Download Place your answer to each question on the space provided. 1. Which

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Algebra I Practice Midterm Exam
Part I Directions: MULTIPLE CHOICE – Place your answer to each question on the space provided.
3x z
1. Which is equivalent to the equation y
?
4
3x z
(a) x
4
(b) x 12 y 3z
4y z
(c) x
3
(d) x y z 4
1
2. The formula for the area of a triangle is A
bh , where b represents the base and h represents
2
the height. Which of the following equations is equivalent to the formula to the area of the
triangle?
(a) 2Ab h
(b)
A
2b
h
(c)
3. Amelia made the following statement: “If 5 x 2
justifies Amelia’s statement?
(a)
(b)
(c)
(d)
2b
A
h
(d)
2A
b
h
15 , then x 2 3 .” Which property
Associative Property of Addition
Division Property of Equality
Addition Property of Equality
Distributive Property
4. Becky knows the formula to convert Celsius degrees to Fahrenheit degrees, F
9
Which of the following is F
C 32 correctly solved for C?
5
169
(a) C F
5
(b) C
(c) C
(d) C
32 F
5
9
F 5
32 9
5
F 32
9
5. The statement below is an example of which property?
“If x y and y z , then x z ”
(a) Symmetric Property of Equality
(b) Commutative Property of Addition
(c) Reflexive Property of Equality
(d) Transitive Property of Equality
9
C 32 .
5
6. Jerri wrote these steps when solving an equation.
Given: 17 x 3 6 4
Step 1: 17 x 51 6 4
Step 2: 17 x 51 2
Step 3: 17 x 49
49
Step 4: x
17
Which property justifies Step 1?
(a)
(b)
(c)
(d)
Distributive Property
Commutative Property of Addition
Associative Property of Addition
Additive Identity Property
7. Darla solved an equation using the steps shown below.
Given: 4 x 7 17
Step 1: 4 x 7 7 17 7
Step 2: 4x 24
4 x 24
Step 3:
4
4
Step 4: x 6
Which property justifies Darla’s computation in Step 1?
(a)
(b)
(c)
(d)
Additive Identity Property
Commutative Property
Substitution Property
Additive Inverse Property
8. What is the solution to the equation: 7 x 3
(a)
(b)
(c)
(d)
4 x 6 ?
15
–15
All real numbers
No solution in the set of real numbers
9. Which equation has a solution of all real numbers?
(a) 4 x 9 4 x 3
(b) 2 x 4
(c) 5 x 6
4 x 12
10 5 x 20
(d) 2x 12 5x 4 3x
10. What is the value of x in the following equation?
(a)
x | x 12
(b)
x| x
6
(c)
5
x 2
3
x| x
x 6
16
3
(d)
x| x
3
11. Which table contains four points x, y that cannot lie on the linear graph of a function, f x ?
(a)
x
1
2
3
4
(b)
(c)
(d)
y
–1
–2
–3
–4
x
1
2
3
2
y
4
2
2
4
x
–1
–2
3
4
y
2
4
6
8
x
2
4
6
4
y
–2
–3
–4
–5
12. The graph shows part of a function f.
What is most likely the range of the function?
(a)
(b)
(c)
(d)
All real numbers.
All real numbers greater than zero.
All real numbers less than or equal to five.
All real numbers between 2 and 5.
13. Which graph best represents f x
3x 1 ?
(a)
(c)
(b)
(d)
14. What is w
2 given w x
x2 8 ?
(b) –12
(a) 12
(c) 4
(d) 6
15. What is the interval notation for the following inequality? “x is greater than or equal to –3”
(a) ( 3, )
(b) ( , 3)
(c) ( ,3]
(d) [ 3, )
16. An inequality is shown.
2 x 10
16
Which inequality is true because of the division property of inequality?
2 x 50 16
2 x 50
(a)
(c)
16
2
2
2
2 x 50 16
2 x 50
(b)
(d)
16
2
2
2
17. 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.
(b) The only solution is 2.
(c) The solutions are both 1 and 2.
(d) The equation has infinitely many solutions.
(e) The equation has no solutions.
18. A relation is shown by the table.
x
1
4
8
20
y
10
2.5
1.25
0.50
Which of the following statements is true.
(a)
(b)
(c)
(d)
It is a direct variation because y
2.5x 12.5 .
It is an inverse variation because y
2.5x 12.5 .
It is a direct variation because 10 xy .
It is an inverse variation because 10 xy .
Part II Directions: FREE RESPONSE – Show all appropriate working out to receive full credit.
19. Write the following equations below.
a. Direct Variation
b. Inverse Variation
c. Slope Formula
d. Slope-Intercept Form
Simplify the following expressions.
20. 2
62 3
5
21. 32 5 6 3
Evaluate the following expressions when x 2 and y
22. 2x
y2
4.
23.
x 2 y 1
Translate the following equation or inequalities and then solve.
24. Twice the sum of eight and a number is 12.
25. The quotient of a number x and 8 is at least –6.
Solve each inequality and graph them.
26. 6 x x 1 12
Solve the following equations.
1
28. 6 x
10 3x
2
30.
2x
6
x 3
27. 4x 3 y
29.
1
x 4
2
31.
x
4
x 4
12
6
1
x 3
2
Evaluate each of following functions.
32. f x 2 x 1 when x
5
33. g x
Graph the following equations or inequalities.
34. 2x y 1
35. 4 y
36. 6x 3 y 12
37.
5x
x 2 6 x when x
12
15
2
38. y varies inversely with x. If y 8 when x
2 . Find y when x
4.
39. Write the equation of the line when the slope is 5 and the y-intercept is 4.
40. Write the equation of the line given the points
41. Write the function for a line given f
2
2, 6 and 0, 4 .
6 and f 0
4.
42. What are the x and y-intercepts for the following equation?
Find the slope given the following points.
43. 6, 3 , 4,3
44.
4, 2 ,
2x 3 y 12
4, 5
Find the coordinate given the following points and slope.
45.
2, 4 , x,3 ; m
46.
2
3, 0 , 6, y ; m
1
2
47. Determine whether the table below represents inverse variation. If it does, write the inverse variation
equation.
x
–3
–2
–1
6
y
4
6
12
–2
48. State whether the two lines y
2x 3 and y
1
x 4 are parallel, perpendicular, or neither.
2
Give justification for your response.
49. Circle the linear equations that are parallel to each other. (You may circle more than one)
1
y
x
y 2x 5
y 2x 3
2y
4x
2
50. Find the mean, median, mode, range, and standard deviation of the set of data below. Then create a box
and whisker plot and also find the MAD.
Test Scores: 69, 89, 58, 72, 79, 92, 65, 90, 72, 83