The document provides information about topics covered in math class today and for an upcoming final exam. It includes reviewing make-up tests, the Pythagorean theorem, and the distance formula. Sample problems are worked through applying concepts like adding, subtracting, multiplying and dividing fractions, using the Pythagorean theorem to find missing sides of right triangles, and applying the distance formula to find distances between points on a coordinate plane. Review for the final exam includes simplifying expressions, solving equations, and using formulas for perimeter, the Pythagorean theorem, and distance.
IT'S A PRESENTATION ON QUADRATIC EQUATION PART 1, CLASS 10, CHAPTER 4, IT STARTS WITH THE SHAPE PARABOLA AND IT'S DAY TO DAY LIFE EXAMPLES, AS WE PROCEED FURTHER WE SOLVE SOME EXPRESSIONS, WE COVERT IT INTO QUADRATIC EQUATIONS. AFTERWARDS, WE LEARN HOW TO FORM STANDARD QUADRATIC EQUATIONS WITH EXAMPLES (WORD PROBLEMS).
IT'S A PRESENTATION ON QUADRATIC EQUATION PART 1, CLASS 10, CHAPTER 4, IT STARTS WITH THE SHAPE PARABOLA AND IT'S DAY TO DAY LIFE EXAMPLES, AS WE PROCEED FURTHER WE SOLVE SOME EXPRESSIONS, WE COVERT IT INTO QUADRATIC EQUATIONS. AFTERWARDS, WE LEARN HOW TO FORM STANDARD QUADRATIC EQUATIONS WITH EXAMPLES (WORD PROBLEMS).
In pursuit of excellence, the CBSE board conducts a thorough research on emerging educational requirements. While designing the syllabus, the board ensures that every topic meets the learning needs of students in the best possible manner. CBSE Class 12 Maths - http://cbse.edurite.com/cbse-maths/cbse-class-12-maths.html
B.Sc (Pass) Nautical & Engineering Model Question 2 Mathematics Second Paper
(Differential Calculus, Integral Calculus, Two-dimensional & Three- dimensional Geometry)
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1. Today
Make-Up Tests?
Review For Final Exam
Review Pythagorean Theorem
New Material: Distance Formula
Class Work 4.10
May 13
2. 2
x2
– x + 2 = 0
(x – 2)(x + 1) Solutions are: x = 2, x = -1
Extraneous Solution is x = -1
Final Exam Review:
Add, Subtract, Multiply, & Divide
𝟑
𝟖
and
𝟕
𝟗
. Reduce to its simplest terms.
a.
𝟑
𝟖
+
𝟕
𝟗
=
𝟑
𝟖
+
𝟕
𝟗
=
𝟖𝟑
𝟕𝟐
= b.
𝟑
𝟖
-
𝟕
𝟗
=
𝟐𝟕−𝟓𝟔
𝟕𝟐
= -
𝟐𝟗
𝟕𝟐
c.
𝟑
𝟖
•
𝟕
𝟗
=
𝟐𝟏
𝟕𝟐
=
𝟕
𝟐𝟒
d.
𝟑
𝟖
÷
𝟕
𝟗
=
𝟑
𝟖
•
𝟗
𝟕
=
𝟐𝟕
𝟓𝟔
=
1
𝟏𝟏
𝟕𝟐
3. Pythagorean Theorem
81 – 26 = 𝟓𝟔 =
A building is on fire and
you need to set the
ladder back 10 ft. to
prevent burning. What is
the shortest ladder (in
feet) that will reach the
third story window ?
What is the
perimeter of
the sail?
9' + 12' + 15' = 36'
2 𝟏𝟒
4.
5. The distance between A and B is
| | | | | | | | | | | | | |
-5 4
A B
| -5 – 4 | = | -9 | = 9
Remember: Distance is always positive
6. A
B
The Distance Formula Is Derived
From The Pythagorean Formula
6
15
6² + 15² = C²
𝟐𝟔𝟏=C
As you can see, the shortest distance between two points is...
A straight line; 16.16 < 21
7. Distance Formula
Dist. = ( x2 - x1 )² + ( y2 - y1 )²
Remember the order ( x , y )
All answers are positive
8. Find the distance between the two points on the graph.
The Distance Formula:
What is the distance
along the x axis?
What is the distance
along the y axis?
Let's first use the P.T. to find the distance: a2 + b2 = c2
Now, let's use the distance
formula....
52 + 42 = 412
9. Find the distance between:
( 3 – 8 )² + ( 6 - 10 )²
( -5 )² + ( -4 )²
25 + 16
41 = 6.40
( 8 – 3 )² + ( 10 – 6 )²
( 5 )² + ( 4 )²
25 + 16
41 =6.40
( 3, 6 ) and ( 8, 10 )
Find the distance between:
( 8, 10 ) and ( 3, 6 )
When Using the distance formula, it does not matter what
point is used for x1 and x2. Be sure your y1 is from the same
coordinate pair as the x1
13. The Distance Formula
There are two different types of problems to solve withe
the distance formula.
A. All four of the coordinates are known. Solve for the
distance.
B. Three of four coordinates and the distance is known.
Solve for the fourth coordinate.
14. Example 1. Find the distance between the two points.
(-2,5) and (3,-1)
• Let (x1,y1) = (-2,5) and (x2,y2) = (3,-1)
A. All four of the coordinates are known. Solve for the distance.