Name: _________________
Block: _______
Date: _________
Date of Mid-term:
_____________
Review for the
Midterm Packet –
Algebra I
Topics on the midterm
include:
PEMDAS, Equations, Linear
equations, linear
inequalities, Slope,
Direct/Inverse Variation,
Literal Equations, and
Systems of Equations.
Directions: Complete the following problems. Show all work.
1.
Which is equivalent to the equation 𝑦 =
a. 𝑥 =
3𝑥+𝑧
4
?
3𝑥+𝑧
4
b. 𝑥 = 12𝑦 − 3𝑧
c. 𝑥 =
4𝑦−𝑧
3
d. x = y – z – 7
2.
The formula for the area of a triangle is A = ½ bh, where b represents the base and h
represents the height. Which of the following equations is equivalent to the formula to
the area of a triangle?
a. 2Ab = h
b.
3.
𝐴
2𝑏
c.
2𝑏
d.
2𝐴
𝐴
𝑏
=ℎ
=ℎ
=ℎ
Amelia made the following statement:
“If 5(x – 2) = 15, then x – 2 = 3”.
Which property justifies Amelia’s statement?
A.
B.
C.
D.
Associative Property of Addition
Division Property of Equality
Addition Property of Equality
Distributive Property.
4.
9
Becky knows the formula to convert Celsius degrees to Fahrenheit degrees, 𝐹 = 5 𝐶 + 32.
9
Which of the following is 𝐹 = 5 𝐶 + 32 correctly solved for C?
169
A. 𝐶 = 𝐹 − (
5
)
5
B. 𝐶 = 32 (𝐹 − )
9
C. 𝐶 =
𝐹
32
−
5
9
5
D. 𝐶 = (𝐹 − 32)
9
5.
This statement is an example of which property?
“If x – y and y = z, then x = z”?
A.
B.
C.
D.
6.
Symmetric property of equality
Commutative property of addition
Reflexive property of equality
Transitive property of equality
Jerri wrote these steps when solving an equation.
Given: 17(x + 3) = 6 – 4
Step 1: 17x + 51 = 6 – 4
Step 2: 17x + 51 = 2
Step 3: 17x = 49
49
Step 4: 𝑥 = 17
Which property justifies Step 1?
A. Distributive property
C. Associative property of addition
7.
B. Commutative property of addition
D. Additive identity property
Darla solved an equation using the steps shown below.
Given: 4x – 7 = 17
Step 1: 4x – 7 + 7 = 17 + 7
Step 2: 4x = 24
4𝑥
24
Step 3: 4 = 4
Step 4: x = 6
Which property justifies Darla’s computation in Step 1?
A. Additive Identity Property
B. Commutative Property
C. Substitution Property
D. Additive Inverse Property
8.
What is the solution to the equation, 7(x + 3) = 4(x – 6)?
A.
B.
C.
D.
9.
10.
Using the quadratic curve of best fit, which equation most closely represents the set of
data?
{(−8,80.4), (−7,57.8), (−6,38.6), (−5,22.8), (3, 18.8), (5.51.8), (7,98.4)}
A. 𝑦 = 𝑥 2 + 2𝑥 − 5
B. 𝑦 = 𝑥 2 − 3𝑥 + 5.2
C. 𝑦 = 1.7𝑥 2 − 3𝑥 + 5
D. 𝑦 = 1.7𝑥 2 + 2.9𝑥 − 5.2
Which equation has a solution of all real numbers?
A.
B.
C.
D.
11.
15
-15
All real numbers
No solution in the set of real numbers
4x – 9 = 4(x – 3)
2(x + 4) = 4x – 12
5(x – 6) + 10 = 5x – 20
3x + 12 = 5x + 4 + 3x
What is the value of x in the following equation?
5
𝑥−2=𝑥+6
3
A. {𝑥|𝑥 = 12}
B. {𝑥|𝑥 = 6}
C. {𝑥|𝑥 =
16
3
}
D. {𝑥|𝑥 = 3}
Which table contains four points (x, y) that cannot lie on the graph of a function, p(x)?
12.
MALGI20013
24
13.
ALGEBRA 1 BMA-2012-2013
QUARTER
24
The graph below represents th
The graph below represents the equation y = 3x.
The graph shows part of a function, f.
What is most likely the range of the function?
Which graph best represents y
A. All real numbers
F
B. All real numbers greater than zero
C. All real numbers less than or equal to five
MALGI20013
ALGEBRA 1 BMA-2012-2013
D. All real numbers between 2 and 6
24
The graph below represents the equation y = 3x.
14.
What
is w(-2)
of w(x) best
= 𝑥 2 + 8?
