Common Core
Semester One Final Review
Chapter 1:
1.
Slope: __________
y-intercept: _______________________
Equation in slope-intercept form: __________________________
2.
Graph the equation:
y = 5𝑥 − 2
3/4. Justify each step below using mathematic properties.
Step 1
Step 2
Step 3
𝟑(𝒙 − 𝟐) + 𝟒 = 𝟏𝟎
𝟑(𝒙 − 𝟐) = 𝟔
𝟑𝒙 − 𝟔 = 𝟔
𝟑𝒙 = 𝟏𝟐
𝒙=𝟒
5. Solve 5(3𝑥 + 4) − (2𝑥 + 6) = 1
Justification
6. Solve the inequality and graph the solution:
7. Solve the equation: -4x + 7 =9
Give an example of an equation in each of the following forms:
8.
Slope-Intercept Form:
9.
Standard Form :
10.
Point-Slope Form
Chapter 2:
11. Solve the system of equations
12. Solve the system of equations.
13. Solve the system of equations.
14. Using the graph:
Name a point that is NOT a solution to the system. ____________
Name a point that IS a solution to the system. ______________
Name a point that IS a solution to one of the inequalities but NOT
a solution to the other. _____________
15. Phillip’s class had a fundraiser selling bracelets and necklaces. They sold bracelets for $4 each and
necklaces for $7 each. If the class sold a total of 35 pieces of jewelry, how many of each did they sell if
they made $200 in total?
16. What is the x-intercept of the equation:
7𝑥 − 4𝑦 = 35?
17. Sketch a graph of each of the following:
One Solution
No Solution
Infinitely Many Solutions
18. Graph the following system of inequalities.
1
𝑦 ≤− 𝑥−2
4
𝑦 ≥ 3𝑥 − 5
19. Find the solution to the system graphed below.
20. Algebraically, how do you know if a system has one solution, no solution, or infinitely many
solutions?
One Solution:
Infinitely Many Solutions:
Chapter 3:
Use the diagram below to answer questions 21-24.
21. What type of sequence is represented above?
No Solution:
22. What is the recursive equation for the sequence on the previous page?
23. What is the explicit equation for the sequence on the previous page?
24. How many dots would there be at 50 minutes?
Questions 25-28: Consider the sequence 4, 16, 64, 256, 1024…
25. What type of sequence is represented above?
26. What is the recursive equation for the sequence above?
27. What is the explicit equation for the sequence above if 𝑓(1) = 4?
28.
Determine the value of the 9th term.
29.
Given the explicit equation: 𝑓(𝑛) = 10𝑥 − 2 , write the recursive equation.
30.
Given the recursive equation: 𝑓(1) = −6 𝑎𝑛𝑑 𝑓(𝑛) = 𝑓(𝑛 − 1) ∙ 3 write the explicit equation.
Chapter 4:
Questions 31-34: Decide if each function represented below is
(a) Linear (b) Exponential or (c) Neither.
_________31.
_________ 32.
x
1
2
3
4
y
3
6
12
24
_________33. 𝑓(𝑥) = 5𝑥 2
_________ 34. 𝑓(𝑥) = −3(𝑥 + 2) + 42
35. What is the rate of change for the following equation: 𝑓(𝑛) = −4(𝑥 − 3) + 20?
36. Create the explicit equation for the following table:
37. Define the following terms:
Decreasing/increasing
x
-15
-10
-5
0
Exponential/linear
y
-27
-17
-7
3
Discrete/continuous
38. What are the only ways to determine if a situation is discrete or continuous?
39. Find the simple interest on a loan of $8,000 at an interest rate of 12% for 4 years. Use the correct
formula below.
40. Calculate the amount owed on a loan of $15,000 at 15% rate, compounded annually for 5
years. Use the correct formula below.