FINAL REVIEW #9
Unit 1: Inductive & Deductive Reasoning
1. Matching exercise:
Terminology: inductive reasoning, deductive reasoning, counterexample, conjecture, proof, circular
reasoning
Definitions:
__________________ a mathematical argument showing that a statement is valid in all cases, or
that no counterexample exists
__________________ a testable expression that is based on available evidence but is not yet
proved
__________________ drawing a general conclusion by observing patterns and identifying
properties in specific examples
__________________ an argument that is incorrect because it makes use of the conclusion to be
proved
__________________ drawing a specific conclusion through logical reasoning by starting with
general assumptions that are known to be valid
__________________ an example that invalidates a conjecture
2. What kind of reasoning uses a variable to conclusively prove a conjecture?
Unit 2: Geometry
1. If a regular polygon has 12 sides,
a) what is total measure of all interior angles?
b) what is the measure of each congruent interior angle?
2. Exterior angles from any convex polygon will add to 360° . What will be the measure of each
exterior angle of a square? ☺
3. From the diagram, and assuming r s , match the relationship between each pair of angles:
∠1 and ∠3
________________
alternate interior angles
b) ∠6 and ∠3
________________
angles on a line
∠4 and ∠6
________________
vertically opposite angles
d) ∠2 and ∠8
________________
alternate exterior angles
e) ∠1 and ∠5
________________
co-interior angles
∠8 and ∠7
________________
corresponding angles
a)
c)
f)
Unit 3: Trigonometry
1. Determine the value of the angle A: 6 2 = 132 + 9 2 − ( 2 ⋅ 13 ⋅ 9 ⋅ cos A)
2. Calculate the length of side c:
c 2 = 10 2 + 8.8 2 − ( 2 ⋅ 10 ⋅ 8.8 ⋅ cos 80°)
3. Calculate the length of side m:
sin 33° sin 74°
=
14
m
4. Calculate the measure of angle B:
sin B sin 44°
=
110
82
5. Determine the value of ∠Y .
6. Determine the value of side x.
Unit 4: Statistical Reasoning
1. Sketch a histogram and a frequency polygon.
Which of the two have bars?
Which of the two show frequency?
Which of the two connect interval points?
2. Given amounts withdrawn from an ATM, in dollars:
$20, $120, $50, $70, $60, $80, $140, $120, $80, $160
a) Determine the mean:
b) Determine the mode:
c) Determine the median:
d) Determine the range:
3. If the lowest data value was $20 and the highest value was $500, and you wish to produce a
frequency table with ten intervals, what would the appropriate interval width be?
4. If we have the following data: 10, 15, 18, 20, 27,
a)
x=
b)
(x − x ) =
c)
(x − x )
d)
∑ (x − x )
2
∑ (x − x )
2
e)
f)
2
=
=
n
∑ (x − x )
2
n
5. The resulting number from #4 f) is called the standard deviation. Like the range, this number
measures: _________________.
6. What percentage of the standard normal distribution curve lies between σ = −2 and σ = 2 ?
7. If µ = 150 and σ = 5 , what percent of the data is between 155 and 160?
Unit 5: Systems of Linear Inequalities
1. If you were to graph 3 x − 4 y < 12 ,
The boundary line would be: solid / dashed
The region above / below the data will be shaded
2. Does (4, -1) satisfy both equations described below?
{(x, y ) 2 x + 3 y > 3, x ∈ ℜ, y ∈ ℜ} {(x, y ) x − 6 y ≤ 9, x ∈ ℜ, y ∈ ℜ}
3. Describe the system of linear inequalities that are shown graphically below:
4. Ribbon flowers and crepe-paper rosettes are being made as decorations for Yale Grad.
At least 50 ribbon flowers and no more than 75 rosettes are needed.
Altogether, no more than 140 decorations are needed.
Each ribbon flower takes 6 minutes to make, and each rosette takes 9 minutes to make.
What combination of ribbon flowers and rosettes will take the least amount of time to make?
Let f = # of ribbon flowers, and r = number of rosettes
a) Set up 3 linear equations that restrict variables f and r
b) What is the objective function?
c) Graph to solve:
Unit 6: Quadratic Functions & Equations
1. Solve each equation by inspection or by factoring:
a)
( x + 9)(3 x − 1)
b)
x 2 − 5 x − 24 = 0
c)
7 x 2 + 14 x = 0
d)
x 2 − 64 = 0
2
*e) x + 5 x − 10 = 0
x=
− b ± b 2 − 4ac
2a
2. Complete the equation for the given graph:
a) Vertex form:
y = __________ _____
X-intercept form:
y = ___________
3. Given: y = 3(x + 6 ) − 7 ,
2
a) What is the vertex?
b) This parabola opens ______ and has a graphing pattern: ____________
c) Equation of Axis of Symmetry? _______
d) Y-intercept? ______
Unit 7: Ratios & Rates
1. The actual diameter of a penny is 19 mm. In a scale diagram, the diameter of a penny is 5.7 cm.
a) What is the scale factor?
b) The surface area of the scale diagram will be how many times as large?
2. The Yale Lions won 16 of their first 20 Rugby games. At this rate, predict how many games they will
win during the 35-game season.
3. If the an object’s volume is 10 cm3 , and the enlarged image’s volume is 270 cm3 , what is the scale
factor?
4. What will the enlarged piece of paper be if an 8.5 cm x 11 cm page was enlarged by 150%?
5. A cellphone company advertises that it has created a similar version of its most popular phone,
reducing the volume and mass of the original phone by 50%. The original phone is a rectangular
prism, 50 mm wide by 95 mm long by 10 mm high. Determine the dimensions of the new phone.