Download PAP Algebra 2 with Trig Mid

PAP Algebra 2 with Trig
Mid-Term Review Topics
First 9-weeks Review
Equations & Inequalities
 Solve absolute value inequalities using interval
notation
 Literal equations
 Classification of real and complex numbers
Polynomials – Lessons 3-1, 3-2 and 3-4
 Add, subtract, and multiply polynomials
 Factoring polynomials using multiple step
Radicals – Lessons 5-6, 5-7, 5-8
 Simplify, add, subtract, multiply & divide
 Rationalize the denominator including use of
conjugates
 Simplify expressions with rational exponents
 Simplify, add, subtract and divide complex
numbers
 Classification of real & complex numbers
 Polynomial identities to complex numbers
 Solve simple radical equations
Additional Topics
 Relation vs. Function
 Representations of functions/relations
 Graph linear functions
 Write the equation of a linear function
 Rate of Change Application Problems
Second 9-weeks Review
Parent Graphs & Transformations – Lesson 1-1, 1-2, 2-1
 Graph Absolute Value
 Graph Quadratics – parabolas
 Graph Square Roots
 Graph Cubic
 Graph Rational
 Identify characteristics of each graph ( vertex,
intercepts, domain, range, max/min, increasing &
decreasing intervals, end behavior
 Graph inequalities
Quadratics – Lessons 2-2 to 2-9
 Solve by graphing, factoring, completing the
square or quadratic formula
 Graph standard form of a quadratic function
 Solve projectile and other application problems
Literal Equations & Absolute Value Inequalities Review
Solve the literal equation for the given variable
1. A  r  kt for t
4. V  4 r 2 h for r
2.
3. S  3xh  2 yh for h
4 x 2a

for y
5 y 3c
BONUS: A cone has a height two times its radius. Express the volume of
the cone in terms of the height using the formula for the volume of a cone
1
3
is 𝑉 = 𝜋𝑟 3 .
Solve each inequality. Write the solution in interval notation. Graph the solution showing the endpoints.
11. x  5  7  18
13.
x5
4
12. 3 x  2  4  23
6
14. 2 x  17  9
Polynomials Review
Part 1: Simplify each expression
1. 5𝑥 4 𝑦 3 (4𝑥 2 𝑦 5 )
4. 4𝑥 3 (3𝑥 2 − 5𝑥 + 7)
2.
24𝑥 6 𝑦 3 𝑧 4
16𝑥 2 𝑦5 𝑧
5. (3x - 4)(2x +7)
2
3.
(4𝑎2 𝑏3 )(2𝑎3 )
32𝑎5 𝑏2
6. (3x +2)(4x2 - 5x + 7)
Part 2: Factor Completely. Show necessary steps for full credit.
7. 9m2 - 49
8. 3y3 + 21y2 + 36y
9. 4x2y - 36y
10. 3x2 - 3xy + 6x - 6y
11. 2x5 - 32x
13. 6x2 + 7x - 3
14. x5 - 9x3 + 8x2 -72
12. 8x3 + 125
15. Which is a perfect square trinomial?
a. 4x2 +18x + 81
b. 9x2- 25
c. 4x2 – 36x + 81
d. 5x2 – 12x + 36
16. What is the factored form of the polynomial functions with x-intercepts at x = 3, x = 0 and
x = - 5?
a. f(x) = (x + 3)(x – 5)
c. f(x) = x(x – 3)(x + 5)
b. c. f(x) = x(x + 3)(x – 5)
d. f(x) = (x – 3)(x + 5)
Part 4: Graphing Calculator
17. For the functions below, use a graphing calculator to:
a) graph the function (draw a rough sketch on the grid)
b) find the zeros of the function
c) write the function in factored form
17. f(x) = 2x3 - 3x2 - 11x + 6
Radical Expressions and Rational Exponent Expressions
Part 1: Radical Expressions – Simplify Each (5 points)
3
1. √9𝑥 2 𝑦 8
2. √24𝑥 3 𝑦 11
3. √(𝑥 − 8)6
4. 3𝑎 √16𝑎9
5. √12𝑥𝑦 ∙ √3𝑥 5 𝑦 8
6.
4
7
√2
Use the window for
x: [-10, 10] and
y: [-10 , 10]
7. 5√27 + 2√12 − 4√75
8.
3
9. √𝑥 6𝑛 𝑦 10𝑛
2+√5
4−√3
10.
4
5
√𝑥 2
Part 2: Translations (3 points)
11.Write in simplest radical form
2
3
7
12. Write in simplest rational exponent
form
4
√𝑥 5
Part 3: Simplifying using rational exponents (5 points)
13.
15.
3
2
81
3
4
14.
1
5
(𝑥 ) (𝑥 )
16.
3
1 4
3
(𝑥 )
−
64
2
3
Parent Functions & Transformations
Part 1: Multiple Choice – Answer each of the following. Write the letter to the correct answer in the blank.
1. In the function 𝑓(𝑥) = 3(𝑥 − 4)2 + 5, what is the vertex?
a. (4, 5)
b. (3, 5)
c. (- 4, 5)
d. (4, - 5)
2. At what point do the asymptotes of the function,
a. (5, - 3)
b. (0, 0)
c. (- 5, - 3)
𝑓(𝑥) =
2
𝑥+5
− 3, intersect?
d. (- 5, 3)
3. Describe the transformation from the parent function, 𝑓(𝑥) = 𝑥 3 , that would be used to graph the function,
1
3
𝑓(𝑥) = (𝑥 + 4)3 − 5.
a.
b.
c.
d.
Vertical compression of 1/3, shift to the left 4, shift down 5
Vertical stretch of 1/3, shift to the right 4, shift down 5
Vertical compression of 1/3, shift to the left 4, shift up 5
Vertical stretch of 1/3, shirt to the left 5, shift up 4
4. What is the range for the 𝑓(𝑥) = |𝑥 + 4| − 3?
a. [-4, ∞)
b. [-3, ∞)
c. (-4, -3)
d. (-∞, -3]
1
5. Which of the following statements are true for the function 𝑓(𝑥) = 2 |𝑥 − 3| + 1?
I.
The axis of symmetry occurs at x = - 3.
II. The vertical compression or “slope” is ½.
III. The vertex occurs at (3, 1).
a. I and II
b. II and III
c. I, II and III
d. None of them
Part 2: Short Answer – Answer each of the following questions, use complete sentences where appropriate.
6. Write the equation of the square root function
7. Write the equation of the graph below.
with a reflection over the x-axis, shifted to the
left 8 units, and shift down 8 units.
8.
9. Graph 𝑦 > |𝑥 − 1| − 4
Graph 𝑓(𝑥) = √𝑥 + 2 + 3
10. Sketch the graph of 𝑓(𝑥) = 2(𝑥 − 1)2 + 3 and list the following characteristics
Graph
Concavity
Intervals of Increase and/or
Decrease
Vertex
End Behavior
Domain & Range
11. Sketch the graph of
𝑓(𝑥) =
Graph
12. Graph 𝑓(𝑥) = (𝑥 − 2)3 + 3
Graph
1
𝑥−2
+ 1 and list the following characteristics
Vertical Asymptote
Horizontal Asymptote
Domain
Range
Point of Inflection
End Behavior
Concave Up
Concave Down