Download Algebra 1 Review for EOC EXAM

1
Algebra 1
Name _______________________________
Semester 1 Review
Date __________________
Fill in the following information (Concept Review)
1. How would you describe the slope of a line?
2. What is the formula to find slope given two points of the line?
3. How do you find the slope of a line from an equation in standard form?
4. What is the equation of a horizontal line?
b. State its slope.
5. What is the equation of a vertical line?
b. State its slope.
6. What two pieces of information are needed to write the equation of a line?
a.
b.
7. What is true about parallel lines in regard to their slope?
8. What is true about perpendicular lines in regard to their slopes?
9. Define a function and describe a “test” that can be used to identify a function.
10. When solving inequalities, we use solving equation skills to get the solution set. What “extra” rule must
we remind ourselves of when solving inequalities?
11. How do you solve a system of equations?
12. What is the x-intercept for a graph?
13. What is the y-intercept of a graph?
14. Define the domain for a graph:
15. Define the range for a graph:
1
2
Functions and Relations Review:
1.
2.
Determine whether the relation is a function.
Antonio’s age (years)
11
12
13
14
15
16
Antonio’s height
(inches)
60
61
62
67
69
69
Give the domain and range of the relation.
x y
2 5
8 17
0 0
–3 –5
3.
a. f(3)
Given that f(x) = 2(1 – x) and g(x) =
b. g(-3)
2
, find:
1 x
c. g(1)
d
3
f( )
4
f. Find x if f(x) is ‒6
e. If f(x) = 4, find x.
Matching
Match each vocabulary term with its definition.
a. domain
b. x-axis
c. range
d. relation
e. dependent variable
f. independent variable
g. y-axis
h. function
____ 4.
a type of relation that pairs each element in the domain with exactly one element in the range
____ 5.
a variable whose value determines the value of the output, also known as the input of a function
____ 6.
the set of output values of a function or relation
____ 7.
the set of input values of a function or relation
____ 8.
a set of ordered pairs
____ 9.
a variable whose value depends on the value of the input, also known as the output of a function
Linear Equations Review:
Graph and label key points: x and y intercepts.
1. ‒2x + 4y = ‒8
2. y = 5x
3. x = 5
4. y = ‒3
5. y = ‒0.6x + 8
2
3
Write each equation in slope- intercept.
3
6. m = , y intercepts (0, ‒ 2)
4
7. through (−3, 4) and (2, −1)
Write and equation in standard form (ax + by = c) for each line described:
8. passes through (−3, 2), and a zero slope
9. x-intercept is -1 and y-intercept is 3
10. parallel to 𝑥 – 2𝑦 = 5 and passes through (2, −1)
Find the x-intercept and the y-intercept of a line from its linear equation.
Graph a line by finding and connecting its x and y-intercepts.
11.
Find the x and y-intercepts
12.
Find the x and y-intercepts and graph 3x  4 y  8 .
2
of y  x  12 .
5
Calculate slope given two ordered pairs.
Find slope by counting from point to point on a linear graph.
13.
Find slope between
(−1, 5) and (−7, 9).
14.
What is the slope of the line
sketched below?
Solve for x or y given slope and two ordered pairs with one x or y missing.
15.
Find y such that the slope between (2, 𝑦) and (5, −3) is 7.
Know special cases of slope for horizontal and vertical lines.
16.
What is the slope of a vertical line?
17.
What is the slope of y  4 .
3
4
Systems:
See the other review and the one for the quiz on 12/12
Mixed Review
Simplify each expression.
1. 15  12  32  21
3. -5x 2 (3x 3 y 4 ) 2
2. 8m – 3[2(-3m 2 + 5m + 8) + 2m] – (6 – 3m + m 2 )
4. (2c – 3)(c 2 - 2c + 5)
5. (5 – 3a) 2
Evaluate the expression if x = ‒6, y = 4, and z = ‒2
6. x + 2y
7. z – x
8. x
9. 2x + y
10. x  y
11. y 2  z 2
Solve each of the following:
12. 7 – 2x = 3
13. 3(4 – 3x) = x – 8
15. 2(x – 1) = 5 – (3 – 2x)
16. ‒3[2a +3(5 – 2a)] = a – [6 – 4a]
14.
3
a + 3 = 2a – 11
5
Simplify:
17. 4 x 2 y(3 y 2  4 xy 3 )
18. (c – 2)(2c – 3)
20. (10n + 3)(10n – 3)
21. 7  4  32  35
22. −2[8 – (−3) 2 ] + 2 + 2  3
23. 8𝑚 – 3[2(−3𝑚 + 8) + 2𝑚] + 6
19. (5 – 3a) 2
4
5
Graph the following and label x-intercepts and y-intercepts.
2
26. ‒2x + 4y = 8
27. f(x) =  x ‒3
3
Domain:
Range:
Domain:
Range:
28. x = ‒3
Domain:
Range:
29. y = 2
Domain:
Range:
5