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MATATAG curriculum

Grade 10 Mathematics

46 learning competencies across 4 quarters, as the Department of Education curriculum guide prints them.

Quarter 1

Content standard

1. the laws of sines and the laws of cosines. 2. translations, reflections, and rotations, in the Cartesian plane. 3. quadratic inequalities in one variable and in two variables. 4. absolute value equations and inequalities in one variable and their graphs.

Performance standard

find sides and angles in oblique triangles using the laws of sines and the laws of cosines. describe translations, reflections, and rotations in the Cartesian plane. solve and graph the solutions of quadratic inequalities in one variable and in two variables. solve absolute value equations in one variable and absolute value inequalities in one variable, and graph the solutions.

Learning competencies (12)

  • MATH-G10-Q1-01

    apply laws of sines in solving oblique triangles, including ambiguous cases.

    Measurement and Geometry

  • MATH-G10-Q1-02

    apply laws of cosines in solving oblique triangles.

    Measurement and Geometry

  • MATH-G10-Q1-03

    describe the position of points in the Cartesian plane.

    Measurement and Geometry

  • MATH-G10-Q1-04

    describe translations, reflections, and rotations, in the Cartesian plane using coordinates.

    Measurement and Geometry

  • MATH-G10-Q1-05

    solve problems involving laws of sines and cosines, including bearings.

    Measurement and Geometry

  • MATH-G10-Q1-06

    illustrate on the number line quadratic inequalities in one variable.

    Number and Algebra

  • MATH-G10-Q1-07

    solve quadratic inequalities in one variable and expresses solutions in various notations.

    Number and Algebra

  • MATH-G10-Q1-08

    solve problems involving quadratic inequalities in one variable.

    Number and Algebra

  • MATH-G10-Q1-09

    solve quadratic inequalities in two variables.

    Number and Algebra

  • MATH-G10-Q1-10

    determine the region of solutions of a linear or quadratic inequality in two variables.

    Number and Algebra

  • MATH-G10-Q1-11

    solve absolute value equations in one variable and express solutions in various notations)

    Number and Algebra

  • MATH-G10-Q1-12

    solve absolute value inequalities in one variable and express solutions in various notations

    Number and Algebra

Quarter 2

Content standard

1. box-and-whisker plots, and cumulative frequency histograms and polygons. 2. quartiles, deciles, and percentiles; interquartile range, and outliers. 3. radical expressions. 4. the roots of a quadratic equation. 5. quadratic functions. 6. equations reducible to quadratic equations.

Performance standard

construct and interpret box-and-whisker plots, and cumulative frequency histograms and polygons. calculate quartiles, deciles, and percentiles; interquartile range, and outliers. simplify, and perform operations, involving radical expressions. determine the nature of roots of a quadratic equation. determine the equation of a quadratic function. solve equations reducible to quadratic equations and radical equations.

Learning competencies (13)

  • MATH-G10-Q2-01

    illustrate measures of position (quartiles, deciles, and percentiles).

    Data and Probability

  • MATH-G10-Q2-02

    construct and interpret box-and-whisker plots and cumulative frequency histograms and polygons.

    Data and Probability

  • MATH-G10-Q2-03

    calculate a specified measure of position, interquartile range, and outliers, from ungrouped data.

    Data and Probability

  • MATH-G10-Q2-04

    calculate the percentile rank of a given score from ungrouped data.

    Data and Probability

  • MATH-G10-Q2-05

    draw conclusions from statistical data using the measures of position.

    Data and Probability

  • MATH-G10-Q2-06

    illustrate the laws of rational non-integral exponents.

    Number and Algebra

  • MATH-G10-Q2-07

    simplify radical expressions.

    Number and Algebra

  • MATH-G10-Q2-08

    perform operations involving radical expressions, including rationalizing the denominator.

    Number and Algebra

  • MATH-G10-Q2-09

    determine the nature of roots of a quadratic equation using the discriminant.

    Number and Algebra

  • MATH-G10-Q2-10

    determine the equation of a quadratic function given:

    • a. a table of values
    • b. its graph, and
    • c. its zeros.

    Number and Algebra

  • MATH-G10-Q2-11

    solve equations reducible to quadratic equations, e.g., 𝑥⁴ − 5𝑥² + 4 = 0

    Number and Algebra

  • MATH-G10-Q2-12

    solve problems involving quadratic functions.

