Welcome to Honors Algebra II with Trigonometry at Metamora High
School!
Summer Review Information
Dear Parents and Students,
Mathematics is a discipline that constantly builds on previous knowledge. Students entering
Honors Algebra II / Trig will be expected to recall and apply the material that they learned in
previous honors courses. The Honors Algebra II / Trig course will begin in Chapter 4 of the
textbook. It will be assumed that you have completely mastered all topics in the first three
chapters. I am including problems from these three chapters. Please take some time this
summer to go over these problems. We have even included the solutions for you!
When you return to school in the fall, be prepared to ask questions on any problems that have
you stumped. There will be a test over this prerequisite material in the first few days of class
to help determine your placement and readiness for Honors Algebra II / Trig. Students will
not turn in this packet. They are not required to do all the problems. Some class time will be
used prior to the test for questions.
If you lose this packet, the high school guidance department will have extra copies available.
Please refer to the school website to find a listing of all of our math classes. Feel free to
contact our department chair, Mrs. Stone, at [email protected] if you have any questions.
Have a wonderful summer!
The Mathematics Department
Metamora High School
Honors Algebra II / Trig
Chapter 1
1.
Name a rational number that is not an integer.
Name an integer that is not a whole number.
Name any irrational number.
Name all the number sets 0 belongs to.
2.
Solve for h: A = 2πr2 + 2πrh
______
______
______
_______________
Solve each equation. Show work!
3.
│2x + 3 │ = 7
4.
│y - 8│ + 6 = 15
Solve each inequality. Show a graph of your solution.
5.
3t – 5 > 31 – t
_____________________
6.
29 – 3x > 2
_____________________
7.
7a – (a – 4) ≤ 25
______________________
Define a variable then solve using an algebraic inequality:
8.
Sarah pays $10 admission to an amusement park then wants to ride the
roller coaster as many times as she can. If she had $32 to start with and
the roller coaster tickets are $3 each, how many times can she ride?
Solve each inequality. Show a graph of your solution set.
9.
5x + 2 ≤ -18 or 2x + 1 > 21
__________________________
11.
│2x + 1 │ ≤ 9
______________________________
13.
│
x
2
−5│+4 > 3
__________________________
10.
-2 < 4y + 10 < 12
_________________________
12.
│x – 2 │ > 4
_____________________________
14.
- 2  3x – 5  < -8
___________________________
Honors Algebra II / Trig
Chapter 2
1.
Graph the relation and name its domain and range.
Then determine whether it is a function.
{(-3,4), (-2,4), (-1,-1), (0,2), (3,-1)}
2.
Determine whether each is a function. Answer yes or no.
a.
b.
c.
d.
e.
D
1
2
R
4
5
6
3.
Let f(x) = x3 – x. Find each of the following:
a.
f(-2) _____
4.
Identify each as linear or not linear.
b.
f(5) _____
a. y + 3│x│ = 4
b. 4x – 2y = 1
d. h(x) = -2x2
e.
y=
c.
f(a) _____
c. f(x) = 0.5x + 3
3
x
5.
Name the x- and y-intercepts for 3x – 2y = 18. Express your answers as
ordered pairs.
6.
Rewrite each in standard form:
a.
y=-½x+7
7.
Find the slope of the line that passes through each pair of points:
a.
(3,-2) and (7,9)
b.
b.
15 – 12y + 9x = 0
(-4,3) and (5,-3)
8.
The median weekly earnings for American workers in 1990 was $414
and in 1999 was $549. Find the average rate of change between 1990
and 1999.
9.
Find the equation of the line that has a slope of -⅓ and passes through
(-6,1).
10.
Write an equation of the line that passes through (2,-5) and (4,3).
11.
Write an equation of the line through (-1,0) that is parallel to the
line whose equation is 6x – 2y = 3.
12.
The table below shows the relationship between the number of field goals
attempted and the number of points scored by one basketball player over
a 6-game period. Enter the data into your graphing calculator.
Field Goals Attempted (a) 8 6 10 9 7 10
Points Scored (p)
12 9 14 14 11 15
a. Find the equation of the best-fit line using your calculator. Round to
the nearest hundredth.
b. Use your equation to predict how many points will be scored when
20 field goals are attempted. Comment briefly on any danger
associated with this prediction.
13.
Determine whether each graph represents a constant function, an absolute
value function, a step function, or a piecewise function. Then identify
the domain and range.
a.
b.
Graph each of the following:
14.
A line through (-3,1) with an undefined slope.
15.
f(x) = 1 – x if x < 2
3
if x ≥ 2
16.
y=│x–4│
19.
