Alg II w/ Trig Fall Semester Review 2013
1) Evaluate the expression − x 2 − 4 x − 4 when x = −3
2) Solve and graph: – 4k + 5 < 21
3) If f(x) = x2 – 3x + 5, find f(-2).
4) Solve the compound inequality and graph the solution set:
5x + 10 > 10 and 7x – 7 < 14
5) Solve the equation: |2x – 1| = 19
6) Solve: |x - 2| < 5
7) How do you determine if a graph represents a function?
8) Suppose f ( x) = 2 x + 3 and g ( x) = x − 2 . Find the value of
f (2)
.
g (−4)
9) Write an equation in standard form for the line through (5, -4) with a slope of 0.
10) Graph the equation 2x + 3y = – 6
11) Write the equation of the line in standard form with slope =
6
through the point (1, –5)
5
12) Find an equation for the line in slope-intercept form through (-2, -2) and (1, 4).
13) A 3-mile cab ride costs $6.00. A 6-mile cab ride costs $7.40. Find a linear equation that models cost c as a function
of distance d and find the cost of a 10-mile cab ride.
14) Using your calculator, find the equation for the line of best fit for the given data and find
the average weight of a kitten born in a litter of 9. (round to the hundredth)
Number of
kittens in
litter
Average
weight of
one kitten
3
5
6
8
10
11
12
7
6.5
5.9
5.5
4.8
4.5
4
15)
For equation y = − | x − 2 | +4 , write the equation of the parent function and describe the translation. Then
graph.
16) Write the equation that is the translation of
right 1 unit and down 3 units.
17) Graph the inequality 2x + 4y < 6
18) Graph the inequality y < |x - 4| +1
19)Solve the system by the method of substitution:
2x – 3y = 6
x + y = -12
3x - 2y = 14
20)Use the elimination method to solve the system. 2x + 2y = 6
21) 128 people were going to see the new James Bond movie. Adult tickets were $12.00 each and students tickets were
$8.50 each. The theater made $1298. How many of each type of ticket were sold?
y ≥ -2
22) Solve the system of inequalities by graphing. y ≤ -|x + 3|
23) Find a quadratic model for the set of values (-1, 13), (4, -32), and (1, 1). Find y when x = 6
24) Graph: y = −3( x + 1) 2 + 2 ?
25) Graph: y = x2 – 6x + 7?
26) Write an equation in vertex form for the parabola shown.
27) What are the solutions to the equation 3x2 - 3x – 18 = 0?
28) Solve by finding square roots:
2 x 2 + 29 = 191
29) Complete the square: x2 – 8x + ?
30) Solve x2 – 6x + 12 = 0.
31) Find the zeros of y = x(x + 4)(x – 1). Then graph the equation.
32) Find the zeros of the polynomial graphed.
33) Write a polynomial function in standard form with zeros at 3, –1, and 8.
34) Factor 2x3 + 12x2 + 16x
35) Factor 3x² − 19x −14
36) Divide (2x3 – 18x2 + 2x – 4) ÷ (2x - 3) using long division
37) Divide (x4 + 12x3 – 13x2 + 8x – 29) ÷ (x + 5) using synthetic division.
38) Factor 8x3 – 216
39) Find all the solutions of x4 – 6x2 – 16 = 0
40) Find the roots of the polynomial equation: x3 + 3x2 + 9x + 27 =0
41) A polynomial equation with rational coefficients has the roots 4 + 7 and 6 − 13 . Find two additional roots.
42) Write a polynomial in standard form whose zeros are 4 and -5i.
43) Simplify
44) Simplify
3
54a 5 b13
144 x 2 y 8
4 xy 4
45) Simplify (3 2 − 6)( 2 + 1)