LEARNING COMPETENCIES IN MATHEMATICS I FIRST GRADING PERIOD Chapter IREAL NUMBER SYSTEM A. REAL NUMBER SYSTEM A1 Describe the real number system, integers, rational numbers, irrational numbers and real numbers.A1.1 Review operations on whole numbers.A1.1.1 Additional and subtraction.A1.1.2 MultiplicationA1.1.3 DivisionA1.2 Describe opposite quantities in real life situationA1.3 Determine the absolute value of a numberA1.4 Solve simple absolute value equations using the number lineA1.5 Perform fundamental operations on integersA1.5.1 AdditionA1.5.2 SubtractionA1.5.3 MultiplicationA1.5.4 DivisionA1.6 Illustrate the different properties of real numbersA1.6.1 CommutativeA1.6.2 AssociativeA1.6.3 DistributiveA1.6.4 IdentityA1.6.5 InverseA1.7 Solve problems involving integersA1.8 Perform operation on fractionsA1.8.1 AdditionA1.8.2 SubtractionA1.8.3 MultiplicationA1.8.4 DivisionA1.9 Solve problems involving fractionsA1.10 Perform operations on decimalsA1.10.1 AdditionA1.10.2 SubtractionA1.10.3 MultiplicationA1.10.4 DivisionA1.11 Solve problems involving decimalsA2. Demonstrate knowledge and skills in solving square roots of positive rational numbersA2. 1 Define the square root of a rational number/give examples of irrational numbersA2.2 Approximate the square root of a positive rational numbersA2.3 Identify the square roots which are rational and which are irrationalA2.4 Identify the square roots which are rational and determine two integers or rational numbers between which it lies

Chapter IIMEASUREMENT B. MEASUREMENT B1 Demonstrate knowledge and skill in measurement and use of measuring devices, conversion of unit’s measurement, and solving real-life problemsB1.1 Illustrate of measurement from primitive to the present international system of unitsB1.2 Use instrument to measure:B1.2.1 Length/areaB1.2.2 Volume and capacity/massB1.2.3 Temperature/ angleB1.3 Convert measurement from one unit to anotherB1.3.1 Length/distance

B1.3.2 AreaB1.3.3 Volume and capacity/ massB1.3.4 TemperatureB1.3.4.1 Convert degree Celsius to degree FahrenheitB1.3.4.2 Convert degree Fahrenheit to degree CelsiusB1.3.5 TimeB1.4 Express relationship between two quantities using ratiosChapter III ALGEBRAIC EXPRESSIONSC. ALGEBRAIC EXPRESSIONS C1 Demonstrate knowledge and skills in simplifying and performing operations on polynomialsC1.1 Define constant, variable and algebraic expressionC1.2 Simplify numerical expressions involving exponents and grouping symbolsC1.3 Translate verbal phrases to mathematical expressions and vice-versaC1.3.1 Translate verbal phrases to mathematical expressionsC1.3.2 Translate mathematical expression to verbal phrasesC1.4 Evaluate mathematical expressions for given values of the variable/s involveSECOND GRADING PERIODC1.5 Apply the laws of exponentsC1.5.1 Product law am.an=am+nC1.5.2 Power of a power law (am)n=amnC1.5.3 Power of a product law (ab)m=ambmC1.5.4 Quotient law am/an=am-nC1.5.4.1 Where m-n is a positive number if m>nC1.5.4.2 Where m-n is a negative number if m<nC1.5.5 power of a quotient law (a/b)m=am/bmC1.6 Express numbers in scientific notationC1.7 Define polynomials. Classify algebraic expressions as polynomials/ non-polynomialsC1.8 Perform operations on polynomialsC1.8.1 Add polynomialsC1.8.2 Subtract polynomialsC1.8.3 Multiply a polynomial by a monomialC1.8.4 Multiply a binomial by another binomialC1.8.5 Multiply a polynomial by another polynomialC1.8.6 Divide a polynomial by a monomialC1.8.7 Divide a polynomial by binomialC1.8.8 Divide a polynomial by another polynomialC1.9 Solve word problems involving polynomialsChapter IV FIRST-DEGREE EUATIONS AND INEQUALTIES IN ONE VARIABLE D FIRST-DEGREE EUATIONS AND INEQUALTIES IN ONE VARIABLED1 Demonstrate knowledge and skill in transforming and solving first degree equation and inequalities in one variableD1.1 Distinguish equations from inequalitiesD1.2 Translate a verbal statement involving general or unknown quantities to an equation and vice-versaD1.3 Translate a verbal statement involving general or unknown quantities to an inequality and vice-versaD1.4 Determine the solution set of a first degree equation or inequality using:D1.4.1 Number lineD1.4.2 Replacement setD1.4.3 InspectionD1.5 State/ illustrate the different properties of equalityD1.6 Apply the properties of equality in finding the solution set of a first degree equationD1.6.1 Addition/subtraction properties of equalityD1.6.2 Multiplication/Division properties of equalityD1.7 Apply the properties of inequality in finding the solution set of a first degree inequalityD1.8 Solve word problems using first degree equations and inequalities in one variable

