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Rectangular 
Coordinate 
Sys tem 
Relations and 
Functions 
Representations of 
Relations and 
Functions 
Ordered Pairs 
Equations/ 
Formulas 
Domain and 
Dependent 
Independent 
Variables 
Slope and 
Intercepts 
6 5 4 3 2 1 
7 8 0 −1 2 0 
0 2 9 1 2 4 
1 
Paper #3a 
CARYL MAE S. PUERTOLLANO 
Subject: ICT in Mathematics Education 
Professor: Ms. Rosemarie Galvez 
* Create a Handout using MS Word 
1. SmartArt 
Here is a sample map of the lessons that will be covered in this module: 
2a. Linear Algebra 
Mapping 
Diagram 
Table 
Graphs 
Range 
and 
Appl ications 
PARTITION OF MATRICES; BLOCK MULTIPLICATION 
Linear 
Functions 
We now consider the following partitioned matrices of the same size to see how the operations work 
in practice: 
퐴 = [ 
1 2 3 4 6 0 
7 8 0 −3 1 6 
0 2 9 1 2 4 
], 퐵 = [ 
0 2 −1 0 −3 5 
1 −2 4 −2 2 −5 
4 −4 6 1 0 −4 
], 퐶 = 
[ 
] 
Now, A + B can be computed blockwise as A and B are partitioned the same way with 
corresponding blocks or submatrices having the same sizes. However, even though A and C are
matrices of the same size (so A + C can be computed adding elements entrywise) A + C cannot be 
computed blockwise as the blocks of A and C are not comparable. 
2b. Number Theory 
Properties of Summation 
1. Σ 푐 푛푖 
=1 = 푐 + 푐 + ⋯ + 푐 = 푐푛. 
2. Σ 푐푥푖 = 푐Σ 푥푖 . 푛푖 
=1 
2 
푛푖 
=1 
3. Σ (푥푖 + 푦푖 ) = Σ 푥푖 + Σ 푦푖 . 푛푖 
=1 
푛푖 
= 1 
푛푖 
=푛 
2c. Algebra 
Simplifying Rational Algebraic Expression 
푥2+3푥+2 
푥2−1 
Solution: 
푥2+3푥+2 
푥2−1 
= 
(푥+1)(푥+2) 
(푥+1)(푥−1) 
= 
푥+2 
푥−1 
2d. Calculus 
Evaluate ∫ 
푥2 
푥3 +1 
푑푥 
1 
0 
Solution: 푢 = 푥 3 + 1 
푑푢 = 3푥 2푑푥 
푑푢 
3푥2 = 푑푥 
∫ 
푥 2 
푥 3 + 1 
푑푥 = ∫ 
푥 2 
푢 
∙ 
푑푢 
3푥 2 = 
1 
3 
∫ 
1 
푢 
푑푢 = 
What factoring method 
is used in this step? 
1 
3 
푥=1 
푥=0 
푙푛|푢| = 
1 
3 
1 
푙푛|푥 3 + 1|| 
0 
푥=1 
푥=0 
1 
0 
= 
1 
3 
푙푛|1 + 1| − 
1 
3 
푙푛|0 + 1| = 
1 
3 
푙푛|2| − 
1 
3 
푙푛|1| = 
1 
3 
푙푛|2| − 0 = 
1 
3 
푙푛|2|
3 
2e. Trigonometry 
The graph of 푦 = 푠푖푛푥 is shown below. 
3. Geometric figures with labels. 
1. Name the parts of the circle. 
F G 
H 
D K 
L 
M 
A 
B 
C 
E 
1 
-1 
휋 
2 
3휋 2휋 3휋 
2 
● 
● 
●

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Paper3a puertollano

  • 1. Rectangular Coordinate Sys tem Relations and Functions Representations of Relations and Functions Ordered Pairs Equations/ Formulas Domain and Dependent Independent Variables Slope and Intercepts 6 5 4 3 2 1 7 8 0 −1 2 0 0 2 9 1 2 4 1 Paper #3a CARYL MAE S. PUERTOLLANO Subject: ICT in Mathematics Education Professor: Ms. Rosemarie Galvez * Create a Handout using MS Word 1. SmartArt Here is a sample map of the lessons that will be covered in this module: 2a. Linear Algebra Mapping Diagram Table Graphs Range and Appl ications PARTITION OF MATRICES; BLOCK MULTIPLICATION Linear Functions We now consider the following partitioned matrices of the same size to see how the operations work in practice: 퐴 = [ 1 2 3 4 6 0 7 8 0 −3 1 6 0 2 9 1 2 4 ], 퐵 = [ 0 2 −1 0 −3 5 1 −2 4 −2 2 −5 4 −4 6 1 0 −4 ], 퐶 = [ ] Now, A + B can be computed blockwise as A and B are partitioned the same way with corresponding blocks or submatrices having the same sizes. However, even though A and C are
  • 2. matrices of the same size (so A + C can be computed adding elements entrywise) A + C cannot be computed blockwise as the blocks of A and C are not comparable. 2b. Number Theory Properties of Summation 1. Σ 푐 푛푖 =1 = 푐 + 푐 + ⋯ + 푐 = 푐푛. 2. Σ 푐푥푖 = 푐Σ 푥푖 . 푛푖 =1 2 푛푖 =1 3. Σ (푥푖 + 푦푖 ) = Σ 푥푖 + Σ 푦푖 . 푛푖 =1 푛푖 = 1 푛푖 =푛 2c. Algebra Simplifying Rational Algebraic Expression 푥2+3푥+2 푥2−1 Solution: 푥2+3푥+2 푥2−1 = (푥+1)(푥+2) (푥+1)(푥−1) = 푥+2 푥−1 2d. Calculus Evaluate ∫ 푥2 푥3 +1 푑푥 1 0 Solution: 푢 = 푥 3 + 1 푑푢 = 3푥 2푑푥 푑푢 3푥2 = 푑푥 ∫ 푥 2 푥 3 + 1 푑푥 = ∫ 푥 2 푢 ∙ 푑푢 3푥 2 = 1 3 ∫ 1 푢 푑푢 = What factoring method is used in this step? 1 3 푥=1 푥=0 푙푛|푢| = 1 3 1 푙푛|푥 3 + 1|| 0 푥=1 푥=0 1 0 = 1 3 푙푛|1 + 1| − 1 3 푙푛|0 + 1| = 1 3 푙푛|2| − 1 3 푙푛|1| = 1 3 푙푛|2| − 0 = 1 3 푙푛|2|
  • 3. 3 2e. Trigonometry The graph of 푦 = 푠푖푛푥 is shown below. 3. Geometric figures with labels. 1. Name the parts of the circle. F G H D K L M A B C E 1 -1 휋 2 3휋 2휋 3휋 2 ● ● ●