File: Alg Readiness 2011 Answers.6.28.11
Updated: June 29, 2011 (No calculators allowed for any units)
Unit 1
1) Find the missing number in the equation
5/6 = x/36
x = (5)(36 6) = 30
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2) For the following proportion, find x
7/8 = x/64
x = (7)(64 8)
8 1
x = 56
Alternative Faster Method – Works when either the numerator or denominator goes in evenly into the other ratio.
3) For the following proportion, find x
1/9 = x/36
x = (1)(36 4)
9 1
x = 4
Alternative Faster Method
4) Solve: 1/5 = x/25
5) Solve: 1/3 = x/12
6) Solve: 12 = x/4
7) Solve: 21/24 = x/8
x = 7
8) Solve: 18/30 = x/5
x = 3
9) Solve: 3/7 = 9/x
x = 21
10) Solve: 5/6 = 25/x
x = 30
11) Solve: 18/27 = 2/x
x = 3
12) Solve: x/4 = 45/20
x = 9
13) Solve: 20/44 = x/4
14) Write 5/55 as an equivalent fraction in lowest terms.
x = 1/11
15) Write 7/21 as an equivalent fraction in lowest terms.
x = 1/3
16) Solve: x/7 = 10/21
x = 10/3
17) Solve: 18/12 = x/3
x = 18/4
x = 9/2
18) Solve: 5/15 = x/21
x = 7
19) For the following proportion, find x
4/16 = x/24
x = 6
20) Solve: 7/35 = x/20
x = 4
21) Find the exact value of x in the equation
55/5 = x/16
x = 176
22) Solve: 55/5 = 16/x
x = 16/11
23) Solve: 5/45 = x/11
x = 11/9
24) Solve: 7/8 = x/3
x = 21/8
25) Solve: 2/3 = x/5
x = 10/3
26) Solve: x/3 = 6/7
x = 18/7
27) Solve: 13/11 = 4/x
x = 44/13
28) A man that is 6 feet tall casts a shadow that is 20 ft long. A building casts a shadow that is 210 ft long. What is the height of the building?
Man Building
Height (ft) 6 x x = (6 3)(210 )
Shadow (ft) 20 210 2 0 .
Building = 63 ft
29) A man that is 7 feet tall casts a shadow that is 21 ft long. A building casts a shadow that is 210 ft long. What is the height of the building?
Man Building
Height (ft) 7 x _
Shadow (ft) 21 210
30) Triangle JHK and triangle MLN are similar.
Find side LN and MN.
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31) Triangle ABC is similar to triangle DEF.
Find side EF and DF.
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32) What is the height of the see-saw?
33) What percent is:13/20
13/20 = x/100
x = 65
34) Convert 7/8 to a percent:
Percent means out of 100. Therefore:
7/8 = X/100
x = (7)(100 25)
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= 175
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= 87 ½
35) Convert 2/5 to a decimal:
One easy way is to find a denominator that is a multiple of 10.
2/5 = X/10
x = (2)(10 2)
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Therefore: 2/5 = 4/10 = 0.4
36) At a dance, there are 5 nerds for every 4 geeks. If 54 total people are at the dance and the only people at the dance are geeks and nerds, how many of the total number of people at the dance are: (a)nerds, (b)geeks?
Nerds 5 a .
Geeks 4 b .
Total 9 54
37) At a rough hockey game, Sam checks his body and finds that he has three bruises for every five cuts. If Sam has a total of 32 total bruises and cuts, how many cuts are on poor old Sam’s body?
Unit 2
38) What is the equation of the scatter plot?
y = 2x + 1
39) State the line equation for the following graph.
Slope intercept form: y = - ½ x + 3
(Slope = - ½ and y-intercept = 3)
40) State the line equation for the following graph.
Slope intercept form: y = - 2x + 1
(Slope = - 2 and y-intercept = 1)
41) State the line equation for the following graph.
y = 2x
(Slope = 2 and y-intercept = 0)
42) State the line equation for the following graph.