D1.8.1 NumbersD1.8.1.1 Number relationD1.8.1.2 Consecutive numbersD1.8.2 GeometryD1.8.3 BusinessD1.8.4 Uniform motionD1.8.5 Money problemsD1.8.6 WorkD1.8.7 MixtureChapter V LINEAR EQUATIONS IN TWO VARIABLESE LINEAR EQUATIONS IN TWO VARIABLES E1 Demonstrate knowledge and skill about linear equations in two variables and apply these in solving real life problemsE1.1 Describe the Cartesian coordinate planeE1.2 Given a point on the coordinate plane, give its coordinatesE1.3 Given a pair of coordinates, Plot the point. Given the coordinate of a point, determine the quadrant where it is locatedE1.4 Define/identify the linear equation in two variables: Ax + By = CE1.5 Construct a table of values for x and y given a linear equation in two variables Ax + By = C. Define the domain and range.E1.6 Identify a table of values for x and y given linear equation in two variables Ax + By = CE1.7 Identify the graph of Ax + By = C based on a table of values for x and yE1.8 Draw the graph of Ax + By = C based on a table of values for x and yE1.9 Define x and y intercepts and slope

Third Grading PeriodE1.10 Determine the properties of the graph of a linear equation Ax + By = CE1.10.1 SlopeE1.10.2 TrendE1.10.3 InterceptsE1.10.4 Domain and rangeE1.11 Given a linear equation Ax + By = C, rewrite i9n the form y=mx + bE1.12 Given a linear equation y=mx + b, rewrite in the form Ax + By = CE1.13 Draw the graph of a linear equation in two variables describe by an equation using:E1.13.1 The interceptsE1.13.2 Any two pointsE1.13.3 The slope in a given pointE1.14 Obtain the equation of the line given:E1.14.1 Slope and interceptE1.14.2 The interceptsE1.14.3 Any two pointsE1.14.4 Slope and a pointE1.15 Use linear equation in two variables to solve problemsE1.15.1 NumberE1.15.2 MotionE1.15.3 AgeE1.15.4 WorkE1.16 Find the solution of an absolute value equationE1.17 Draw the graph of absolute value equationsChapter VI SPECIAL PRODUCTSF SPECIAL PRODUCTS F1 Demonstrate knowledge and skill in finding special products and factors of certain polynomialF1.1 Identify Special products

