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Math 1B Final Review - PowerPoint PPT Presentation

Math 1B Final Review. Unit 6 Standards. Day 1: Distance and Midpoint. Find the distance between (4, 2) and (-4, -4). What is the perimeter of  BDE? . 3. Find the distance from (2, 5) to the x-axis. Day 1: Distance and Midpoint.

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Math 1B Final Review

Unit 6 Standards

• Find the distance between (4, 2) and (-4, -4).

• What is the perimeter

of BDE?

3. Find the distance from (2, 5) to the x-axis.

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?

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)

7. What is the MOST specific name for quadrilateral ABCD?

a. rhombus

b. trapezoid

c. parallelogram

d. isosceles trapezoid

8. What is the MOST specific name for quadrilateral LMNO?

a. parallelogram

b. rectangle

c. rhombus

d. square

• 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?

• Parallelogram c. Trapezoid

• Pentagon d. Triangle

• 10. Isosceles triangle ABC has vertices A(0, 0), B(8, 0), and C(x, 12).

• Find a possible value of x.

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)

• 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?

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.

• Sarah did not get all A’s c. Sarah made all A’s and got a scholarship

• Sarah did not get a d. Sarah attends a four-year scholarship college and has a scholarship

• 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.

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.

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. FG = 4 + 2

b. FG = (4 + 2)2

c. FG2 = 42 + 22

d. FG2 = 42 + 22

21. To find the length of AC, we could use the Pythagorean Theorem and AC2 = 32 + 22. What other formula could we use?

a. AC = (0 + 3)2 – (1 + 3)2

b. AC =  (0 + 1)2 – (3 + 3)2

c. AC =  (0 – 3)2 + (1 – 3)2

d. AC =  (0 – 1)2 + (3 – 3)2

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.

• Triangle Centers!

• Angle bisectors intersect at INCENTER

• Altitudes intersect at ORTHOCENTER

• Perpendicularbisectors 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?***

• Reasoning/Logic

• Inductive & Deductive reasoning

• Conjecture & Counterexample

• Converse, Inverse, & Contrapositive (truth values)

• 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

• 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 )

• If x2 = 16, x = ?

• Random Vocabulary

• Complementary

• Supplementary

• Integer, Nonnegative

• Perpendicular/right angle

• Parallel

• Perimeter

• Area

• Vertex, Vertices