Slope intercept form: y = 1/3 x – 4
(Slope = 1/3 and y-intercept = - 4)
43) State the line equation for the following graph.
Slope intercept form: y = - 5x + 1
44) State the line equation for the following graph.
Slope intercept form: y = -x – 3
45) State the line equation for the following graph.
Slope intercept form: y = 5x
46) State the line equation for the following graph.
Slope intercept form: y = - 2x + 1
47) In slope-intercept form what is the equation of the line below?
y = -2x + 2
3
48) In slope-intercept form what is the equation of the line below?
y = 4x – 2
3
49) Find the slope between points:
(-1, 4) and (5, 9)
Slope (m) = DY = (y1 – y2) = (9 – 4) = 5 _
DX (x1 – x2) (5 – -1) 6
50) Find the slope between points:
(3, 5) and (0, 4)
Slope (m) = DY = (y1 – y2) = (5 – 4) = 1 _
DX (x1 – x2) (3 – 0) 3
51) What is the slope between points (0, 5) and (0, 9)?
One could draw out a sketch of these two points and find the equation as done previously. Alternatively:
Slope (m) = DY = (y1 – y2) = (9 – 5) = 4 = Undefined
DX (x1 – x2) (0 – 0) 0
Solve the following both mathematically and graphically
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52) In slope-intercept form write the equation of a line with a slope of -2 that passes through (-1, 3).
(a) Mathematical Method
y = m x + b
(3) = (- 2)(- 1) + b
3 = 2 + b
-2 -2
b = 1 y = - 2x + 1
(b) Graphic Method
53) In slope-intercept form write the equation of a line that passes through (0, -2) and (3, 4).
(a) Mathematical Method
Slope (m) = DY
DX y = mx + b
m = (y1) – (y2) (4) = (2)(3) + b
(x1) – (x2) 4 = 6 + b
= ( - 2) – (4) - 6 - 6 _
(0) – ( 3) - 2 = b
= - 6
-3 y = mx + b
m = 2 y = 2x – 2
(b) Graphic Method
54) In slope-intercept form write the equation of a line that passes through (-4, 5) and (4, 1).
Solve both (a) mathematically and (b) graphically.
(a) Mathematical Method
Slope (m) = DY
DX y = mx + b
m = (y1) – (y2) (5) = (-½ )(-4) + b
(x1) – (x2) 5 = 2 + b
= (5) – ( 1) - 2 - 2 _
(- 4) – ( 4) 3 = b
= 4
- 8 y = mx + b
m = - ½ y = - ½ x + 3
(b) Graphic Method
55) In slope-intercept form write the equation of a line that passes through (1, 3) and (2, 5) [#38]
y = 2x + 1
56) In slope-intercept form write the equation of a line that passes through (2, 2) and (6, 0) [#39]
y = - ½ x + 3
57) In slope-intercept form write the equation of a line that passes through (-1, 3) and (1, -1) [#40]
y = -2x + 1
58) In slope-intercept form write the equation of a line that passes through (-3, -6) and (-1, -2) [#41]
y = 2x
59) In slope-intercept form write the equation of a line that passes through (-6, -6) and (-3, -5) [#42]
y = 1/3 x – 4
60) In slope-intercept form write the equation of a line that passes through (-1, 6) and (1, -4) [#43]
y = -5x + 1
61) In slope-intercept form write the equation of a line that passes through (0, -3) and (2, -5) [#44]
y = -x – 3
62) In slope-intercept form write the equation of a line that passes through (1, 5) and (-1, -5) [#45]
y = 5x
63) What are the next three terms in the pattern:
0, 5, 10, __, __, __?
0, +5 5, +5 10, +5 15, 20, 25
64) What are the next three terms in the pattern:
-1.5, 0, 1.5, 3, ___, ___, ___?