F1.1.1 Polynomial whose terms have a common monomial factorF1.1.2 Trinomial which is a product of two binomialsF1.1.3 Trinomial which is a product of the square of a binomialF1.1.4 Product of the sum and difference of two quantitiesF1.1.5 Cube of a binomialF1.2 Given the factors, find the special productF1.2.1 Polynomial whose terms have common monomial factorsF1.2.2 Trinomial which is a product of two binomialsF1.2.3 Trinomial which is a product of the square of a binomialF1.2.4 Product of the sum and difference of two quantitiesF1.2.5 Cube of a binomialF1.3 Factor polynomialF1.3.1 Polynomial whose terms have a common monomial factorF1.3.2 Trinomial which is a product of two binomials where c is positiveF1.3.3 Trinomial which is a product of two binomials where c is negativeF1.3.4 Trinomial which is a product of two binomial where a is not equal to 1F1.3.5 Trinomial which is not a product of two binomials where a is equal to 1F1.3.6 Trinomial which is a square of a binomialF1.3.7 Difference of two squaresF1.3.8 Difference of two cubesF1.4 Given a polynomial factor completelyF1.5 Factor polynomial by groupings

IKALAWANG TAON Competencies

A1.1 Define a system of linear in two variablesA1.2 Given a pair linear equation in two variables, identify those graphs whose graph coincideA1.3 Given a system of linear equation in two variables, find the solution graphicallyA1.4 Given a system of linear in two variables, find the solution with eliminationA1.5 Use systems of linear equations to solve problemsA2.1 Define a system of linear inequalitiesA2.2 Translates certain situation in real life to linear inequalitiesA2.3 Draw the graph of a linear inequalities two variablesB1.1 Distinguish a quadratic equation fro linear equationB1.2 Determine the solution set of a quadratic equation ax2+bx+c= 0 by algebraic methodsB1.3 Solve rational equation which can be reduced to quadratic equationB1.4 Use quadratic to solve problemC1.1a Define rational algebraic expressionC1.2b Define the domain of rational algebraic expressionC1.2 Translate verbal expression into rational algebraic expressionC1.3 Simply rational algebraic expressionC1.4 Perform rational equation and check for extraneous solutionC1.5 Simply rational algebraic expressionC1.6 Solve rational equation and check for extraneous solutionC1.7 Solve problem involving rational algebraic expressionD1. Demonstrate knowledge of variation relationships and apply these in problem solvingD1.1 Demonstrate understanding of expression with

Positive exponent Negative exponent Zero exponentD1.2 Evaluate numerical expression involving integral exponentD1.3 Rewrite algebraic expression with zero & negative exponentD1.4 Solve problems involving expression with exponentE1.1 Identify expression which are perfect square and perfect cubesE1.2 Find the square root or cube root of expressionE1.3 Given the number inequalities the form where x is not a perfect cubesE1.4 Use laws of exponents to simplify expressions containing rational exponentE1.5 Rewrite expressions with rational exponents radical expressions and vice-versaE1.6 Simplify the radical expressions inequalities such a way that the radical contains no perfectNth rootE1.7 Rationalize a friction whose denominator contains square rootsE1.8 Perform operations on radical expressionsE1.9 Solve radical equationsE1.10 Solve problems involving radical expressionsF1.1 List the few termsF1.2 Derive from pattern searching A mathematical expression (rule) for generating thesequenceF1.13 Describe an arithmetic sequence by any of ff. ways Giving the first few terms Giving the formula for the nth term Drawing the graphF1.4 Given the first few term of as arithmetic sequence find the Common difference Nth termF1.5 Given two terms of an arithmetic sequence find the Nth term Common difference or A specifiedF1.6 Solve problems involving arithmetic meansF1.9 Solve problems involving arithmetic sequenceF2.1 Describe A geometric sequence inequalities any of ff ways Giving the first few terms of the sequence giving the formula for the nth term Drawing the graphF2.2 Given the first few terms of geometric sequence, find the Common ratio Nth termF2.3 Given two specified terms of geometric sequence, find the First term Common ratioF2.4 Solve problems involving geometric meansF2.6 Find the sum of the terms of geometric sequenceF2.8 Solve problems involving geometric sequence

IKAAPAT NA TAON MATH III: BUDGET OF WORK (First Quarter)

RECITATION DAYS SPECIFIC COMPETENCIES 1 Undefined TermsDescribe the ideas of points, lines, and planes.Define, identify, and name the subsets of a line.

