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Final Exam Review
Foundations 20
Know all these concepts for the final exam. All formulas and the z-score table will be provided on the
exam. The assignment questions are at the end of this document.
Chapter 1
Making conjectures, inductive reasoning, deductive reasoning, number tricks, counter examples,
invalid proofs
Chapter 2
Definitions – transversal, converse, corresponding angles, same-side interior angles, alternate
exterior angles, alternate interior angles
When a transversal intersects 2 parallel lines…
the alternate interior angles are equal
the corresponding angles are equal
the same-side interior angles are supplementary
the alternate exterior angles are equal
The sum of the measures of the interior angles of any triangle is 180°
The measure of an exterior angle of a triangle is equal to the sum of the measures of
the 2 non-adjacent interior angles.
The sum of the measures of the interior angles of any n-sided convex polygon is ( n  2)180
The measure of each interior angle of a regular polygon is
(n  2)180
n
The sum of the measures of the exterior angles of any convex polygon is 360°
Chapter 3
Sine Law:
a
b

sin A sin B
Cosine Law: a2 = b2 + c2 – 2bc CosA
SOH CAH TOA (right triangles only)
Pythagorean Theorem: a2 + b2 = c2 (right triangles only)
Angle of Elevation, Angle of Depression, Compass Directions (N30⁰E, S48⁰W)
Word Problems – Be sure to write a final sentence which includes units.
Chapter 4
For any angle θ:
sin θ = sin (180 – θ)
cos θ = - cos (180 – θ)
tan θ = - tan (180 – θ)
The Sine Law and the Cosine Law can be used to solve acute and obtuse triangles.
Note: When using Sine Law, you must decide if you are solving for an acute or an obtuse
angle. (Your calculator will only give the acute angle measurement).
Ambiguous Case – only occurs when given ASS (two sides and a non-included angle)
A. Acute Triangles – 3 cases
B. Obtuse Triangles – 2 cases
Solving Word Problems
Chapter 5
Measures of Central Tendency – Mean, Median, Mode
Range – the difference between the maximum value and the minimum value in a data set.
Frequency distribution chart, Histogram (bar graph) and Frequency Polygon (line graph)
Standard Deviation :  
 ( x  x)
n
2
z-scores: z 
xx

or
z
x

Normal Distribution
Definitions - Confidence level, Confidence Interval, Margin of Error
Chapter 6
Graphing linear inequalities with 2 variables – example: 2x + 3y > 8


Solid line / Dotted line / Dashed Lines
Shading – use a point like (0, 0) to check where to shade/ dot
Graphing Systems of Linear Inequalities – example: x + 3y < 6 and 2x – y >1



Graph 2 (or more) inequalities on the same set of axes.
Shade each appropriately
Find points of intersection (overlapping shaded regions)
Optimization Problems – finding the maximum or minimum solutions
Chapter 7
Quadratic Function (y = ax2 + bx + c) – has a degree of 2 and graph is a parabola
If y = ax2 + bx + c, then:
a) y-intercept = c
b) graph opens up if a > 0, graph opens down if a < 0
c) x-intercept: set y = 0 and solve (factor or use quadratic formula)
Solving, finding roots/zeroes, determining x-intercepts – factor or use quadratic formula
Finding vertex:  fully factor equation (this gives x-intercepts, then find axis of symmetry),
then use the axis of symmetry to find the vertex and then draw the graph
Assignment:
Chapter 1 – 2 Cumulative Review: Page 110 #1 – 6, 10 – 12
Chapter 3 – 5 Cumulative Review: Page 287 #1 – 7, 9 – 14
Chapter 6 – 8 Cumulative Review: Page 520 #1, 2, 4, 6 – 11