Review of Math 101
College Algebra
Math 110
Ben Woodruff
January 11, 2006
Ben Woodruff
College Algebra
Review of Math 101
D&C 88: 122-123
Appoint among yourselves a teacher, and let not all be spokesmen
at once; but let one speak at a time and let all listen unto his
sayings, that when all have spoken that all may be edified of all,
and that every man may have an equal privilege.
See that ye love one another; cease to be covetous; learn to impart
one to another as the gospel requires.
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Things to know
Solving equations in one and two variables
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Things to know
Solving equations in one and two variables
Constructing models to solve problems
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Things to know
Solving equations in one and two variables
Constructing models to solve problems
Distance, midpoints, circles
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Things to know
Solving equations in one and two variables
Constructing models to solve problems
Distance, midpoints, circles
Graphing points in the plane
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Things to know
Solving equations in one and two variables
Constructing models to solve problems
Distance, midpoints, circles
Graphing points in the plane
Perfect square trinomials (a + b)2 = a2 + 2ab + b 2
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Things to know
Solving equations in one and two variables
Constructing models to solve problems
Distance, midpoints, circles
Graphing points in the plane
Perfect square trinomials (a + b)2 = a2 + 2ab + b 2
Lines and slope
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Things to know
Solving equations in one and two variables
Constructing models to solve problems
Distance, midpoints, circles
Graphing points in the plane
Perfect square trinomials (a + b)2 = a2 + 2ab + b 2
Lines and slope
Quadratic formula, factoring, foiling
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Things to know
Solving equations in one and two variables
Constructing models to solve problems
Distance, midpoints, circles
Graphing points in the plane
Perfect square trinomials (a + b)2 = a2 + 2ab + b 2
Lines and slope
Quadratic formula, factoring, foiling
Interval notation, inequalities, absolute value
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples
1
Solve 7 + 3x = 4(x − 1).
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples
1
2
Solve 7 + 3x = 4(x − 1).
1
1
1
1
Solve −
=
+ .
x
3x
2x
6x
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples
1
2
3
Solve 7 + 3x = 4(x − 1).
1
1
1
1
Solve −
=
+ .
x
3x
2x
6x
Solve 3(x − 6) = 3x + 18.
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples
3
Solve 7 + 3x = 4(x − 1).
1
1
1
1
Solve −
=
+ .
x
3x
2x
6x
Solve 3(x − 6) = 3x + 18.
4
Solve |2x + 6| = 10.
1
2
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples
3
Solve 7 + 3x = 4(x − 1).
1
1
1
1
Solve −
=
+ .
x
3x
2x
6x
Solve 3(x − 6) = 3x + 18.
4
Solve |2x + 6| = 10.
5
Solve |4 − 3x| = 0.
1
2
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples
3
Solve 7 + 3x = 4(x − 1).
1
1
1
1
Solve −
=
+ .
x
3x
2x
6x
Solve 3(x − 6) = 3x + 18.
4
Solve |2x + 6| = 10.
5
Solve |4 − 3x| = 0.
6
Solve 6 − 4|x + 3| = −2.
1
2
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples
3
Solve 7 + 3x = 4(x − 1).
1
1
1
1
Solve −
=
+ .
x
3x
2x
6x
Solve 3(x − 6) = 3x + 18.
4
Solve |2x + 6| = 10.
5
Solve |4 − 3x| = 0.
6
Solve 6 − 4|x + 3| = −2.
7
Solve |x − 5| = −1.
1
2
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples
1
The equation for simple interest is I = Prt. Solve for t.
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples
1
The equation for simple interest is I = Prt. Solve for t.
2
A pharmacist needs to obtain a 70% alcohol solution. How
many ounces of a 30% alcohol solution must be mixed with
40 ounces of an 80% alcohol solution to obtain a 70% alcohol
solution?
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples
1
The equation for simple interest is I = Prt. Solve for t.
2
A pharmacist needs to obtain a 70% alcohol solution. How
many ounces of a 30% alcohol solution must be mixed with
40 ounces of an 80% alcohol solution to obtain a 70% alcohol
solution?
3
If you borrow $100 and pay back $102 at the end of one
month, what is the simple annual interest rate, using the
model I = Prt.
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples - distance, circles, lines
1
Plot the points (2, 3), (0, 4), (−5, 0).
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples - distance, circles, lines
1
Plot the points (2, 3), (0, 4), (−5, 0).
2
Find the distance between (0, 2) and (3, −2).
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples - distance, circles, lines
1
Plot the points (2, 3), (0, 4), (−5, 0).
2
Find the distance between (0, 2) and (3, −2).
3
Give an equation of the circle of radius 4 centered at (0,0).
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples - distance, circles, lines
1
Plot the points (2, 3), (0, 4), (−5, 0).
2
Find the distance between (0, 2) and (3, −2).
3
Give an equation of the circle of radius 4 centered at (0,0).
4
Give an equation of the circle of radius 2 centered at (1,3).
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples - distance, circles, lines
1
Plot the points (2, 3), (0, 4), (−5, 0).
2
Find the distance between (0, 2) and (3, −2).
3
Give an equation of the circle of radius 4 centered at (0,0).
4
Give an equation of the circle of radius 2 centered at (1,3).
