LEARNING COMPETENCY DIRECTORY

Teacher's Name: RAYMOND A. GORDA Subject:: MATHEMATICS IVReference Used: (1) Math @ Work 4: Advanced Algebra, Trigonometry, & Statistics by Janet D. Dionio

(2) Advanced Algebra with Trigonometry & Statistics by Soledad Jose-Dilao, et. al.

CompetenciesNo. ofDays

Covered

Covered Unit/Chapter Target Activities

Lessons Book # Page #Letter/

No.Book # Page #

Define a function and demonstrate understanding of the definition; 1 Definitions of Functions 1 1-6 A – D 1 2 – 6

Given some real life relationships, identify those are functions. 1 Identifying Functions in Real Life Situations 1 7-9 A – C 1 8 – 9

Determine whether a given set of ordered pairs is a function or mere relations. 2 Representing Functions by Ordered Pairs 1 10 – 13 A – C 1 11 – 13

Draw the graph of a given set of ordered pairs; determine whether the graph represents a function or a mere relation.

1 Graphs of Relations and Functions12

14 – 1810 – 12 A – B 1 14 – 16

Use the vertical line test to determine whether the graph represents a function or not. 1 The Vertical Line Test 1 19 – 21 A – B 1 20 – 21

Illustrate the meaning of the functional notation f(x); determine the value of f(x) given a

value for x.1 The Functional Notation f(x) 1 22 – 24 A – B 1 23

Define the linear function f(x) = mx + b; given a linear function Ax + By = C, rewrite in

the form of f(x) = mx + b and vice–versa2 Linear Function 1 27 – 29 A – C 1 28 – 29

Draw the graph of a linear function given the following: any two points; x and y intercepts; slope and one point; or slope and y-intercept

2 Graphs of Linear Function 1 30 – 38 A – E 1 31 – 38

Given f(x) = mx + b, determine the following: slope; trend; increasing or decreasing; x and y intercept; or some points.

2Finding the Slope, Intercepts, Points & Trend of the Linear Function f(x) = mx + b 1 39 – 41 A – C 1 40 – 41

Determine f(x) = mx + b given: slope and y-intercept; x and y intercepts; slope and one point; or any two points

2 Equation of the Linear Function 1 42 – 47 A – F 1 43 – 47

Apply knowledge and skills related to linear functions in solving problems. 3 Problem Solving 1 48 – 50 1 49 – 50

Define a quadratic function ax2 + bx + c = 0; identify quadratic function 1 Quadratic Functions 1 51 – 53 A – C 1 52 – 53

Rewrites a quadratic function ax2 + bx + c = 0 in the form of f(x) = a(x – h)2 + k and vice–versa

2Transforming Quadratic Functions to f(x) = a(x – h)2 + k 1 54 – 55 A, B 1 55

Given a quadratic function, determine: highest or lowest point (vertex); axis of symmetry; or direction of opening of the graph.

1 Properties of the Graph of the Quadratic Functions 1 56 – 59 A, B 1 57 – 59

Draw the graph of a quadratic function using the vertex, axis of symmetry, or assignment of points.

2 Drawing the Graph of a Quadratic Functions 1 60 – 66 1 62 – 66

Analyze the effects on the graph of changes in a, h, and k in f(x) = a(x – h)2 + k. 1The Effects of the Changes in a, h, and k on the Graph of

f(x) = a(x – h)2 + k1 67 – 70 A – C 1 68 – 70

Determine the “zeros of a quadratic function” by relating this to “roots of a quadratic equation”; find the roots of a quadratic equation by factoring, quadratic formula, or completing the square.

3 Zeros of Quadratic Functions 1 71 – 76 A – D 1 73 – 76

Derive a quadratic function given zeros of a function or table of values. 2 Deriving Quadratic Functions 1 77 – 79 A – C 1 78 – 79

Apply knowledge and skills related to quadratic functions and equations in problem solving. 3 Application of Quadratic Functions 1 80 – 83 1 81 – 83

Review the definition of polynomials; identify a polynomial from a list of algebraic expressions.

1 Polynomials 1 91 – 94 A – D 1 92 – 94

Define a polynomial function; identify a polynomial function from a given set of relations; determine the degree and number of terms of a given polynomial function

3 Polynomial Functions 1 95 – 100 A – F 1 97 – 100

Find the quotient of polynomials by algorithm & synthetic division; find by synthetic division the quotient and the remainder when p(x) is divided by (x – c) 3 Division of Polynomials 1 101 – 105 A – D 1 103 – 105

State and illustrate the Remainder Theorem; find the value of p(x) for x = k by synthetic division or remainder theorem; state and illustrate the factor theorem

4 The Remainder Theorem & the Factor Theorem 1 106 – 109 A – D 1 108 – 109

Find the zeros of polynomial functions of degree greater than 2 by factor theorem, factoring, synthetic division, or depressed equations.

