Connected Math Midterm Review
2014
th
Midterm on January 20 and 21st
Calculator will be allowed on both parts.
TWMM SKILLS
1) Recognize Linear Relationships
2) Write Linear Equations (Y = mX + b) given:
a) Graph
b) Table
c) Word problem
d) 2 points
e) Determine if a point lies on a given line
3) Make predictions from Linear Equations
4) Solve equations in one variable for X
5) Identify when lines are parallel
Examples:
1)
2) Match Linear Equation and its graph
Name_____________________
Period ___
b = Y-Intercept
m= slope or change in Y
change in X
3) What is the slope of the line through the following points?
(Hint make a table)
a) (2, 3) & (3, 1)
b) (2, 4) & ( 3, 6)
c) (2,4) & (4, 1)
4) Write the equation for each of the above. Put in form 𝑦 = 𝑚𝑥 + 𝑏
a)
b)
c)
5) Given the equation y  3x  4 , tell which of the following points lies on the line.
a) (4,8)
b) (2,-1)
c) (0,-4)
d) (-4,0)
6) Which of the following lines is parallel to y = -2x + 7
WHY?
1
a) y = 2X – 1
b) y= 4x -1
c) y= x + 3
d) y= -2X +6
2
7) Which of the following lines is perpendicular to y = -2x + 7 WHY?
1
a) y = 2X – 1
b) y= 4x -1
c) y= x + 3
d) y= -2X +6
2
8) Solve the following for X:
a) 3𝑥 + 4 = 10
b) 6𝑥 + 3 = 4𝑥 + 11
c) 4𝑥 + 2𝑥 − 3 = 11
d) 7 = 5 − 3𝑥
f) −2𝑥 + 7 + 4𝑥 = 6 − 2𝑥 + 9
g) 3𝑥 + 3 = −2𝑥 − 12
e) 2𝑥 − 6 = 4𝑥 + 5 + 2𝑥 + 1
h) 3𝑥 − 5 + 2𝑥 = −4𝑥 + 7
The following is an example of an Inverse Relationship
8
The Equation is x  y = 8 or y =
X
because the X and y numbers always multiply to give 8.
X 1 2 4 8
Y 8 4 2 1
Tell whether the relationship between x and y is an inverse variation or not
If it is, write an equation for the relationship
X 1
2 3 4 5 6 7
Y 10 9 8 7 6 5 4
9)
10)
X 1
2 3 4 6
Y 12 6 4 3 2
11) Students in Mr. Einstein’s science class complain about the length of his tests. He argues
a test with more questions is better for students because each question is worth fewer points. All of
Mr. Einstein’s tests are worth 100 points. Each question is worth the same number of points.
a. Make a table to show how the number of points
per question changes as the number of questions increases. Show
#of
# of
point values for 5 to 25 questions in intervals of 5.
questions points per
question
b. Write an equation for the relationship between the number of
questions x and the points per question y.
5
10
15
20
25
c) Is a test with more
questions better for the
students?
Why or why not?
d) What would the graph look
like?
12) Given the Inverse Equation 𝑦 =
30
𝑥
a) find y when x = 3
b) find x when y = 15
c) Show 2 other ways that you can write this equation?
13. Given the Inverse Equation 𝑦 =
24
𝑥
a) find y when x = 3
b) find x when y = 12
Find the value of Y for which both ordered pairs satisfy the same Inverse Variation
14)
(3, 12), (2, y)
15) (-3, 10), (-5, y)
y=__________ Equation ________________
y=__________ Equation ________________
Looking for Pythagoras SKILLS
1) Estimate Square Roots, determine what 2 integers a square root is between
2) Relate area of square to length of side
3) Find area of Irregular figures
4) Identify parallel and perpendicular lines
Find two consecutive whole numbers the square root is between and explain:
16)
√27
17)
√10
18) √17
19) Given the area of each square, find the length of each segment
a) A = 25 m2
b) A = 30 m2
c) A = 49 m2
d) A = 55 m2
Area of irregular figures:
Find area for the following:
20)
22)
21)
23) Graph the following set of numbers in order on a number line:
30 ,
16 , 𝜋,
19
 4,
24) Which 2 equations form parallel lines?
1
a) 𝑦 = 6𝑥 + 2
b) 𝑦 = 6 𝑥 + 4
c) 𝑦 = −6𝑥 + 3
25) Which 2 equations form perpendicular lines?