5
Find the center and radius of the circle x 2 + 6x + y 2 = 16.
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples - distance, circles, lines
1
Plot the points (2, 3), (0, 4), (−5, 0).
2
Find the distance between (0, 2) and (3, −2).
3
Give an equation of the circle of radius 4 centered at (0,0).
4
Give an equation of the circle of radius 2 centered at (1,3).
5
Find the center and radius of the circle x 2 + 6x + y 2 = 16.
6
Graph the lines y = 5x − 3, 2x − 3y = 6, and x = −3.
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples - distance, circles, lines
1
Plot the points (2, 3), (0, 4), (−5, 0).
2
Find the distance between (0, 2) and (3, −2).
3
Give an equation of the circle of radius 4 centered at (0,0).
4
Give an equation of the circle of radius 2 centered at (1,3).
5
Find the center and radius of the circle x 2 + 6x + y 2 = 16.
6
Graph the lines y = 5x − 3, 2x − 3y = 6, and x = −3.
7
Find the slope of each of those lines.
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples - distance, circles, lines
1
Plot the points (2, 3), (0, 4), (−5, 0).
2
Find the distance between (0, 2) and (3, −2).
3
Give an equation of the circle of radius 4 centered at (0,0).
4
Give an equation of the circle of radius 2 centered at (1,3).
5
Find the center and radius of the circle x 2 + 6x + y 2 = 16.
6
Graph the lines y = 5x − 3, 2x − 3y = 6, and x = −3.
7
Find the slope of each of those lines.
8
Give an equation of the line through (1, 4) and (5, −1).
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples - distance, circles, lines
1
Plot the points (2, 3), (0, 4), (−5, 0).
2
Find the distance between (0, 2) and (3, −2).
3
Give an equation of the circle of radius 4 centered at (0,0).
4
Give an equation of the circle of radius 2 centered at (1,3).
5
Find the center and radius of the circle x 2 + 6x + y 2 = 16.
6
Graph the lines y = 5x − 3, 2x − 3y = 6, and x = −3.
7
Find the slope of each of those lines.
8
Give an equation of the line through (1, 4) and (5, −1).
9
Give an example of two parallel, and two perpendicular lines.
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples - quadratic equations
1
Solve x 2 = 4.
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples - quadratic equations
1
Solve x 2 = 4.
2
Solve x 2 − 5x + 6 = 0.
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples - quadratic equations
1
Solve x 2 = 4.
2
Solve x 2 − 5x + 6 = 0.
3
Solve x 2 + 2x − 5 = 0 by completing the square.
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples - quadratic equations
1
Solve x 2 = 4.
2
Solve x 2 − 5x + 6 = 0.
3
Solve x 2 + 2x − 5 = 0 by completing the square.
4
Solve x 2 + x − 1 = 0 using quadratic formula.
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples - interval notation
1
Write in interval notation 1 ≤ x < 2, and graph.
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples - interval notation
1
Write in interval notation 1 ≤ x < 2, and graph.
2
Write in interval notation 2 < x, and graph.
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples - interval notation
1
Write in interval notation 1 ≤ x < 2, and graph.
2
Write in interval notation 2 < x, and graph.
3
Solve 2x + 1 < 6.
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples - interval notation
1
Write in interval notation 1 ≤ x < 2, and graph.
2
Write in interval notation 2 < x, and graph.
3
Solve 2x + 1 < 6.
4
Find the union (−∞, 0) ∪ [−2, 4), and graph.
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples - interval notation
1
Write in interval notation 1 ≤ x < 2, and graph.
2
Write in interval notation 2 < x, and graph.
3
Solve 2x + 1 < 6.
4
Find the union (−∞, 0) ∪ [−2, 4), and graph.
5
Find the intersection (−∞, 0) ∩ [−2, 4), and graph.
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples - interval notation
1
Write in interval notation 1 ≤ x < 2, and graph.
2
Write in interval notation 2 < x, and graph.
3
Solve 2x + 1 < 6.
4
Find the union (−∞, 0) ∪ [−2, 4), and graph.
5
Find the intersection (−∞, 0) ∩ [−2, 4), and graph.
6
Solve |2x − 3| ≤ 5.
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples - interval notation
1
Write in interval notation 1 ≤ x < 2, and graph.
2
Write in interval notation 2 < x, and graph.
3
Solve 2x + 1 < 6.
4
Find the union (−∞, 0) ∪ [−2, 4), and graph.
5
Find the intersection (−∞, 0) ∩ [−2, 4), and graph.
6
Solve |2x − 3| ≤ 5.
7
Solve |x − 1| > 3.
Ben Woodruff
College Algebra
Review of Math 101
Things to Know
Examples
Examples - interval notation
1
Write in interval notation 1 ≤ x < 2, and graph.
2
Write in interval notation 2 < x, and graph.
3
Solve 2x + 1 < 6.
4
Find the union (−∞, 0) ∪ [−2, 4), and graph.
5
Find the intersection (−∞, 0) ∩ [−2, 4), and graph.
6
Solve |2x − 3| ≤ 5.
7
Solve |x − 1| > 3.
8
Solve |1 − 4x| ≥ 0.
Ben Woodruff
College Algebra