    Number and Algebra

  • MATH-G10-Q2-13

    solve radical equations, including equations reducible to linear or quadratic equations.

    Number and Algebra

Quarter 3

Content standard

1. equation of a circle and the graph of a circle. 2. evaluation of statistical reports. 3. union and intersection of events, dependent and independent events, and complementary events.

Performance standard

transform the equation of a circle from center-radius form to general form, and vice versa, and determine the center and radius from a given equation. graph a circle from a given equation of the circle. evaluate statistical reports. calculate probabilities in relation to union and intersection of events; dependent and independent events; and complementary events.

Learning competencies (9)

  • MATH-G10-Q3-01

    transform the equation of a circle from center-radius form to general form, and vice versa.

    Number and Algebra

  • MATH-G10-Q3-02

    determine the center and the radius of a circle from a given equation.

    Number and Algebra

  • MATH-G10-Q3-03

    sketch the graph of a circle given its equation.

    Number and Algebra

  • MATH-G10-Q3-04

    find the equation of a circle from given conditions, e.g., given two points as the endpoints of a diameter.

    Number and Algebra

  • MATH-G10-Q3-05

    solve problems involving geometric figures on the Cartesian plane.

    Number and Algebra

  • MATH-G10-Q3-06

    evaluate statistical reports by linking claims to displays, statistics, and representative data.

    Data and Probability

  • MATH-G10-Q3-07

    illustrate mutually exclusive events and non-mutually exclusive events.

    Data and Probability

  • MATH-G10-Q3-08

    identify complementary events.

    Data and Probability

  • MATH-G10-Q3-09

    solve probability problems involving:

    • a. union and intersection of events, including mutually and non-mutually exclusive events;
    • b. dependent and independent events, including conditional probability where the solution is limited to the use of contingency tables or Venn diagrams; and
    • c. complementary events.

    Data and Probability

Quarter 4

Content standard

1. simple interest, compound interest, and depreciation. 2. central angles; inscribed angles; and angles and lengths formed by intersecting chords, secants, and tangents of a circle. 3. sectors and segments of a circle, and their areas.

Performance standard

calculate compound interest and depreciation. apply properties and relationships of central angles, inscribed angles, chords, secants, and tangents of circles. define sectors and segments of a circle, and find their areas.

Learning competencies (12)

  • MATH-G10-Q4-01

    explore inductively the relationship between simple interest and compound interest.

    Number and Algebra

  • MATH-G10-Q4-02

    calculate compound interest by repeated applications of simple interest.

    Number and Algebra

  • MATH-G10-Q4-03

    solve problems involving compound interest by repeated applications of simple interest.

    Number and Algebra

  • MATH-G10-Q4-04

    explain inductively the formulas for compound interest and depreciation.

    Number and Algebra

  • MATH-G10-Q4-05

    explore inductively the differences in the amount of compound interest obtained on amounts of money invested:

    • a. annually,
    • b. quarterly, and
    • c. monthly.

    Number and Algebra

  • MATH-G10-Q4-06

    solve real-life problems involving:

    • a. compound interest, and
    • b. depreciation.

    Number and Algebra

  • MATH-G10-Q4-07

    establish properties and relationships for central angles, inscribed angles, secants, and tangents, of a circle.

    Measurement and Geometry

  • MATH-G10-Q4-08

    solve problems involving:

    • a. central angles,
    • b. inscribed angles,
    • c. angles formed by two intersecting chords,
    • d. angles formed by two secants intersecting outside the circle,
    • e. angles formed by two intersecting tangents, and
    • f. angles formed by intersecting secant and tangent.

    Measurement and Geometry

  • MATH-G10-Q4-09

    establish properties and relationships for chords, secants, and tangents.

    Measurement and Geometry

  • MATH-G10-Q4-10

    solve problems involving lengths of:

    • a. intersecting chords,
    • b. two secant segments intersecting outside a circle, and
    • c. two intersecting tangent segments.

    Measurement and Geometry

  • MATH-G10-Q4-11

    define sectors and segments of a circle and finds their areas.

    Measurement and Geometry

  • MATH-G10-Q4-12

    solve problems involving area of a sector of a circle, segment of a circle, and shaded regions in other figures that involve sectors or segments.

    Measurement and Geometry

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