1 AnglesName and identify an angle.Name and identify parts of an angle.Find the measurement of an angle.1 Name, identify and identify the different kinds ofangles.

Geometric RelationsDefine a midpoint.1 Apply the definition of betweens in determiningwhich point is between the other two.Define a midpoint .1 Formulate conclusions based from the definition ofan midpoint.Apply the definition of a midpoint in finding thecoordinate of the midpoint of a segment.Define and identify an Angle Bisector.Formulate Conclusions based from definition of an1 Angle Bisector.Apply the definition of an Angle Bisector in findingthe measurement of an angle.Define and identify the different Angle Pairs.1 Find the measure of an Angle by applying therelationships of the different Angle Pairs.Solve problems by applying the relationships of the1 different Angle Pairs.Define and identify perpendicular lines.Define and identify the Perpendicular bisector of a1 segment.Formulate conclusions based from the definition ofperpendicular lines and Perpendicular Bisector andsegment.

Angles formed by Parallel Cut by Transversal Define and identify parallel lines.1 Define and identify a transversal.Identify the angles formed by lines cut by a transversal.1 Prove the relationships of the angles formed by lines cut by a transversal.1 Find the measures of angles by applying the relationships of the angles formed by lines cut by a transversal. 1 Find the measures of angles by applying therelationships of the angles by the lines cut by transversal.

1 Find the measures of angles by applying therelationships of the angles formed by // lines cut by a transversal.1 PolygonsDefine and identify a polygon.Identify the different kinds of polygons and their partsDefine a triangle.1 Identify the different kinds of triangles according to sides and angles.1 Name and identify the Basic and Secondary Parts of a T triangle.1 Find the measures of the interior angles and relationships of a triangle.1 Identify the measurements which could be the possible sides of a triangle and range of values for the third side.1 Determine the sum of the measures of the interior angles of convex polygon .1 Find the perimeter of a triangle.1 Derive and apply the formula in finding the area of a triangle.1 Name, define, and identify a quadrilateral and its parts.1 Name, identify the different kinds of quadrilaterals1 Derive and apply the formula in finding the perimeter square and rectangle.1 Find the perimeter of polygons.1 Derive and apply the formula in finding the area of square.Derive and apply the formula in finding the area of a rectangle.1 Derive and apply the formula in finding the area of parallelogram.1 Derive and apply the formula in finding the area of a trapezoid.1Circles1 Name, define, and identify the parts of a circle.1 Derive and apply the formula in finding circumference of a circle.1 Derive and apply the formula in finding the area of a circle.

Solid Figures1 Define a solid figure.1 Identify solid figures and their parts.1 Derive and apply the formula in finding the Surface Area of a cube.1 Derive and apply the formula in finding the Surface Area of a Rectangular Prism.1 Derive and apply the formula in finding the Surface Area of a Square Pyramid.1 Derive and apply the formula in finding the Surface Area of a Cylinder.1 Derive and apply the formula in finding the Surface Area of a Cone.1 Derive and apply the formula in finding the Volume of a Cone.1 Derive and apply the formula in finding the Volume of a Cube.1 Derive and apply the formula in finding the Volume of a Rectangular Prism.1 Derive and apply the formula in finding the Volume of a Square Pyramid.1 Derive and apply the formula in finding the Volume of a Cylinder.1 Derive and apply the formula in finding the Volume of a Cone.1 Derive and apply the formula in finding the Volume of a Sphere.

