g )( x)
6
25. Given
f ( x)  2  3x , find f (5) .
26. Given
f ( x) 
1 x
 2 , find f (3) .
2
27. Use synthetic division to simplify
28. Use long division to simplify
5x3  6 x  8
.
x2
.
29. Simplify
30. Simplify
x 2  y 2
x 1  y 1
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31. Simplify
32. In right triangle ABC, with angle B being the right angle,
a. If AB = 16 and m
A = 53 , find BC
b. If AB = 36 and AC = 47, find m
A
33. Find the unknown sides.
45⁰
8 in.
15cm.
34. Determine whether the relation determines a function.
a) A person and their birthday
b) 2
11
2
10
3
8
4
5
5
1
c)
8
60⁰