-1.5, +1.5 0, +1.5 1.5, +1.5 3, 4.5, 6, 7.5
65) What are the next three terms in the pattern:
5, 5.5, 6, 6.5, ___, ___, ___?
5, +0.5 5.5, +0.5 6, +0.5 6.5, 7, 7.5, 8
66) Given the following table, write the equation.
Term Number (x) / Term Value (y)1 / 2.5
2 / 4.5
3 / 6.5
4 / 8.5
(y) = (m)(x) + b
(8.5) = (2)(4) + b y = mx + b
b = 0.5 y = 2x + 0.5
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67) Given the following table, write the equation.
Term Number (x) / Term Value (y)1 / 2.5
2 / 3
3 / 3.5
4 / 4
(y) = (m)(x) + b
(4) = (½)(4) + b y = mx + b
b = 2 y = ½ x + 2
68) Given the following equation: y = 1/3 x + 3, predict the 99th term.
y = 1/3 (x) + 3
y = 1/3 (99/1) + 3
y = 36
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69) Given the following equation: y = 2x – 4, predict the 50th term.
y = 2(x) – 4
y = 2(50) – 4
y = 96
70) Given the following table, write the equation.
Term Number (x) / Term Value (y)1 / 6
2 / 11
3 / 16
4 / 21
(y) = (m)(x) + b
(21) = (5)(4) + b y = mx + b
b = 1 y = 5x + 1
71) Find the equation of the following pattern
(y) = (m)(x) + b y = mx + b
(8) = (1)(4) + b y = 1x + 4
b = 4 y = x + 4
72) Analyze the graph below:
a) Identify the independent and dependent variables.
The independent variable is always the x. So in this case it is the Day of the Week.
The dependent variable is always the y. So in this case it is the Height of Plant.
b) What was the height of the bean plant on Tuesday?
Draw a line up from Tuesday until you hit the graph, then draw a line to the left to find the height. In this case the plant was 15 mm.
c) What was height of the bean plant on Thursday?
Draw a line up from Thursday until you hit the graph, then draw a line to the left to find the height. In this case the plant was 30 mm.
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73) Analyze the graph below. It shows the average temperature in the United Kingdom between the years 1997 and 2006.
a) In what year was the temperature the highest?
Find the highest temperature on the graph. Next draw a line down to the year that corresponds. In this case the year was 2006.
b) What was the average temperature in Degrees Celsius in the year 2000?
Draw a line up from 2000 until you hit the graph, then draw a line to the left to find the temperature. In this case it was 9 0C.
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74) Suppose you receive $12.50 every week in allowance from your parents. You want to purchase a video game that costs $150. How many weeks will you have to save up your allowance in order to buy the video game?
$ 12.5 150 x = (1)(150) = 1500
week 1 x 12.5 125
= 150 60 = 12 weeks
125 5
75) Suppose you receive $11 every week in allowance from your parents. If you do not spend any of your allowance for 9 months, how much money will you have saved? (Assume each month has only 4 weeks)
$ 11 x x = (11)(9)(4) = $396
week 1 (9)(4) 1
76) Solve: x – 9 = 45
+ 9 + 9
x = 54
77) Solve: x + 7 = 40
– 7 – 7
x = 33
78) Solve: 4x = 44
4x = 44
4 4
x = 11
79) Translate the following phrase into an algebraic expression: five divided by x.
5/x
80) Translate the following phrase into an algebraic expression: eight more than four times x.
4x + 8
81) Translate the following algebraic expression into a phrase: ½ x + 9
Nine more than half a number
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82) Evaluate:
a) 20
Anything to the zero power = 1
b) 54
(5)(5)(5)(5)
(25)(25)
= 625
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83) Find the inequality that makes the following statement true:
7/10 ? 2/3
Find a common denominator first, then make equivalent fractions.
21 20
30
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84) 9 – (-4) = Modify
Subtract a negative means to add.