(Second Quarter) Recitation Days Specific Competencies Triangle Congruence Conditions for Triangle Congruence 1 a. Define congruent triangles and identify the corresponding congruent parts.a. Use the symmetric, reflexive, and transitive1 properties of congruence in proving conditions for triangle congruence.b. Apply SSS Congruence in proving that two1 triangle are congruent.1 a. Apply SAS Congruence in proving that two triangles are congruent.1 a. Apply the ASA Congruence in proving that two triangles are congruent.

1 a. Apply SSA Congruence in proving that two triangles are congruent.Congruence Segments and Congruent Angles1 a. Use the definition of congruent triangles and conditions for triangle congruence in proving congruent segments and angles between two triangles. Congruence Between Right Triangles 1 a. Prove LL Congruenceb. Apply LL Congruence in proving triangles are congruent.1 a. Prove HyL Congruenceb. Apply the HyL Congruence in proving two congruent right triangles.1 a. Prove HyA Congruenceb. Apply the HyA Congruence in proving two congruent right triangles.Slide and Angle Relations in a triangle1 a. Prove Isosceles Triangle Theorem and its Converse.b. Apply the ITT in finding the measure ofb.1 Base angles of a triangle.1 b.2 Length of legs of a triangle.Inequalities in a Trianglea. Name the angles of a triangle in increasing/ decreasing order given the lengths of its sides.1 b. Name the sides of triangle in increasing/ decreasing given its measure of angles.Quadrilateral1 a. Recall different kinds of quadrilaterals.b. Define and identify parts of a quadrilateral.The Trapezoid and its Properties1 a. Prove the midline of a triangleb. Find the measure of the midline of a trianglea. Apply the midline of a Triangle Theorem in proving the Median of a Trapezoid Theorem.1 b. Apply the Median of a Trapezoid Theorem in finding:b.1. The length of the median.1 b.2. The length of the base.1 b.3. Solve problems involving median a trapezoid.Isosceles Trapezoid1 a. Prove that the base angles and diagonals and isosceles trapezoid congruent.b. Apply the properties of an isosceles trapezoid in finding.b.1. The length of its diagonal.

IKAAPAT NA TAON Learning competencies in Math IV

I. RELATIONS AND FUNCTIONS1.1 Define a function.1.2 Differentiate and identify a function from a mere relation givena. The set of ordered pairsb. Graph of the given set of ordered pairsc. Vertical line testd. Equation1.3 Express the given equation in function notation f(x).1.4 Find the value of f(x) given the value of x.1.5 Perform operation on functions:a. Perform addition and subtraction of functions.b. Perform multiplication and division of functions.1.6 Find the composition of functions.a. Evaluate composition of functions.1.7 Identify and cite examples of real life relations involving functions.1.8 Express the given situation as an equation/function notation.1.9 Solve word problems involving functions.

