Download Document

Review
Advanced Algebra/Trigonometry Honors
Name ______________________
Basic Things You Absolutely Need to Know: Remember?
Special Triangles
Domain, Range, Roots
Domain: x-values
 x 0  x  4
Range: y-values
 y 3  y
Roots: where the function crosses the x-axis
(“zeros”)
Simplifying Fractions
Ratios
Adding/Subtracting: Find the LCM of the denominators…
2 1
2 3 1 5
6
5 11

    


5 3
5 3 3 5
15 15 15
3
2 3 20 60
60 15 4
=
now simplify
2 = 

5
9 5 9
45 15 3
45
Dividing: Multiply the numerator by the reciprocal of the denominator
Multiplying: Multiply across and simplify…
2
1 12 16 12 15
3 4 35 9
1
now make ones…
2 1 

 

 or 2
5 15 5 15 5 16
5
44 4
4
**When multiplying or dividing, change mixed numbers into improper fractions.
Proportions
Cross-multiply!!
5x  1 7
now cross-multiply 10 x  2  28 simplify 10x  30  x  3

4
2
Fractions with Radicals
When a single radical is in the denominator
3 2 3 2 7 3 14


7
7
7 7
multiply the top and bottom by the radical.
When a sum/difference of a radical is in the denominator, multiply the top and bottom by the conjugate


3 x 7
3
3x  3 7

 2
x 7
x 7
x 7 x 7

C. Hunsberger


Page 1 of 11
Review
Advanced Algebra/Trigonometry Honors
Name ______________________
Practice
Special Triangles
Simplify:
Fill in the missing angles and sides:
1. x  4
7
11
2x
2. 7
5y
3
30°
8
3.
2 3
5
4.
4
x 5
5.
6 x 1

7
3
6.
7 x 1 2x

3
4
5
Functions
Factor Completely
1. 9 x 2  49
Domain __________________
2. 2 x 2  10 x  28
Range ___________________
Root(s) ___________________
C. Hunsberger
3.
2 xy  5 y  6 x2  15x
Page 2 of 11
Review
Advanced Algebra/Trigonometry Honors
Name ______________________
More Practice!!
C. Hunsberger
Page 3 of 11
Review
Advanced Algebra/Trigonometry Honors
Name ______________________
More Practice!!
C. Hunsberger
Page 4 of 11
Review
Advanced Algebra/Trigonometry Honors
Name ______________________
Factoring:
C. Hunsberger
Page 5 of 11
Review
Advanced Algebra/Trigonometry Honors
C. Hunsberger
Name ______________________
Page 6 of 11
Review
Advanced Algebra/Trigonometry Honors
C. Hunsberger
Name ______________________
Page 7 of 11
Review
Advanced Algebra/Trigonometry Honors
Name ______________________
Remember… linear functions? Lines, slope, intercepts, slope-intercept form, pointslope form, standard form, x-axis, y-axis, origin, quadrants, distance and mid-point formulas,
perpendicular, parallel, etc.
Take a look at the following problems. Try to do the problems you know, and begin those you are unclear
about. When you have looked through all of the problems and worked through them, complete a K-W-L
chart on linear functions. Ask yourself what you already KNOW about linear functions and what you
WANT to know; at the end of the first unit, we will fill in what you have LEARNED.
1. Let A = (-4, 7) and and B = (4, -5).
a. Find the length of segment AB.
(4  4) 2  (7  5) 2
 (8) 2  (12)2
 64  144
 208  16 13  4 13
b. Find the coordinates of the midpoint of segment AB.
 4  4 7  5 
,


2 
 2
  0,1
2. Find the value of a if it is known that the point (-3, 7) lies on the line 2𝑥 + 𝑎𝑦 = 26.
2( 3)  a (7)  26
6  7 a  26
7 a  32
32
a
7
3. Solve the system of equations 3𝑥 − 2𝑦 = 3 and 5𝑥 + 4𝑦 = 16 for the variables. What does your
solution mean in reference to the graph of the system?
 6x  4 y  6
3(2)  2 y  3
2(3x  2 y  3)  
5
x

4
y

16

6  2y  3
11x  22
x2
2 y  3
y
3
 3
  2, 
2
 2
The solution is the intersection points of the two lines.
4. Find the slope and the y-intercept of the line 3𝑥 + 2𝑦 = −1.
3 x  2 y  1
3
1
Slope: 
Y-intercept: 
2 y  3 x  1
3
1
y  x
2
2
C. Hunsberger
2
2
Page 8 of 11
Review
Advanced Algebra/Trigonometry Honors
Name ______________________
5. Tell which of the following equations have parallel line graphs and which have perpendicular line
graphs.
a. 3𝑥 − 2𝑦 = 12
3x  2 y  12
2 y  3 x  12
3
y  x6
2
3
b. 𝑦 = 2 𝑥 + 1
y
3
x 1
2
c. 4𝑥 + 6𝑦 + 20 = 0
4 x  6 y  20
6 y  4 x  20
2
10
y
x
3
3
a b, a c , bc
6. Write an equation of the line through the points (6, -2) and (3, 7).
Slope:
7  2
9

 3
36
3
7  3(3)  b
7  9  b
16  b
y  3x  16
7. Write an equation of the line through the point (2, 5) and parallel to the line 4𝑥 − 3𝑦 = −50.
4
(2)  b
3
4 x  3 y  50
8
4
7
y  x
5  b
3 y  4 x  50
3
3
3
4
50
7
y  x
b
3
3
3
8. Write an equation of the line with x-intercept 2 and y-intercept -3.
5
(2, 0)
(0, 3)
C. Hunsberger
3  m(0)  b
3  b
0  m(2)  3
3  2m
3
m
2
y
3
x 3
2
Page 9 of 11
Review
Advanced Algebra/Trigonometry Honors
Name ______________________
9. Write an equation of the vertical line through the point (5, 1).
x=5
10.
a. Writing: Describe the steps for finding an equation of the median from vertex A in triangle ABC.
1. Get midpoint of segment BC
2. Use point A and midpoint, and plug them in for x and y to solve for the slope and y-intercept of the
line.
3. Put it into slope-intercept form.
b. Write an equation of the median from A if A(2,1), B(4, 8), and C(8,-2) are the vertices of triangle ABC.
Midpoint of BC: (6,3)
Use (2, 1) and (6,3)
2
1
m=4=2
1
3  (6)  b
2
3  3b
0b
y
1
x
2
11. Twyla buys a 10-ride pass so that she can use public transportation to go to and from work. The pass
costs $15 and is worth $0 after the tenth ride.
a. Give an equation of the linear function that models the value of the pass as a function of the number of
rides completed.
0  m(10)  15
15  10m
3
m
2
1.5  m

y  1.5 x  15
b. Use the equation to find the value of the pass after the sixth ride.
y  1.5(6)  15
y6
C. Hunsberger
So, the pass has $6.00 left on it after six rides.
Page 10 of 11
Review
Advanced Algebra/Trigonometry Honors
Name ______________________
Linear Functions
K
C. Hunsberger
NOW
W
ant to know
What I
L
earned
Page 11 of 11