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Transcript
Name: _________________________________________
Hour: ___________
Algebra 1 Review
Final Exam
1. Define the following words and given example of each.
a. Rational
b. Irrational
c. Integer
d. Whole
e. Natural
2. What is the value of x?
π‘₯
9
=
16 4
Solution:
x = 36
3. Solve.
4(π‘₯ + 2) βˆ’ π‘₯ = 29
Solution:
x=7
4. What is the slope of the linear function?
2
Slope: m = 3
5. Simplify.
3(2π‘₯ βˆ’ 4𝑦 + 2) βˆ’ (2π‘₯ + 4𝑦 βˆ’ 5)
Solution: 4x – 16y + 11
6. Given the following equation, solve for y.
βˆ’π‘₯ + 2𝑦 = 6
Solution:
1
y =2π‘₯ + 3
7. Identify the equation of the graph shown.
Equation: y = 2x OR y = 2x + 0
8. The cost of tuition at Meramec Community College is $195.00 per credit hour. Each student
also has to pay $75.00 in fees. Model the cost, C, for x amount of credit hours taken.
Equation:
C = 195x + 75
9. Find the rate of change represented in the given graph.
Rate of Change:
40 mph
10. What is the y – intercept of the given graph? (Remember to write your answer as a point)
Solution: (0, 6)
11. Graph the following equation.
5π‘₯ βˆ’ 3𝑦 = 12
12. On a family vacation Kayla’s family traveled 620 miles in 10 hours. How far did they go in 4
hours?
Solution: x = 248 miles
13. Simplify.
4(2π‘₯ βˆ’ 3𝑦 + 5𝑧) + 3(6π‘₯ βˆ’ 𝑦 βˆ’ 4𝑧)
Solution: 26x – 15y + 8z
14. Solve for x.
6(π‘₯ + 4) = 2π‘₯ + 36
Solution: x = 3
15. Solve for x.
βˆ’5π‘₯ + 12 = 47
Solution: x = -7
16. Write an equation for the line that passes through points A and D.
Equation:
2
8
𝑦 = 7π‘₯ βˆ’ 7
17. Jason works in a factory and makes $11.15 per hour. He does this for 12 weeks of the
summer. He works about 28 hours each week. Estimate about how much money he will make
this summer.
Solution: $3746.40
18. Simplify the following expression.
3(π‘š + 4) + 2(𝑛 βˆ’ 7)
Solution: 3m + 2n - 2
19. Estimate the value of the y intercept for the given graph.
Y- Intercept: about (0, 2.7)
1
20. Write an equation of a line that has a slope of βˆ’ 4 and passes through the point (8 ,3).
Equation:
1
𝑦 = βˆ’4π‘₯ + 5
21. A golf driving range charges a fee of $23.00 to practice and then $2.25 for a bucket of balls.
Write an equation in slope intercept form that models the charges C in terms of the number of
bucket of balls b that you use.
Equation: C = 2.25b + 23
22. Christopher’s weight is 15 pounds greater than his brother’s. Together they weigh 315
pounds. Let x represent the weight of Christopher’s brother, write an equation that can be used
to determine what each one weighs.
Equation: Chris = 165 lbs Brother = 150 lbs
23. Simplify.
7βˆ’3
62 βˆ’24
Solution:
1
3
24. Make a table for the following equation.
𝑦 = 2π‘₯ + 3
Table:
x
Y
-2
-1
-1
1
0
3
1
5
25. Use the following table to determine the Range when the Domain is 4.
X
Y
0
1
2
3
4
5
Range:
When x = 4, y = 5
26. Solve and graph the inequality.
7π‘₯ + 4 β‰₯ 6π‘₯ βˆ’ 8
Solution: π‘₯ β‰₯ βˆ’12
Graph: Closed circle on -12, shade to the right.
27. Label the slope and the y – intercept for the given equation.
2
𝑦 = βˆ’5π‘₯ βˆ’ 7
2
Slope: βˆ’ 5
Y – Intercept: -7
28. Write the following equation in function notation.
𝑦 = 5π‘₯ + 2
Solution: f(x) = 5x+2
29. Solve the proportion.
2π‘₯+3
4
=
3π‘₯
3
Solution: x = 1.5
30. Write an algebraic equation for the following sentence.
Three times a number x plus fourteen is the same as twenty nine.
Equation: 3x + 14 = 29
31. The table shows the number of people who have signed up to go to the renaissance field
trip each day. How many people would you expect to sign up on day 5?
Days
People
1
32
2
38
3
44
4
50
Solution: 56 people
32. Using the provided graph, estimate the rental cost for 8 days.
Solution: 240 Miles
33. Describe in words what the graph represents.
Description: As gallons increase, cost
increases.