Download Objective 1: Add, subtract, and multiply matrices to solve problems

Name: _____________________________
Date: __________
Hour: _____
ALGEBRA II – 1st Semester Test Review
Sequences and Series:
n
(a1  an )
2
a (1  r n )
and Sn  1
1 r
Arithmetic Sequence and Series:
an  a1  (n  1)d and Sn 
Geometric Sequence and Series:
an  a1  r n 1
Infinite geometric sequence: S 
a1
; r 1
1 r
1. Find the first four terms in the sequence t n  n(2n  5)
2. Find the recursive and explicit rules for the arithmetic sequence when a1  2 and a4  11.
Define and distinguish between relations and functions.
3. A function is a relation in which…
a)
b)
c)
d)
no two different ordered pairs have the same y coordinate
no two different ordered pairs have the same x coordinate
no two different ordered pairs have the same x or y coordinate
it does not pass the horizontal line test
Use functional notation and specify domain and range.
4. For f(x) = -6x + 5 and g(x) = 3x – 2, find:
a) f(-4) + g(3)
b)
f (6)
g (2)
5. Find the domain and range and determine whether it is a function.
y
–3
–2
y
3
3
2
2
1
1
–1
–1
1
2
3
x
–3
–2
–1
–1
–2
–3
A.)
–2
–3
B.)
1
2
3 x
Display data involving two variables on a scatter plot and find the best fit linear or quadratic equation and interpret results.
6. Graph the set of data. Decide whether a linear model is reasonable.
If so, draw a trend line and write its equation.
1
7
-2
1
3
13
-4
-3
0
5
Solve systems of equations using any method
7.
3x  y  10

4 x  4 y  8
8. When solving a system of equations by graphing the solution is
a) The vertex
b) The shaded region
c) The point of intersection
d) The y-intercept
9. If the system of equations graphs parallel lines then how many solutions does it have?
10. What will the graph of a system of equations look like if the solution is “many solutions?”
11. If two lines intersect, how many solutions does the system of equations have?
Solve systems of linear inequalities.
5
12. Which point is a solution to the system of inequalities?
a)
b)
c)
d)
(2, 0)
(3, -2)
(-1, -1)
(0, 2)
-5
5
-5
Identify characteristics of graphs based on general equations. (y=ax 2 + bx + c)
13. Identify the quadratic, linear, and constant terms. y = (3 – x)(2x + 1)
14. Does the graph of y  8  7x2  3x open up or down?
15. Write the quadratic equation given the solutions of 2 and –5.
16. Use vertex form to write the equation
of the parabola.
y
6
4
2
–6 –4 –2 O
–2
2
4
6
x
–4
–6
Graph a quadratic function and identify the x- and y-intercepts and maximum or minimum value,
using various methods and tools, which may include a graphing calculator.
17.
f ( x)  3( x  4) 2  6 V(_____, _____)
18. Graph y = -3x² + 6x + 5.
Does the function have a maximum or minimum
value? What is the value of the maximum or
minimum value? What is the y intercept?
19. A manufacturer determines that the number of drills it can sell is given by the formula
a.
b.
, where p is the price of the drills in dollars.
At what price will the manufacturer sell the maximum number of drills?
What is the maximum number of drills that can be sold?
20. Identify the vertex and the y-intercept of the graph of the function. Then graph.
y = -3(x + 2)² + 2.
21. Suppose that you are throwing a water balloon to a friend on the third floor. After t seconds, the height of the
water balloon in feet is given by h  16t  38.4t  .96 . Your friend catches the balloon just as it reaches its
highest point. How long does it take the balloon to reach your friend and at what height does your friend catch it?
2