II. LINEAR FUNCTIONS2.1 Define and identify linear functions from equation, table of values and graphs.2.2 Transform Ax + By = C to y – form and express it in function notation.2.3 Transform y – form of linear function to standard form.2.4 Given f(x) = mx + b, find the slope, trend, intercepts and some points.2.5 Given the graph of f(x) = mx + b, find the slope, trend, intercepts and some points.2.6 Analyze the effects of the slope m and y – intercepts b in the graph of linear functions.2.7 Determine f(x) = mx + b givena. slope and y – interceptsb. x and y – interceptsc. slope and 1 pointd. any two points2.8.1 Determine the slopes of parallel lines.2.8.2 Find the equation of the line parallel to another line passing through a given point.2.9.1 Determine the slopes of perpendicular lines.2.9.2 Find the equation of the line perpendicular to another line passing through a given point.III. QUADRATIC FUNCTIONS3.1 Define and identify quadratic functions given the equations and table of values.3.2 Rewrite quadratic functions f(x) = x² + bx + c to f(x) = (x- h)² + k.3.3 Rewrite quadratic functions f(x) = x² + bx + c to f(x) = a(x - h)² + k.3.4 Rewrite quadratic functions f(x) = a(x – h)² + k to f(x) = x² + bx + c.3.5.1 a. Draw and analyze the changes of a in the graph of quadratic function of the form f(x) = ax²B. construct the graph of quadratic functions of the form f(x) = ax² wherea = 1, a = 2, a = ½, a = -1, a = -2, a = -½.C. analyze the effects of the changes of a in the graph of f(x)= ax².D. determines the line of symmetry and the vertex of each graph.3.5.2. a. construct the graph of quadratic function in the form f(x)=ax²+k.B. analyze the effect of the changes of a and k in the graph of f(x)=ax²+k.C. determines the line of symmetry and the line of each graph.3.5.3. a. Construct the graph of quadratic function of the form f(x)=a(x-h)².B. analyze the effect of the changes of a and h in the graph of f(x)=a(x-h)².C. determines the line of symmetry, the vertex and direction of the opening of the graph.3.5.4. a. construct the graph of the quadratic function of the form f(x)=a(x-h)²+k.B. analyze the effect of the changes of a, h, and k in the graph of f(x)=a(x-h)²+k.C. determines the line of symmetry, the vertex and direction of the opening of the graph.3.6. a. determine the function whose movement is being described given f(x)= ax².B. describes the movement of the graph given the function.3.7. Find the zeros of the functions and the roots of the related quadratic and find the roots of quadratic functions.A. by factoring methodB. by quadratic formulaC. by completing the squaresC.1. a=1C.2. a=13.8. Derive the quadratic function givenA. zeros of the functionB. by quadratic formulaC. table of values or set of ordered pairsC.1. when one or more of the ordered pairs have 0 as x and / or y.C.2 when the given ordered pairs have no 0 as values of x or y3.9. Solve word problems involving quadratic functions.

IV. POLYNOMIAL FUNCTIONS4.1 identify polynomial function from the given set of relations and determine its degree.4.2. Evaluate polynomial functions.4.3. Find the quotient and remainder of polynomials by synthetic division when p(x) is divided by (x-c)4.4. Write the Division Algorithm for polynomials given a certain division problem.4.5. Illustrate the use of Remainder Theorem and find the value of P(x) for x=k by synthetic Division and Remainder Theorem4.6 Find the value of the missing term of a polynomial to meet the given condition.4.7. Illustrate the use of the Factor Theorem and determine if the given condition.4.8. Find the value of the missing term of a polynomial which the binomial is a factor of the given polynomial.4.9. Find the zeros of Polynomial Function of degree greater than 2 by Factor Theorem.4.10. Find the zeros of polynomial function of degree greater than 2 by factoring.4.11. Find the zeros of polynomial function of degree greater than 2 by synthetic division.4.12. Find the zeros of polynomial function of degree greater than 2 by any method.4.13. Describe the properties of polynomial function of degree greater than 2 by its graph.

V. EXPONENTIAL AND LOGARITHMIC FUNCTIONS5.1 Identify certain relationships in real life which are exponential and determine whether given table of ordered pairs is exponential or not.5.2 Describe some properties of the exponential function f(x) = ax, where a>15.3 Describe some properties of the exponential function f(x) =ax, where 0<a<1.5.4 Given the graph of an exponential function, determine the domain, range, intercepts, trend and asymptote.5.5 Solve Exponential Equations.5.6 Use the laws on exponential to find the zeros of exponential.5.7 Define inverse function and determine the inverse of a given function.5.8 Define the logarithmic function f(x) = loga x as the inverse of the exponential function f(x) = ax and vice versa.5.9 Describe some properties of logarithmic function from its graph.5.10 Determine the value of a given logarithm.5.11 Apply the laws for logarithms in simplifying expressions.5.12 Solve simple logarithmic equation if the number is missing.5.13 Solve simple logarithmic equation if the exponent is missing.5.14 Solve simple logarithmic equation if the base is missing.5.15 Solve complex logarithmic equation applying the laws of logarithms.5.16 Solve problems involving exponential and logarithmic functions (compound interest)5.17 Solve problems involving exponential and logarithmic functions (exponential growth)5.18 Solve problems involving exponential and logarithmic functions (exponential decay)

VI. CIRCULAR FUNCTIONS AND TRIGONOMETRY6.1 Define unit circle, degree measure of an angle and the radian measure. Determine whether the coordinate given lies on a unit circle.