3 Zeros of Polynomial Functions of Degree Greater than 2 1 113 – 117 A – D 1 116 –117

Identify certain relationships in real life which are exponential; define the exponential function f(x) = ax and differentiate it from other functions; given a table of ordered pairs, state whether the trend is exponential or not

2 Definition of Exponential Functions 1 122 – 126 A – C 1 123 – 126

Draw the graph of an exponential function f(x) = ax ; describe some properties of the exponential function or its graph; given the graph of an exponential function determine the domain, range, intercepts, trend, & asymptote

2 Properties of Exponential Function & Its Graph 1 135 – 138 A – E 1 136 – 138

Use the laws on exponents to find the zeros of exponential functions 2 Laws of Exponents 1 139 – 141 A – D 1 140 – 141

Define inverse functions; determine the inverse of a given function 2 Inverse Functions/Relations 1 142 –146 A – D 1 144 –146

Define the logarithmic function f(x) = loga x as the inverse of the exponential function

f(x) = ax.1 The Logarithmic Function 1 147 – 148 A – B 1 148

State the laws for logarithms; apply the laws for logarithms; solve simple logarithmic equations.

4Laws of LogarithmsApplication of the Laws of Logarithms

1 150 – 153 A – C 1 152 – 153

Solve problems involving exponential and logarithmic functions. 3 Application of Exponential and Logarithmic Functions 1 154 – 156 A 1 155 – 156

Define unit circle, arc lengths, & unit measures of an angle; convert from degree to radian and vice–versa.

3 The Unit Circle 1 157 – 159 A – C 1 158 – 159

Illustrates angles in standard position, coterminal angles, & reference angle. 3 Angles in Standard Position 1 160 – 162 A – C 1 161 – 162

Visualize rotations along the unit circle and relate these to angle measures (clockwise orcounterclockwise directions): length of an arc, angles beyond 360o or 2 radians

2 Rotations Along the Unit Circle 1 163 – 165 A – B 1 163 – 165

Given an angle in standard position in a unit circle, determine the coordinates of the point of intersection of the unit circle and the terminal side.

3Coordinates of the Point of Intersection of the Unit Circle and the Terminal Side

1 170 – 171 A – E 1 170 – 171

Define sine functions; state the sine of an angle; define cosine functions; state the cosine of an angle

3The Sine Function & the Cosine Function of Special Number

1 172 – 175 A–C 1 173 – 175

Define tangent function and other circular functions; state the tangent and other circular functions of an angle

4The Tangent Function and Other Circular Functions of θ.

Use of Calculator to Get sin θ, cos θ, & tan θ.1 176 – 181 A – D 1 177 – 181

Describe the properties of the graphs of sine, cosine, & tangent functions. 2 Graphs of Sine, Cosine, & Tangent Functions 1 182 – 183 A – D 1 183

State the fundamental trigonometric identities and use these identities to solve other identities.

2 The Eight Fundamental Identities 1 184 – 186 A – E 1 185 – 186

Solve simple trigonometric equations. 2 Simple Trigonometric Equations 2 240 – 243 5 – 9 2 243

Solve problems involving right triangles. 3Solving Right TriangleApplications of the Trigonometric Functions

2246 – 247248 – 250

1 – 51 – 5

2247

249 – 250

Solve problems involving triangles using the sine law. 2 The Law of Sine 2 250 – 253 2 257 – 258

Solve problems involving triangles using the cosine law. 2 The Law of Cosine 2 254 – 258 2 257 – 258

Define statistics, sample, & population; give the importance of the study of statistics 2 Statistics Defined 2 264 – 267 2 266 – 267

State and explain the different sampling techniques 2 Sampling 2 267 – 272 2 272

Analyze, Interpret accurately, and draw conclusion from graphic and tabular presentation of statistical data

4Organizing DataTable & Graphs

2 273 – 280 2275, 278, 279, 281

Construct frequency distribution table 2 Frequency Distribution 2 282 – 285 2 284 – 285

Use the rules of summation to find sums 2 Summation 2 286 – 289 2 289

Find the arithmetic mean, grouped & ungrouped 3 The Mean 2 290 – 294 2 294

Find the median, grouped & ungrouped 4 The Median 2 295 – 298 2 298

Find the mode, grouped & ungrouped 2 The Mode 2 299 – 301 2 300 – 301

calculate the different measures of variability relative to a given set of data, grouped orungrouped, range & standard deviation; give the characteristics of a set of data using the measures of variability

5 Measures of Variability 2 302 – 307 2303, 305,

307

from a given statistical data, analyze, interpret, draw conclusions, make predictions, and make recommendations / decisions.

4 Analyzing Data Set 2 308 – 311 2 310 – 311