Download Warm-up for Honors Functions

Nichols School Mathematics Department
Summer Assignment
Warm-up for Honors Functions
Who should complete this packet? Students who will be taking Honors Functions in the fall of
2016.
Due Date: The first day of school
How many of the problems should I do? – ALL OF THEM
How should I organize my work? You should show all work in a separate sheets of loose-leaf
paper. If a problem requires a graph, then you should use graph paper. Keep your materials in
a 3-prong folder.
How will my teacher know that I’ve done the work? –Your teacher will collect your
notebook on the first day of school. Your teacher may choose to QUIZ or TEST you on this
material if he or she feels it is necessary – BE PREPARED!
How well should I know this material when I return? – You should recognize that you’ve
seen this material before, and you should also be able to answer questions like the ones in this
packet. If the material is revisited in your next class, it will only be for a brief amount of time –
your teacher will assume that all you need is a quick refresher.
Note from your teachers:
We feel that this summer work will truly help you succeed this year. We understand that
summer is a time for relaxation and fun, but it is imperative that you spend some time before
you return reviewing your materials. This packet is mandatory, and you must treat it as you
would any other extremely important homework assignment. You will be held accountable for
this material. We also highly suggest that you do a bit of it at a time in the weeks leading up to
school – don’t leave it for the last day!!!
Warm-up for Honors Functions
Instructions:
▪ Complete the problems on loose-leaf paper in pencil. If a problem requires a graph paper.
▪ If a problem requires a graph or a diagram, please a ruler, and draw accurately.
▪ Complete all the problems carefully. Show enough work to indicate your method of
solution.
▪ Make sure your work justifies your answer.
▪ At the top of each page of your work, write your name and the page number.
▪ Keep the packet and your work in a folder.
▪ Arrange your completed work in page order; staple the pages together or put the pages in a 3prong report folder.
Remember, your teacher will collect your work on the first day of school! Late work will be
penalized, and it may NOT be accepted.
What if I get stuck? - You should check out other additional study materials. Consult a
standard algebra textbook. Find a study buddy or a classmate to help you remember the
material. Consult the following websites for hints and examples:
http://www.coolmath.com/prealgebra/index.html
http://www.math.com/practice/PreAlgebra.html
http://www.brightstorm.com/math
http://www.khanacademy.org
Warm-up for Honors Functions
page 1
1.
A set S of real numbers is closed under if the sum of any two numbers of S is in S. A set S is
closed under multiplication if the product of any two numbers of S is in S. Is the set of real
numbers 1,0,1 closed under (a) addition and (b) multiplication? If the set is not closed, give
an example to show this.
2.
1
Solve s   gt 2  vt for g.
2
3.
A car traveled for ½ hour at r min/h, then increased the speed by 10 mi/h and traveled for 1 1 2 h
more, How far did the car go?
4.
Two cars leave City A at the same time to travel to City B. One car travels at 72 km/h and the
other at 78 km/h. If the slower car arrives 20 min after the faster car, how far apart are City A
and City B?
5.
Determine k so that the line through  k  2, k  and  3, 2  has slope 3.
6.
Find an equation in standard form of the line perpendicular to x  y  5 that passes through
the point  0, 8 .
7.
Graph f  x   x  1  2 with domain D  2, 1, 0,1, 2 .
8.
If f  x  is a linear function and f  0   10 and f 10   14 , find f  5 and f  5 .
9.
If x and y are integers, find the domain of
 x, y  : y  x
and
x  4 . Graph the relation. Is
it a function? Justify your answer.
10. Solve each equation. Identify all double roots.
a. 8 x 2  1  6 x
b. x 4  25 x 2  0
Nichols School Mathematics Department
c.
 x  3   x  3
3
2
0
Warm-up for Honors Functions
page 2
11. Solve the equation 4
3
1
12. Solve the equations
method.
18
0 by the method of completing the square.
30
2√
18
45 using substitution-by-variable
13. Find and graph the solution set x 3  16 x  0 .
14. If you fill half of a container whose capacity is t liters and then remove 2 liters, how full is the
container? Express your answer in simplest form in terms of the variable t.
15. Find the reciprocal of √2
√3
√5.
16. Find a quadratic equation with integral coefficient having roots 4
2
4
2.
17. At 1:30 PM two planes leave Chicago, one flying east at 540 km/h and the other flying west at
620 km/h. At what time will they be 1450 km apart?
18. It takes 6 hrs for a plane to travel 720 km with a tail wind and 8 hours to make the return trip
with a head wind. Find the air speed of the plane and the speed of the wind current.
19. The height of a triangle is 3 cm less than the length of its base, and its area is 20 squared
centimeters. Find the height.
x 2  x  12
.
20. Find (a) the domain and (b) the zeros of the function f  x  
3x  2
21. Solve.
a.
3
1
4

 2
x  2 x  8 x  2 x  16
2
b.
1
2

0
x  2 x 1
Nichols School Mathematics Department
Warm-up for Honors Functions
page 3
22. Simplify.
a.
t2  9 t  3

t  2 t2  4
b.
x y
x y
d.
1 1

x y
1
c.
1
2
 2
s 1 s 1
ab  1
a 1b  1
23. The Simon brothers rowed 18 km upstream in 3.75 h. The return trip with the same current
took only 2.5 h. What was the speed of the current?
24. One crew can finish a job in 6 days. Another crew can do the same job in 4 days. If the slower
crew works alone for the first two days and then is joined by the faster crew, how long will it
take the crews to finish?
25. A bicycle trip of 90 mi would have taken an hour less if the average speed had been increased
by 3 mi/h. Find the average speed of the bicycle.
26. Find x such that
2
3
.
27. Resolve the algebraic fraction
4 x 2  6 x  11
into partial fractions.
 x2  1  x  4 
28. Linear Programing. The X Company makes two products: VCRs and DVDs players. Each
VCR gives a profit of $30, while each DVD player produces a $70 profit. The company must
manufacture at least 10 VCRs per day to satisfy one of its customers, but no more than 50,
because of production restrictions. The number of DVD players produced cannot exceed 60 per
day, and the number of VCRs cannot exceed the number of DVD players. How many of each
should the company manufacture to obtain maximum profit?
Nichols School Mathematics Department
Warm-up for Honors Functions
page 4
29. Solve: a)
3
2 x 2  x  1  1 , b) 11  x  5 x  1 .
30. Find all real values of k for which 3t 2  6t  k  0 has two real roots.
31. Find an equation of the form y  a  x  h   k for the parabola that has vertex 1, 5  and
2
contains  4,3 . Give the domain, range and zeros of your function.
32. Find a quadratic function f  x   ax 2  bx  c whose graph has maximum value of 25 and
x-intercepts  3 and 2.
1
33. Find P   given that P  x   2 x3  5 x 2  6 x  5 using synthetic division.
2
34. Use synthetic division to divide 6
7
1
2
3.
 2 x  5 y  4 z  18

35. Solve the system using Gauss method  x  3 y  5 z  7 .
3x  2 y  4 z  22

36. Given the equations of the line x  2 y  1 and the parabola y  x 2  4 x  4 . Let D  x  represent
the vertical distance between the straight line and the parabola in the between the points of
intersection. Find the maximum vertical distance between the straight line and the parabola in
the between the points of intersection.
37. Area Problem. A rectangular field is to be enclosed by a fence and divided into two parts by
another fence. The total amount of fencing that can be enclosed and separated in this way is 800
meters. What dimensions will give a maximum area, and what will this area be?
Nichols School Mathematics Department