Download Final Review Question Set

Final Review Question Set
Algebra 1
2014-2015
Objective: to prepare for the Final Exam
Do-Now: Please grab a whiteboard, marker, and
eraser.
Question 1 – Classifying Numbers
What sets of numbers make up the Real Number
System? Provide an example of each.
Question 2 – Standard Form/Intercepts
Find the x- and y- intercepts of the following
equation, then graph using the intercepts:
4𝑥 − 2𝑦 = −12
What is the slope of the line?
Question 2 – Standard Form/Intercepts
Find the x- and y- intercepts of the following
equation, then graph using the intercepts:
4𝑥 − 2𝑦 = −12
What is the slope of the line?
𝑥 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡: −3,0
𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡: 0, 6
𝑚 = 2
Question 3 – Quadratics
Find the vertex of the following equation:
𝑦 = 3𝑥 2 − 4𝑥 − 12
Will it have a maximum or minimum? How do
you know?
Question 3 – Quadratics
Find the vertex of the following equation:
𝑦 = 3𝑥 2 − 4𝑥 − 12
Will it have a maximum or minimum? How do
you know?
Axis of symmetry: 𝑥 =
2
40
2
3
plug in to find the vertex
Vertex: , −
3
3
Minimum since the leading coefficient is positive
Question 4 – Parallel/Perpendicular
a. Find the equation of the line that passes
through the following coordinates:
(1, 1) (−2, 7)
b. Write an equation of a line that is parallel to
the line you found in part a.
c. Write an equation of a line that is
perpendicular to the line you found in part a.
Question 4 – Parallel/Perpendicular
Find the equation of the line that passes
through the following coordinates: 𝑦 = −2𝑥 + 3
(1, 1) (−2, 7)
Write an equation of a line that is parallel to the
line you found in part a.
𝑠𝑙𝑜𝑝𝑒 𝑜𝑓 − 2 𝑎𝑛𝑑 𝑎 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡
Write an equation of a line that is perpendicular
to the 1line you found in part a.
𝑠𝑙𝑜𝑝𝑒 𝑜𝑓
2
𝑎𝑛𝑑 𝒕𝒉𝒆 𝒚 − 𝒊𝒏𝒕𝒆𝒓𝒄𝒆𝒑𝒕 𝒄𝒂𝒏 𝒆𝒒𝒖𝒂𝒍 𝒂𝒏𝒚𝒕𝒉𝒊𝒏𝒈
Question 5 – System of Equations
Solve the following equation:
𝑥 − 2𝑦 = 17
𝑦 = 2𝑥 − 4
Question 5 – System of Equations
Solve the following equation:
𝑥 − 2𝑦 = 17
𝑦 = 2𝑥 − 4
𝑆𝑜𝑙𝑣𝑒 𝑏𝑦 𝑠𝑢𝑏𝑠𝑡𝑖𝑡𝑢𝑡𝑖𝑜𝑛: (−3, −10)
Question 6–Inequality
Solve the inequality and graph the solutions.
𝟑 − 𝒙 + 𝟐 >𝟕
Question 6– Solving/Graphing
Inequalities
Solve the inequality and graph the solutions.
𝟑 − 𝒙 + 𝟐 >𝟕
𝑥<2
Question 7 – Simplify each expression!
a. −3 120
b. 3 5
c.
2
81𝑥 14
9𝑥 12
d. (2𝑥 3 𝑦 4 )3
e. (2𝑥 − 4)2
Question 8 – Solving Quadratics
Solve for x:
𝑥 2 + 2𝑥 − 8 = 0
Question 9 – Writing Equations
• Write an equation to represent the following
graph
Question 9 – Writing Equations
• Write an equation to represent the following
graph
3
𝑦 = 𝑥 −2
4
Question 10 – Linear Inequalities
• Write an inequality to represent the following
graph
Question 10 – Linear Inequalities
• Write an inequality to represent the following
graph
Question 11 – Standard Form
Write the following equation in standard form:
𝑦 − 7 = −2(𝑥 + 5)
Question 11 – Pyth. Theorem
Could the following dimensions form a right
triangle?
a. 5, 7, 8
b. 8, 15, 17
c. 20, 29, 21
d. 23, 25, 32
Question 11 – Pyth. Theorem
Could the following dimensions form a right
triangle?
a. 5, 7, 8 No
b. 8, 15, 17 Yes
c. 20, 29, 21 Yes
d. 23, 25, 32 No
Find the slope given the each set of
coordinates:
a.
b.
c.
d.
e.
(2, 3) (-5, 3)
(2, 3) (2, 17)
(-3, 0) (0, -3)
(1,1) (4, 4)
(-4, -5) (-7, 8)
General Questions?!
Look back at past material and ask any questions
that you might have. 