Math 1B Final Review

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Math 1B Final Review
Unit 6 Standards
Day 1: Distance and Midpoint
1. Find the distance between (4, 2) and (-4, -4).
2. What is the perimeter 3. Find the distance
from (2, 5) to the
of BDE?
x-axis.
Day 1: Distance and Midpoint
4. Find the midpoint of the segment connecting
(4, 7) to (-2, 3).
5. A ship sails from
point (1, 2) to point
(5, 5), as shown. At
which point had the
ship completed
exactly HALF of its
trip?
Day 1: Distance and Midpoint
6. On a coordinate grid, the movie theater is
located at (0, 0) and the mall is located at (4, 3).
If the bowling alley is located at the midpoint
between the theater and the mall, what is the
approximate distance from the bowling alley to
the mall? (Note: 1 unit = 1 mile)
Day 2: Polygons (Quads & s)
7. What is the MOST specific name for
quadrilateral ABCD?
a. rhombus
b. trapezoid
c. parallelogram
d. isosceles trapezoid
Day 2: Polygons (Quads & s)
8. What is the MOST specific name for
quadrilateral LMNO?
a. parallelogram
b. rectangle
c. rhombus
d. square
Day 2: Polygons (Quads & s)
9. The points (5, 3), (3, -4), (10, 3), and (8, -4)
are the vertices of a polygon. What type of
polygon is formed by these points?
a. Parallelogram
b. Pentagon
c. Trapezoid
d. Triangle
10. Isosceles triangle ABC has vertices A(0, 0),
B(8, 0), and C(x, 12).
Find a possible value of x.
Day 2: Polygons (Quads & s)
11. One interior angle of a rhombus is 75.
What are the other 3 angles?
12. In parallelogram ABCD, find m<A.
Day 3: Reasoning
(Choose from inductive, deductive, and counterexample)
13.John concludes that, since (x – 5) is a factor of
the polynomial x2 – 25, if he performed the
long division (x2 – 25) ÷ (x – 5), the remainder
would be a zero.
This is an example of ______________ reasoning.
Day 3: Reasoning
(Choose from inductive, deductive, and counterexample)
14. Adam studied the
problems to the right
and concluded that
when you divide
exponential terms
with the same base,
you subtract their
exponents.
What type of reasoning
is he using?
Day 3: Reasoning
(Choose from inductive, deductive, and counterexample)
15. Ivan takes the square root of numerous
nonnegative numbers and concludes that
the square root of a nonnegative number
will always be a positive number.
Josh says Ivan is wrong because 0 is a
nonnegative number and 0 = 0, which is
not positive.
What type of reasoning is Josh using?
Day 3: Reasoning
16. Based on the given statements, which
statement must be true?
I: If Sarah makes all A’s and gets a scholarship, she
will attend a four-year college.
II: Sarah will attend a junior (two-year) college.
III: Sarah made all A’s.
a. Sarah did not get all A’s
b. Sarah did not get a
scholarship
c. Sarah made all A’s and got
a scholarship
d. Sarah attends a four-year
college and has a scholarship
Day 3: Reasoning
17. First, write the inverse, converse, and
contrapositive of the following statement.
If an angle measures 30°, then it is acute.
Then, decide whether each of these four
statements are TRUE or FALSE.
Day 4: Mixed Review
18. Parallelogram ABCD has the following
coordinates. A: (1, -3) B: (1, 0) C: (4, 2)
What are the coordinates of point D?
19. Square ABCD has the following coordinates.
A: (2, 2) B: (1, 4) C: (3, 5)
Find the coordinates of point D.
Day 4: Mixed Review
20. We can find the length of FG using the
Distance Formula: FG = (3 – 1)2 + (-1 – 3)2
Which formula also represents the length of
FG?
a.
b.
c.
d.
FG = 4 + 2
FG = (4 + 2)2
FG2 = 42 + 22
FG2 = 42 + 22
Day 4: Mixed Review
21. To find the length of AC, we could use the
Pythagorean Theorem and AC2 = 32 + 22. What
other formula could we use?
a.
b.
c.
d.
AC = (0 + 3)2 – (1 + 3)2
AC =  (0 + 1)2 – (3 + 3)2
AC =  (0 – 3)2 + (1 – 3)2
AC =  (0 – 1)2 + (3 – 3)2
Day 4: Mixed Review
22. Given: Two angles each measure less than 90.
Conjecture: The angles are complementary.
If the given statement and conjecture are false,
find a counterexample to show this.
23. Jamal states that the conjecture is true:
If a and b are integers, then a ÷ b is an integer.
Provide a counterexample to prove this
conjecture false.
Day 5: What should I study for this final?
• Triangle Centers!
–
–
–
–
Angle bisectors intersect at INCENTER
Altitudes intersect at ORTHOCENTER
Perpendicular bisectors intersect at CIRCUMCENTER
Medians intersect at CENTROID
• How to find distance/length and midpoint given 2
points or a graph.
***The SHORTEST distance is the
PERPENDICULAR distance***
***How is the PYTHAGOREAN THEOREM
related to the DISTANCE FORMULA?***
Day 5: What should I study for this final?
• Reasoning/Logic
– Inductive & Deductive reasoning
– Conjecture & Counterexample
– Converse, Inverse, & Contrapositive (truth values)
• Special Quadrilaterals
– Parallelogram, Rhombus, Rectangle, Square,
Trapezoid, Isosceles Trapezoid, Kite
– How they LOOK in the coordinate plane
– Their special properties (especially about their angles!)
– Sum of interior angles of a quadrilateral
Day 5: What should I study for this final?
• If x2 = 16, x = ?
• Random Vocabulary
–
–
–
–
–
–
–
–
Complementary
Supplementary
Integer, Nonnegative
Perpendicular/right angle
Parallel
Perimeter
Area
Vertex, Vertices
• Important Formulas
– Slope:
m = (y2 – y1)/ (x2 – x1)
– Pythagorean Thm:
a2 + b2 = c2
– Distance:
d = (x2 – x1) 2 + (y2 – y1) 2
– Midpoint:
M=( x1 + x2 , y1 + y2 )
( 2
2 )

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