Scope and Sequence Senior Mathematics
Introduction to Advanced Mathematics (Level 2)
1133
To review properties of angles and triangles Learn definitions of the six trigonometric functions
for acute angles. Find the values of the trigonometric functions using a graphing calculator
Establish and use basic trigonometric identities Show that the values of the trigonometric
functions depend only on the angle Solve problems involving right triangles Begin a study
notebook for trigonometry Study the eternal nature of God and His plan for mankind
Memorize Revelation 1:8; 2 Corinthians 4:18 and Hebrews 5:9
SM 3
Applications of Trigonometric Ratios: The study of directions and bearings, and contour lines
and maps, using geometrical facts, angles of elevation and depression, directions and
bearings, contour lines and maps, and average slope
SM 5 Univariate Data: Working with data - variables, the collection of data, categorical data
and numerical data.
SM 6 Indices and Logarithmic Functions: incorporating the index form. Tarional indices,
exponential functions, and indicial equations
SM 8 Data descriptors: The study of the mean of grouped and ungrouped data. The advantages
and disadvantages of the use of the mean and its standard deviation. The study of the
median, the mode and skewed data.
SM 9 Relations and functions: define and describe functions and relations. Define table values,
domain, rand and odd and even functions. Sketch graphs to test and to model different
functions and relationships. Find the permissible x and y values for a variety of functions.
SM 10 Periodic functions: the radian measure. Geometrical definitions of the tangent function,
specific periodic functions, reciprocal trigonometric functions and special angles.
1122
Arithmetic Sequences and Series: Arithmetic Sequences; The nth Term; Arithmetic Means;
Arithmetic Series; Summation Notation. Geometric Sequences and Series: Geometric
Sequences; The nth Term; Geometric Means; Geometric Series; Infinite Geometric Series.
Open Sentences in One Variable: Algebraic Terminology; Adding Polynomials; Subtracting
Polynomials; Combining Polynomials; Solving the Open Sentence; Inequalities.
1123
Linear Equations: Graphing Ordered Pairs; Graphing Linear Equations; Slope Formula; Slope
of the Line Ax + By =C. Graphs and Linear Equations: Graphing by Using the Slope Method;
Point-Slope Equation; Two-Point Equation; Slope-Intercept Equation; Parallel and
Perpendicular Lines.
Systems of Linear Equations: Classifications of Two Linear Equations; Solving Simultaneous
Equations by Using the Linear Combinations Method; Inconsistent and Dependent Systems of
Equations.
1124
Reviewing Polynomials: Laws of Exponents; Product or Quotient of a Monomial and a
Polynomial; Product of Two Binomials; Squares of Binomials; Product of a Binomial and a
Trinomial. Factoring: Integers and Monomial Factoring; Factoring Monomials from
Polynomials; Reviewing Trinomial Factoring; Group Factoring; Factoring the Difference of
Squares; Factoring Perfect Square Trinomials; Factoring the Sum and Difference of two
Cubes. Solving Algebraic Expressions: Fractional Exponents; