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FINAL EXAM REVIEW
Spring 2014
SLOPE
ο‚‘Find the slope of the line that passes through
the points:
(0, 5) and (6, 2)
Answer:
𝟏
βˆ’
𝟐
SLOPE
ο‚‘ 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
ο‚‘ Fill in the blanks:
Parallel lines have ____ slopes.
Perpendicular lines have ___ slopes.
Answer: same, opposite reciprocal
GRAPHING
ο‚‘Graph the line:
𝟏
π’š= 𝒙
𝟐
Answer:
GRAPHING
ο‚‘Graph the line:
𝟐
π’š= π’™βˆ’πŸ“
πŸ‘
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: π’š = πŸ‘π’™ + πŸ“
WRITING EQUATIONS
Write an equation of the line that
passes through (5, -2) and has a
𝟏
slope of βˆ’ .
πŸ‘
Answer: π’š =
𝟏
βˆ’ 𝒙
πŸ‘
βˆ’
𝟏
πŸ‘
WRITING EQUATIONS
Write an equation in slopeintercept form for the line that
passes through (-5,2) and is
𝟏
perpendicular to π’š = 𝒙 + πŸ’.
πŸ‘
Answer: π’š = βˆ’πŸ‘π’™ βˆ’ πŸπŸ‘
FUNCTION NOTATION
For 𝒇 𝒙 = πŸ‘π’™ βˆ’ πŸ’, find 𝒇 βˆ’πŸ“ .
Answer: -19
PERMUTATIONS AND COMBINATIONS
ο‚‘ Find the number of outcomes.
How many ways can 4 lockers be
chosen out of 15 lockers?
Answer: 1365
FUNDAMENTAL COUNTING PRINCIPLE
ο‚‘ 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
ο‚‘ What is the standard form of a linear
equation?
________________
Answer: 𝐴π‘₯ + 𝐡𝑦 = 𝐢
SLOPE-INTERCEPT FORM
ο‚‘What is the slope-intercept form of a linear
equation?
____________
Answer: 𝑦 = π‘šπ‘₯ + 𝑏
SLOPE
ο‚‘What is the slope formula?
_____________
Answer: π‘š =
𝑦2 βˆ’π‘¦1
π‘₯ 2 βˆ’π‘₯ 1
SCIENTIFIC NOTATION
ο‚‘ Simplify the following expression. Write your
answer in both scientific notation and
standard form.
πŸ–
(πŸ“. πŸ” × πŸπŸŽ )(𝟐. πŸ— × πŸπŸŽ
βˆ’πŸ“
)
Answer: 1.624 × 10 4 π‘Žπ‘›π‘‘ 16,240
TREE DIAGRAM
ο‚‘ 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
ο‚‘ Solve the system of equations by graphing.
πŸπ’™ + πŸ‘π’š = 𝟏𝟐
πŸπ’™ βˆ’ πŸ• = πŸ’
Answer: (3,2)
SYSTEMS: SUBSTITUTION
ο‚‘ Solve the system of equations by substitution.
π’š = πŸ’π’™ + πŸ“
πŸπ’™ + π’š = πŸπŸ•
Answer: (2,13)
SYSTEMS: ELIMINATION
ο‚‘ Solve the system of equations by elimination.
πŸπŸπ’™ βˆ’ πŸ‘π’š = βˆ’πŸ‘
πŸ”π’™ + π’š = 𝟏
Answer: (0,1)
SYSTEMS WORD PROBLEM
ο‚‘ 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: π‘₯ + 𝑦 = 14
π‘₯βˆ’π‘¦=4
9 and 5
SYSTEMS WORD PROBLEM
ο‚‘ 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
ο‚‘ 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
ο‚‘ Use exponent rules to multiply.
𝒃 πŸ– 𝒄 πŸ” 𝒅 πŸ“ πŸ•π’ƒ πŸ” 𝒄 𝟐 𝒅
Answer: πŸ•π’ƒ
πŸπŸ’ πŸ–
𝒄 𝒅
πŸ”
MONOMIALS: DIVIDE
ο‚‘ Use exponent rules to divide.
πŸ–
𝟐
π’ˆ 𝒉 π’Ž
π’‰π’ˆ πŸ•
Answer: π’ˆπ’‰π’Ž
SCIENTIFIC NOTATION
ο‚‘ Simplify. Write your answer in both standard
form and in scientific notation.
πŸ•. πŸŽπŸ– × πŸπŸŽ
πŸπŸ’
πŸ“ × πŸπŸŽ
βˆ’πŸ—
Answer: πŸ‘. πŸ“πŸ’ × πŸπŸŽ πŸ” 𝒂𝒏𝒅 πŸ‘, πŸ“πŸ’πŸŽ, 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.
π‘š=
𝑦2 βˆ’π‘¦1
π‘₯ 2 βˆ’π‘₯ 1
d. The change in y over the change in x
e.
f.
π’š = π’Žπ’™ + 𝒃
A number, variable, or product of a
number and one or more variables .