Transcript Final exam review

FINAL EXAM REVIEW
Spring 2014
SLOPE
Find the slope of the line that passes through
the points:
(0, 5) and (6, 2)
Answer:
𝟏
−
𝟐
SLOPE
 Name the four types of slope.
1.
2.
3.
4.
_________
_________
_________
_________
Answer: positive, negative, zero, undefined
SLOPE
Which has a slope of zero – a
horizontal line, or a vertical line?
Answer: A horizontal line has a slope
of 0, while a vertical line has a slope
of undefined.
SLOPE
 Fill in the blanks:
Parallel lines have ____ slopes.
Perpendicular lines have ___ slopes.
Answer: same, opposite reciprocal
GRAPHING
Graph the line:
𝟏
𝒚= 𝒙
𝟐
Answer:
GRAPHING
Graph the line:
𝟐
𝒚= 𝒙−𝟓
𝟑
Answer:
WRITING EQUATIONS
Write an equation of a line in
slope-intercept form with a slope
of 3 and a y-intercept of 5.
Answer: 𝒚 = 𝟑𝒙 + 𝟓
WRITING EQUATIONS
Write an equation of the line that
passes through (5, -2) and has a
𝟏
slope of − .
𝟑
Answer: 𝒚 =
𝟏
− 𝒙
𝟑
−
𝟏
𝟑
WRITING EQUATIONS
Write an equation in slopeintercept form for the line that
passes through (-5,2) and is
𝟏
perpendicular to 𝒚 = 𝒙 + 𝟒.
𝟑
Answer: 𝒚 = −𝟑𝒙 − 𝟏𝟑
FUNCTION NOTATION
For 𝒇 𝒙 = 𝟑𝒙 − 𝟒, find 𝒇 −𝟓 .
Answer: -19
PERMUTATIONS AND COMBINATIONS
 Find the number of outcomes.
How many ways can 4 lockers be
chosen out of 15 lockers?
Answer: 1365
FUNDAMENTAL COUNTING PRINCIPLE
 Find the number of outcomes.
How many desserts can be made
with 3 ice cream flavors, 5
toppings, and either whipped
cream or chocolate syrup?
Answer: 30
STANDARD FORM
 What is the standard form of a linear
equation?
________________
Answer: 𝐴𝑥 + 𝐵𝑦 = 𝐶
SLOPE-INTERCEPT FORM
What is the slope-intercept form of a linear
equation?
____________
Answer: 𝑦 = 𝑚𝑥 + 𝑏
SLOPE
What is the slope formula?
_____________
Answer: 𝑚 =
𝑦2 −𝑦1
𝑥 2 −𝑥 1
SCIENTIFIC NOTATION
 Simplify the following expression. Write your
answer in both scientific notation and
standard form.
𝟖
(𝟓. 𝟔 × 𝟏𝟎 )(𝟐. 𝟗 × 𝟏𝟎
−𝟓
)
Answer: 1.624 × 10 4 𝑎𝑛𝑑 16,240
TREE DIAGRAM
 Create a tree diagram to find the number of
outcomes.
How many breakfasts can be made with
the a choice of French toast, waffles, or
pancakes, and either sausage or bacon,
and apple juice or orange juice?
Answer: 12 breakfasts
SYSTEMS: GRAPHING
 Solve the system of equations by graphing.
𝟐𝒙 + 𝟑𝒚 = 𝟏𝟐
𝟐𝒙 − 𝟕 = 𝟒
Answer: (3,2)
SYSTEMS: SUBSTITUTION
 Solve the system of equations by substitution.
𝒚 = 𝟒𝒙 + 𝟓
𝟐𝒙 + 𝒚 = 𝟏𝟕
Answer: (2,13)
SYSTEMS: ELIMINATION
 Solve the system of equations by elimination.
𝟏𝟐𝒙 − 𝟑𝒚 = −𝟑
𝟔𝒙 + 𝒚 = 𝟏
Answer: (0,1)
SYSTEMS WORD PROBLEM
 Write a system of equations and solve:
Sean is trying to find two numbers
with a sum of 14 and a difference of
4. Find the two numbers.
Answer: 𝑥 + 𝑦 = 14
𝑥−𝑦=4
9 and 5
SYSTEMS WORD PROBLEM
 Write a system of equations and solve:
Chris bought 24 baseball cards for $50.
One type cost $1 per card, and the
other cost $3 per card. Find the number
of each type of card he bought
Answer: 𝑓 + 𝑐 = 24
𝑓 + 3𝑐 = 50
11 $1 cards and 13 $3 cards
SYSTEMS: WORD PROBLEM
 Solve the system of equations by defining
variables, setting up a system, and solving.
Veronica has been saving dimes and
quarters. She has 94 coins in all and the
total value is $19.30. How many dimes
and how many quarters does she have?
Answer: 28 dimes and 66 quarters
MONOMIALS: MULTIPLY
 Use exponent rules to multiply.
𝒃 𝟖 𝒄 𝟔 𝒅 𝟓 𝟕𝒃 𝟔 𝒄 𝟐 𝒅
Answer: 𝟕𝒃
𝟏𝟒 𝟖
𝒄 𝒅
𝟔
MONOMIALS: DIVIDE
 Use exponent rules to divide.
𝟖
𝟐
𝒈 𝒉 𝒎
𝒉𝒈 𝟕
Answer: 𝒈𝒉𝒎
SCIENTIFIC NOTATION
 Simplify. Write your answer in both standard
form and in scientific notation.
𝟕. 𝟎𝟖 × 𝟏𝟎
𝟏𝟒
𝟓 × 𝟏𝟎
−𝟗
Answer: 𝟑. 𝟓𝟒 × 𝟏𝟎 𝟔 𝒂𝒏𝒅 𝟑, 𝟓𝟒𝟎, 𝟎𝟎𝟎
VOCABULARY MATCH
a. the use of addition or subtraction to
1. Slope-intercept Form
eliminate one variable and solve a
system of equation
2. Substitution
3. Rate of Change
4. Monomial
5. Elimination
6. Slope Formula
b. Use of algebraic methods to find an
exact solution of a system of
equation
c.
𝑚=
𝑦2 −𝑦1
𝑥 2 −𝑥 1
d. The change in y over the change in x
e.
f.
𝒚 = 𝒎𝒙 + 𝒃
A number, variable, or product of a
number and one or more variables .