Download 5 Math Review

Algebra:
A man lived one-fourth of his life as a boy in
Baltimore, one-fifth of his life as a young man in
San Francisco, one-third of his life as a man in
Manitoba, and the last thirteen years of his life in
Thurmont. How old was the man when he died?
Write down your algebraic equation, your work,
and box your answer.
Word Problems
Read the entire problem through. Note that not all information given is
relevant.
1.
Write Given, Assign Variables, Sketch and Label Diagram
1. Whenever you write a variable, you must write what that variable
means.
2. What are the quantities? Assign variable(s) to quantities.
3. If possible, write all quantities in terms of the same variable.
2.
Write Formulas / Equations
What are the relationships between quantities?
3.
Substitute and Solve
Communication: All of your work should communicate your thought
process (logic/reasoning).
4.
Check Answer, then Box Answer
ALGEBRAIC SOLUTION:
Define the unknowns:
X = man’s total age.
X/4 = years as a boy
X/5 = years as a youth
X/3 = years as a man
Write an equation:
X = X/4 + X/5 + X/3 + 13
Solve the equation:
60X = 15X + 12X + 20X + 780
60X = 47X + 780
13X = 780
X = 60 years
Systems of Equations
•
Because two equations impose two conditions on the
variables at the same time, they are called a system of
simultaneous equations.
• When you are solving a system of equations, you are
looking for the values that are solutions for all of the
system’s equations.
• Methods of Solving:
1. Graphing
2. Algebra:
1. Substitution
2. Elimination
1. Addition-or-Subtraction
2. Multiplication in the Addition-or-Subtraction Method
Systems of Equations
•
Solve the following system by graphing:
y = x2
y = 8 – x2
What is the solution?
(2, 4) and (-2,4)
Systems of Equations
•
Solve the following system algebraically:
1) y = x2
2) y = 8 – x2
Substitute equation 1 into equation 2 and solve:
x2 = 8 – x2
2x2 = 8
x2 = 4
x = 2 and -2
Now substitute x-values into equation 1 to get y-values:
when
x = 2,
y=4
when
x = -2, y = 4
Solution: (2, 4) and (-2,4)
Systems of Equations
•
Systems of equations can have:
One Solution
Multiple Solutions
No Solutions
Systems of Equations – Word Problems
•
Solve using the same method as single equation problems:
1.
Write Given, Assign Variables, Sketch and Label Diagram
1. Whenever you write a variable, you must write what that
variable means.
2. What are the quantities? Assign variable(s) to quantities.
3. If possible, write all quantities in terms of the same
variable.
Write Formulas / Equations
What are the relationships between quantities?
Substitute and Solve
Communication: All of your work should communicate your
thought process (logic/reasoning).
Check Answer, then Box Answer
2.
3.
4.
Systems of Equations – Word Problems
Examples:
Algebra A:
Jenny and Kenny together have 37 marbles, and Kenny has
15. How many does Jenny have? (Solve algebraically, then
graphically to check.)
Algebra B:
The admission fee at a small fair is $1.50 for children and $4.00 for
adults. On a certain day, 2200 people enter the fair and $5050 is
collected. How many children and how many adults attended?
Algebra C:
Three times the width of a certain rectangle exceeds twice its
length by three inches, and four times its length is twelve more
than its perimeter. Find the dimensions of the rectangle.
Systems of Equations – Word Problems
Classwork:
Algebra A:
The perimeter of a rectangle is 54 centimeters. Two times the
altitude is 3 centimeters more than the base. What is the area
of the rectangle?
Algebra B:
The sum of the digits in a two-digit numeral is 10. The number
represented when the digits are reversed is 16 times the
original tens digit. Find the original two-digit number.
Hint: Let t = the tens digit in the original numeral and u = the
units digit in the original numeral.
Notes
•
Systems of Equations:
– Use the multiplication / addition-or-subtraction
method to simplify and/or solve systems of
equations:
• Eliminate one variable by adding or
subtracting corresponding members of the
given equations (use multiplication if
necessary to obtain coefficients of equal
absolute values.)
Geometry Review
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Area of a circle: pi*r2
Volume of a sphere: (4/3)*pi*r2
Volume of a cylinder: h*pi*r2
Surface area of a sphere: 4*pi*r2
Surface area of a cylinder: 2*pi*r2 + 2*pi*r
Surface area of a rectangular prism: 2*a*b + 2*a*c + 2*b*c
Area of a triangle: (1/2)*b*h
Volume of a pyramid: (1/3)*Abase*h