Download Objective 3: Manipulate basic algebraic

Summer Review Packet for
Pre-AP Algebra II
You should write out each problem (on another sheet of paper)
and justify your answers by showing work on each. Please do
not cram it all on to one sheet of paper. These packets will be
due the day of the test, which will take place on the 4th – 8th
day of school. The test will consist of all objectives listed in
the packet.
PRE-AP ALGEBRA 2 SUMMER HOMEWORK
Name: ______________________________________________
Date: __________
Objective 3: Manipulate basic algebraic expressions using order of operations and properties of real numbers.
a) -6(2y – 4) – 9y
b) 10x + 16y – (24x + 13y – 3x)
c)  a 
2
1
3
a  4a 2  a
3
4
1.
Simplify:
2.
Evaluate:
3.
The expression –16t² + 1800 models the height of an object t seconds after it has been dropped from a height of 1800
feet. Find the height of an object after falling for 3.5 seconds.
4.
The expression 0.01E + 0.003E² gives the thickness in millimeters of the insulation needed for the high voltage cable. E
is the number of kilovolts carried by the cable. Find the thickness of insulation material needed for 20 kilovolts.
a) -2x² - 3x + 6, if x = -3.
b)
8c  ab
a
if a = 1/3 b = 2 and c = -4
Objective 4: Review multi-step linear equations.
Solve:
5.
4 y  16  8  6 y
9.
6.
2y – 6 = -3(y + 1).
10. I =prt, solve for r.
7.
4x - 3(x + 2) – 4 = 6(x – 1) + 3
11. df–3g = 4h, solve for f.
8.
4 – 2(1 - w) = -38
12. 6(x – 0.8) – 0.2(5x – 4) = 6
4y – 1 = 3y + 4
10
5
13. The sides of a triangle are in the ratio 3 : 4 : 5. What is the length of each side if the perimeter of the triangle is 90 cm?
14. The sides of a rectangle are in the ratio 5 : 6. What is the length of each side if the perimeter of the rectangle is 110 mm?
15. The sides of a rectangle are in the ratio 2 : 5. What is the length of each side if the perimeter of the rectangle is 84 cm?
Objective 5: Solve inequality equations and graph solutions on a number line including compound inequalities.
16. Solve and graph on a number line: 3(3x + 1) < -6 .
3 x < -6 or 5x > 2
8
18. Solve the compound inequality and graph on a number line:
2 < 10 – 4x < 6
17. Solve the compound inequality and graph on a number line:
19. Solve the compound inequality and graph on a number line. 3x < -6 or 5x – 6 > 24
20. Solve the compound inequality and graph on a number line -12 < 3x + 2 < 8
Objective 6: Define and distinguish between relations and functions.
21. Sketch a picture of a graph that is a function. Sketch another that is not a function. Explain the differences between the
two.
22. Does the following relation represent a function? Explain why or why not. {(2, -3), (4, 6), (3, -3)}
23. 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
Objective 7: Use functional notation and specify domain and range.
24. For f(x) = -6x + 5 and g(x) = 3x – 2,
a) f(-3) + g(2)
Find:
f (4)
g ( 2)
b)
c) (f + g)(3)
d) (f - g)(-1)
e) (fg)(x)
25. For f(x) = -x² - 4x – 4, find f(-5).
26. State the domain and range of the function {(2, -3), (4, 6), (3, -3)}.
27. Find the domain and range and determine whether it is a function. (Not multiple choice!!)
y
–3
–2
y
y
3
3
3
2
2
2
1
1
1
–1
–1
1
2
3
x
–3
–2
–1
–1
–2
–2
–3
–3
A.)
1
2
3 x
–2
–1
–1
1
3 x
2
–2
–3
B.)
D:
R:
Function?
–3
C.)
D:
R:
Function?
D:
R:
Function?
Objective 8: Graph linear equations and write equations of lines.
28. Graph the equation: 6x – 5y = 30. What is the slope and y –intercept and x-intercept?
29. Write an equation of a line in slope intercept form thru (-1, -4) with m = 3.
3
.
2
30. Write an equation of a line in slope intercept form through the point (-3, 7) with a slope of
31. At your job at the local Jeans R Us store, you make $350 a week plus 12% commission on all of your sales.
Write an equation (for one week) to model your salary, S, in terms of total sales, t.
32. The cost of producing 4 t-shirts is $80.80. The cost of producing 8 t-shirts is $92.60.
What is the cost of producing 100 shirts? How many shirts can you get with $125?
33. Write equations of the lines (below).
y
y
7
6
3
5
2
4
1
3
2
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
1
–7 –6 –5 –4 –3 –2 –1
–1
–2
1
2
–2
–3
–3
–4
–4
–5
–5
–6
–6
–7
–7
34.
Graph the line a) y = 
1
x  3 b) 3x – 4y = 6
4
c) 3 y 
1
x3 0
4
3
4
5
6
7
x
Objective 9: Determine slope when given an equation, graph or two points.
35. Find the slope of the line through the points  4 , 2  and  3 , 1  .
 5 3
 4 2
36. Find the slope of the line through the points: a) (3, -6) and (4, -6)
c) (4, -1) and  3 , 3  .


5 2
b) (3, 2) and 3, 7)
y
37. What is the slope of the line gx – y = h?
40
38. The graph below represents Alan’s trip on his bike. What is the slope and what does it represent?
30
20
Miles
10
2
4
6
8
x
Hours
Objective 11: Collect data involving two variables, display on a scatter plot and find the best-fit equation. Interpret
results and make predictions.
39. Sketch a scatter plot with a, negative correlation and draw the line of best fit.
40. Graph the set of data. Decide whether a linear model is reasonable. If so, draw a best-fit line and write its equation.
(GRAPH PAPER!)
1
7
-2
1
3
13
-4
-3
0
5
41. HEATING COSTS The table shows the average monthly outside temperature and the corresponding average monthly
heating cost for a two story home during the fall and winter of 2000. Use your graphing calculator to determine the
equation to the line of best fit.
Temperature
58
47
34
28
38
44
Cost
$51
$73
$96
$145
$102
$85
42. What would be a good line of best fit? What would be a likely score for someone who studied for 8 hours?
Use your graphing calculator.
43. What is the approximate volume of an eruption had it occurred in 1938?
Study Regents
Hours Score
3
80
5
90
2
75
6
80
1
50
2
65
1
40