−1
a) 𝑦 = 6𝑥 + 2
b) 𝑦 = 6 𝑥 + 4
c) 𝑦 = −6𝑥 + 3
d) 𝑦 = −6𝑥 − 4
d) 𝑦 = −6𝑥 − 4
26) Find volume of a cube or find the missing edge of a cube given the volume:
Find the volume of a cube if:
a) edge = 10”
Find the edge of a cube if:
b) edge = 6”
c) volume= 125 in3
d) volume = 27 in3
Growing, Growing, Growing SKILLS:
1)
2)
3)
4)
5)
Write equation for Exponential relationship using: Tables, Graphs & Verbal Problems
Solve Problems involving: Exponential Growth
Compare Exponential and Linear Relationships
Rewrite numbers using Scientific Notation
Perform operations using numbers written in Scientific Notation
EXAMPLES:
Y  a  bx
a = ___________
b=_____________
27)As a biology project, Alisha is studying the growth of a beetle population.
She starts her experiment with 3 beetles. The next month she counts 12 beetles.
a. Suppose the beetle population is growing exponentially. Fill in the table Month Beetles
b. Write an equation for the number of beetles b after m months
c. How long will it take the beetle population to reach 200 if it is growing
exponentially?
d. Which is the Independent Variable?________Which is the dependent Variable?______
Explain:
28) Fruit flies are often used in genetic experiments because they reproduce very quickly
a. What is the growth factor for this fruit-fly population? Explain how you found your
answer.
b. Suppose this growth pattern continues. How many fruit flies will be in the fifth
generation?
c. Write an equation for the population p of generation g.
d. After how many generations will the population exceed one billion?
29) The following graph represents the population of a certain type of lizard
Write an
equation:_______________
Write an equation for each of the following
30) ____________
31) Fill in the missing information in each table
Growth Rate Growth Factor
20%
1.03
50%
1.7
2%
Decay Rate Decay Factor
20%
.60
50%
.25
2%
.05
Identify each of the following as being Linear, Inverse, Exponential Growth or
AND WRITE THE EQUATION.
32)
X
2
3
6
.5
Y
-3
-2
-1
-12
33)
X
1
2
3
4
34)
Y
10
20
40
80
X
2
3
4
5
Scientific Notation:
Write the following in Scientific Notation:
36) 3456.78
37) 12,000,000
38) .12
Write the following in Standard form:
40) 4.3×103
41) 1.234×104
42) 1.2×10-2
Simplify.
44) (3 ∙ 10−2 )(2 ∙ 104 )
47)
(6∙10−2 )
48)
(2∙104 )
50) (4 ∙ 10
−2
45) (4 ∙ 103 )(6 ∙ 107 )
−4
)(2 ∙ 10 )
43) 2.1E3
46) (5 ∙ 10−2 )(2.1 ∙ 106 )
49)
(5∙104 )
51) (1 ∙ 10
X
2
3
4
5
39) .00987
(2.5∙108 )
3 )(.5
35)
Y
108
324
972
2916
7
∙ 10 )
52)
(4.8∙107 )
(4∙10−3 )
(4∙102 )
(8∙104 )
Find the missing values in each equation:
53) (4 ∙ 103 )(1.2 ∙ 10𝑥 ) = 4.8 ∙ 107
54) (2 ∙ 10−3 )(1.2 ∙ 10𝑥 ) = 2.4 ∙ 107
56) (3 ∙ 10−2 )(1.2 ∙ 10𝑥 ) = 3.6 ∙ 10−7
57)
(16∙10𝑥 )
(8∙104 )
= 2 ∙ 105
Y
-3
-6
-9
-12
Solve each problem. Put your final answer in Scientific notation:
58. The population of dogs in the U.S. is estimated at 7 ∙ 106 . The average weight of each
dog is 8.4 ∙ 102 . what is the total weight for the U.S. dog population.
59) In 2000 the U.S. had 8.8 ∙ 1010 pounds of waste. The population then was about
2.2 ∙ 108 . How many pounds of waste per person?
60) The national debt. in 2006 was approximately 8.8 ∙ 1012 . The population was about 2∙
106 . If the debt is divided equally how much would each person owe?
61)
Area of Irregular shapes:
18
62) Find shaded area
11
20
16
4
8
8
x
4
x=_______
y= _______
P=_______
A= _______
63) Find the area of the shaded region use 𝜋 = 3.14
8”
8”
64) Barry has test scores of 93, 84, 86 and 75. He is going to have one more test, what does he need
to raise his average to an 87?
65) Jane got 70, 78, and 80 on the first three tests what does she need on the fourth to have an
average of 75?
66) Andrea has scores of 84, 73, 92 and 88. What does she need on her next test for her median to
be an 86.
67) Michael has scores of 74, 73, 72 and 88. What does he need on his next test for his median to
be a 74.
Without a calculator, Simplify:
68) −3 ∙ 52
69) 10 − 2 ∙ 4
70) 20 − 3 ∙ 23
71) −3 + 4 ∙ 52