A school is buying new computers. They will buy desktop computers
costing $1,000 per unit, and laptop computers costing $1,200 per unit.
The total cost of the computers cannot exceed $80,000. Write an
inequality that describes this situation then graph it.
17.
y≥½x+1
18.
6 – 2y < 3x
Computers Purchased
20. Determine the value of t so that the line through (1.6, t) and (2,5) has
slope - 32 .
21. Graph: y < 3 │x - 2│ + 1
Honors Algebra II / Trig
Chapter 3
Calculator Portion
Solve using your graphing calculator. Express your answer as an ordered pair
or an ordered triple.
1.
3x + 2y = 8
-5x + y = -9
2.
2x – 4y + z = -10
5x + 2y – z = 11
-3x + 2y – 3z = 3
3.
Find the coordinates of the vertices of the figure formed by the solution
of the system below.
x≤ 2
-4 ≤ y ≤ 3
x + y ≥ -3
4.
Solve.
Beth and Doug opened a sports memorabilia shop. They decided to sell
pennants and hats. On the first day of operations, Beth sold 22 pennants
and 70 hats and collected a total of $1,292. Doug sold 37 pennants and
42 hats, collecting $1,037. Set up a system of equations (show the
system) and solve for the price of a single pennant and a single hat.
Honors Algebra II / Trig
Chapter 3
Non-Calculator Portion
Solve each system using the indicated method. Express your answer as an
ordered pair.
1.
2x – y = 7
y = -5x +14
SUBSTITUTION
2.
2x + 5y = 26
7x – 3y = 9
ELIMINATION
Set up a system of equations (BUT DO NOT SOLVE).
3.
The swim team paid $446 for team suits. The suits for men cost $18 each
and the suits for women cost $32 each. Seventeen suits were purchased.
Set up a system of equations that could be used to find the price of each
gender’s suits.
4.
Bill, Gertrude, and Harriet each went shopping for hot dogs, buns, and
ketchup. Bill purchased 50 dogs, 25 buns, and 5 bottles of ketchup and
spent $117.50. Gertrude bought 40 dogs, 60 buns, and 3 bottles of
ketchup and spent $73. Harriet bought 125 dogs, 70 buns, and 20 bottles
of ketchup and spent $180. Set up a system of equations that could be
used to find the individual prices of dogs, buns, and bottles of ketchup.
Honors Algebra II / Trigonometry
Summer Review Answer Sheet
Chapter 2
Chapter 1
1.
1
; −5 ;
4
π ; whole, rational,
1.
Domain: {−3, −2, −1, 0,3}
Range: {−1, 2, 4}
It is a function.
2.
(a)
(b)
(c)
(d)
(e)
(a)
(b)
(c)
(a)
(b)
(c)
(d)
(e)
real, integer.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
A
−r
2π r
x = {2, −5}
h=
y = {17, −1}
t >9
x<9
7
a≤
2
x = # tickets
22
x≤
; she can ride a
3
maximum of 7 times.
x ≤ −4 or x > 10
1
−3 < y <
2
−5 ≤ x ≤ 4
x > 6 or x < −2
all real numbers
1
x < or x > 3
3
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
yes
yes
yes
no
no
−6
120
a3 − a
not linear
linear
linear
not linear
not linear
(6, 0) & (0, −9)
(a) x + 2 y = 14
(b) 3x − 4 y = 5
11
4
2
(b) −
3
$15 / year
1
y = − x −1
3
y = 4 x − 13
(a)
y = 3x + 3
(a) pˆ = 1.35a + 1.25
13.
(b) 28.25 points. We are
extrapolating from our
data.
(a) absolute value or piecewise function.
Domain: ℝ
Range: x ≥ −2
(b) step function
Domain: −4 ≤ x ≤ 2
Range: {−1, 0,1, 2,3, 4}
17.
18.
14.
19.
y = # desktops
x = # laptops
1, 000 y + 1, 200 x ≤ 80, 000
15.
16.
20.
21.
35
4
Chapter 3 (calculator portion)
1.
2.
3.
4.
(2,1)
(1,3,0)
(-6,3), (2,3), (2,-4), (1,-4)
$11 pennant; $15 hat
(Non-calculator portion)
1.
2.
3.
4.
(3,-1)
(3,4)
x=number of male suits
y=number of female suits
18x+32y=446
x+y=17
d=price of hot dog
b=price of hot dog bun
k=price of ketchup
50d+25b+5k=117.50
40d+60b+3k=73
125d+70b+20k=180