What is mosty
likely
the
Which
graph
represents
=3
x range
– 1?of the function?
Which graph best represents y
A.
FB.
C.
D.
15.
QUARTER 2
F
G
H
J
12
−12
4
6
23
All
All
All
All
real
real
real
real
numbers
numbers greater than zero
numbers less than or equal to five
numbers between 2 and 6
F
G
If w (2) = 13, which could be the equation for w (x)?
Which
graph
best represents
1x
Which
graph
best represents
y =A3x – w1 (x) =y3x=+23
2
F
G
B
C
D
w (x) = x + x
w (x) = 2x 3 + 5
w (x) = x 2 + 8
G
H
G
H
H
J
H
– 1?
16.
Write the following equations below.
a. Direct Variation
b. Inverse Variation
_______________
________________
c. Slope formula
d. Slope Intercept Form
________________
Simplify the following expressions.
17.
2 – (−62 + 3) – 5
______________
18.
32 − 5(6 − 3)
Evaluate the following expressions when x = -2 and y = -4
19.
2x - 𝑦 2
20. -x + 2(y + 1)
Solve the inequality and graph them below.
21.
6x – (x – 1) >12
22. 4𝑥 − 3𝑦 ≤ −6
Translate the following equations or inequalities and solve.
Twice the sum of eight and a number n is
23.
23. The quotient of a number x and 8 is at least
12.
Solve the following equations.
25.
6x – ½ =10 – 3x
-6.
26. ½ (x – 4) = -½x + 3
27.
2𝑥 𝑥 − 3
=
6
4
Evaluate the function.
29.
f(x) = 2x – 1 when x = -5
28. 𝑥 = − 𝑥 − 4
4
12
30. g(x) = 𝑥 2 − 6𝑥 𝑤ℎ𝑒𝑛 𝑥 = −2
Graph the following equations or inequalities.
31. 2x – y = 6
32. -4y = -12
33. 6x – 3y < 12
34. -5x > -15
35. What is the interval notation for the following inequality: x is greater than or equal -3.
a. (−3, ∞)
b. (−∞, −3)
c. (−∞, 3]
d. [−3, ∞)
36.
𝑦 varies inversely with 𝑥. If 𝑦 = 8 when 𝑥 = −2. Find 𝑦 when 𝑥 = −4.
37.
Write the equation of the line when the slope is -5 and the y-intercept is 4.
38.
Write the equation of the line given the points (-2, 6) and (0, -4).
39.
Write the function for a line given f(-2) = 6 and f(0) = 4.
40.
Determine whether the table below represents inverse variation. If it does, write the
inverse variation equation.
41.
X
-3
-2
-1
6
y
4
6
12
-2
What are the x and y intercepts for the following equation: -2x – 3y = 12?
a. (-6, 0), (0, 4)
C. (6, 0), (0, 4)
42.
b. (6, 0), (0, -4)
d. (-6, 0), (0, -4)
Given the table below:
X
y
1.2
10
1.8
7
What is the line of best fit?
2.3
5
3.0
-1
a.
b.
c.
d.
Y = -6x + 17.7
Y = 6x - 17.7
Y = -7x + 17.7
y = -.16x + 3
Find the coordinate given the following points and slope.
43. (-2, 4), (x, 3); m = -2
44. (-3, 0), (6, y ); m = ½
Find the slope given the following points.
45. (6, -3), (-4, 3)
47.
46. (-4, 2), (-4, -5)
Michelle correctly solved a linear equation and the last line of her work was: 1 = 2
Which statement best describes the solution to the equation Michelle was solving?
a. The only solution is 1.
c. The solutions are both 1 and 2.
e. The equation has no solutions.
48.
49.
A relation is shown by the table.
X
1
4
8
Y
10
2.50
1.25
b. The only solution is 2.
d. The equation has infinitely many
solutions.
20
.50
a. It is a direct variation because y = -2.5x + 12.5
b. It is an inverse variation because y = -2.5x + 12.5
c. It is a direct variation because 10 = xy
d. It is an inverse variation because 10 = xy
An inequality is shown.
−2(𝑥 + 10) ≥ 16
Which inequality is true because of the division property of inequality?
A.
50.
−2(𝑥+50)
−2
16
−2
B.
−2(𝑥+50)
−2
≤
16
−2
C.
−2(𝑥+50)
−2
≥ 16 D.
−2(𝑥+50)
−2
≤ 16
Circle the linear equations that are parallel to each other.
a. y = -2x + 5
c. 2y = -4x
51.
≥
b. y = 2x – 3
d. y = -1/2x
The linear equations y = 2x – 3 and y = -1/2x + 4 are perpendicular. ______(True/False)