Identify the parent graph of the function y  x 2 and predict the effects of transformations on the parent graph
and find domain and range.
22. Use the graph of y = (x – 3)² + 5.
a. If you translate the parabola to the right 4 units and down 6 units, what is the equation of the
new parabola in vertex form?
b.
If you translate the original parabola to the left 3 units and up 7 units, what is the equation of the
new parabola in vertex form?
c.
How could you translate the new parabola in part (a) to get the new parabola in part (b)?
Factor quadratic equations.
23. Factor the following:
a. x2 -5x + 6
b. x  2 x  48
c. 4x² - 29x -63
d. 36x² - 25
2
Solve quadratic equations by factoring and graphing.
24. Solve for x.
a. 12 x  5 x  3  0
2
b. 3x² + 25x – 18 = 0
Simplify, add, subtract, and multiply complex numbers.
(3+8i)²
25..
26.
Solve quadratic equations by using the quadratic formula or by square rooting, including complex solutions.
27. x  3 x  28 =0
28. 2 x  2 x  1
30. 25x² + 81 = 0
31.  5 x  2   10  2
2
29. 9 x  6 x  7
2
2
2
Write a polynomial in standard form and classify by degree and number of terms.
32.
x
2
 2 x  5   2 x  3
33.
 2x
4
 2 x 2    x 4  2 x3  x 2  x  2 
Display data involving two variables on a scatter plot and find the best fit linear or quadratic equation and interpret results.
34. Mrs. Kay’s bakery showed increasing profits until June and then her profits began to decrease. The information
is shown in the table below (profits in thousands of dollars). Find a quadratic model, determine which pair(s) of
values would best complete the table.
FEB
APR
JUNE
AUG
OCT
2.5
3.1
3.25
3.0
2.4
a)
( March, 3.25)
b) (July, 3.5)
c)
(July, 3.15)
Sketch a graph of a polynomial function..
35. Determine the end behavior of y = x – x³ + 5.
36. Graph the polynomial?
f ( x)   x 3  4 x  2
Given the graph a polynomial, identify the x – and y – intercepts, relative maximums and relative minimums,
using various methods and tools which may include a graphing calculator.
37. What do the right and left ends of the function do?
f ( x)  3x3  x 2  2 x  4
f ( x)  3x3  x 2  2 x  4
38. What is the maximum possible number of x-intercepts for the function?
39. Use the graph to answer the following questions.
y
8
a) What are the x-intercepts?
6
b) What is the y-intercept?
4
c) Are intercepts numbers or points?
2
d) What are the zeros of the function?
–4
e) Which is a relative maximum function value?
–3
–2
–1
–2
1
–4
f) Name the relative minimum.
–6
g) State the domain and range of the function.
–8
40. Solve. x 3  3x 2  13x  15  0
41. Use synthetic division to find P(-1) if P(x) = x 2  5x  7
42. Determine which binomial is a factor of
a.
x+5
b.
x + 20
.
c.
x – 24
d.
x–5
Solve polynomial equations by factoring to include sum and difference of two cubes..
43. Solve 64x3 + 8 = 0 for x.
44. Solve. x3 – 7x + 6x = 0 for x.
2
3
4
x
Find rational zeros and the connection of zeros, factors, and solutions of polynomial equations.
45. When finding the solutions of a polynomial equation that is set equal to zero by looking at the graph,
what part of the graph should you look at?
y
50
40
46. What are the zeros for the polynomial that is graphed?
30
20
47. What are the linear factors of the polynomial?
10
–5
–4
–3
48. What is the equation of the graph?
–2
–1
–10
1
2
3
4
–20
–30
–40
–50
Find rational zeros and the connection of zeros, factors, and solutions of polynomial equations.
49. List all the possible solutions to the function? 3x3 + 4x2 - 3x – 18 = 0
50. Solve x4+7x2-18=0 for x
51. Given that one of the roots is 4, find the other 2 roots. P(x) = x 3 -6x2 + 5x + 12
52. Write the equation of a polynomial with the zeros 4, -2, and 1.
53. If the factors are (x – 3),(x + 2) and (x -5), what are the zeros?
54. Find the zeros of 2x3 + 10 x2 + 12x = 0.
Simplify radical expressions
55. Simplify the expression
225x10 y 4
Multiply and Divide Rational Expressions
3
57.
640w 3 z 8
3
5wz 4
56.
Simplify the Expressions
58.
(3x 4 )3 (2 x2 ) 2
Simplify the expression
4
64x 9 y16 z 23
5
x
Simplify the Expressions
Add and Subtract radical expressions and multiply and divide binomial radical expressions
to include rationalizing fractions that contain complex numbers
59.
18 + 2 72
3
60.
3  2 5 1  3 15 
Convert expressions from radical notation to rational exponents and vice versa.
Add, subtract, multiply, divide, and simplify expressions containing rational exponents.
3
2x 4
61.
Write the exponential expression in radical form.
62.
Write the radical expression in exponential form and simplify.
5
256x2
Simplify the Expressions
 2 1  1 1 
63.  s 5 t 3  s 2 t 2 






Simplify the Expressions
65.
1
3
1
2

3
4
1
2
x y
x y
Solve radical equations.
2
66.
67.
 x  2 3  4  5
x 3  x 5
64.
8ab  8ab 
1
2 2
2
1
2