6.2 Convert degree measure to radian.6.3 Convert radian measure to degree measure.6.4 Define and illustrate angle in standard position. Identify the quadrant of the given angle.6.5 Define and illustrate co terminal angles. Find the co terminal angles of the given angles.6.6 Define and illustrate the reference angle. Give the corresponding references angle of a given angle.6.7 Find the length of an arc intercepted by a central angle.6.8 Find the radian measure of a central angle.6.9 Find the radius of a circle.6.10 Given an angle in standard position in a unit circle, determine the coordinate of its terminal side when one coordinates is given (with review if the Pythagorean Theorem).6.10.1 When the given coordinate is in the form of a decimal.6.10.2 When the given coordinate is in the form of a fraction.6.11 Given an angle in standard position in a unit circle, determine the coordinates of its terminal side when the angle is of the form 1800n+300, 1800n+600, 1800n+450 or 900n.6.11.1 When 00 ≤0≤36006.11.2 When 0≤0 or 0≥0 3600 (with review of co terminal angles)6.12 Find the six circular function of angles with special values.6.12.1 Using scientific calculator or table of trigonometric values.6.12.2 Find the angle when the value of circular is given.6.13 Describe the properties of the graph of sine, cosine, and tangent.6.13.1 With the equation in the form y=a sin bx, y=a tan bx (with changes on the amplitude and period).6.13.2 With equation in the form y=sin (x±h) ±k, y=cos (x±h) ±k, y=tan (x±h) ±k, (transformation).6.14 Find then the values of six trigonometric functions of 0(with review of the Pythagorean Theorem)6.14.1 Given 3 sides of a right triangle given two sides of the right triangle.6.14.2 Given the values of trigonometric function6.15 Solve simple trigonometric equations.6.16 Prove the trigonometric identities (with the review of factoring and operation on function).6.16.1 by simply complex expression in the terms of sine and cosine.6.17 Find the sum and difference of sine and cosine using formulas.6.17.1 Finding the sum and difference of sine.6.17.2 Finding the sum and differences of cosine.6.18 Apply the trigonometric function to solve problem involving right triangle.6.18.1. Given the right triangle with corresponding values6.18.2. Given word problems (including problems on angle of elevation depression)6.18.3. Given the word problems involving overlapping g triangles6.18.4. Given the word problems involving directions and bearing of a line6.19. Apply the law of sines to solve problem on oblique triangles6.19.1. When two angles and the sides are given6.19.2. When two sides and a non-included angle are given

6.20. Apply the law of cosine to solve problems on oblique triangles6.20.1 When two sides and the included angle in the triangle are given6.20.2. When three sides are given6.21. Define statistic, sample, population and explain the different sampling techniques6.22. Use the rules of summation to find the sums6.22.1. Express the sums of terms using the sum of summation notation6.22.3. Evaluate the terms in summation notation6.23. Organize a statistical data by constructing frequency distribution tables6.24. Find the measure of central tendency using ungrouped data6.24.1. Find the mean, median and mode of ungrouped data6.24.2. Solve word problems on the characteristic of a data using a mean median and mode6.25. Find the measures of central tendency using grouped data6.25.1. Find the mean grouped of data6.25.2. Find the median grouped of data6.25.3. Find the mode of grouped data6.26. calculate the difference measure of variability relative to given of data6.26.1. Calculate the range and standard deviation of ungrouped data6.26.2. Calculate the standard deviation of grouped data6.26.3. Solve word problems on the characteristic of the data using range and standard deviation6.27. From a given statistical data, analyze,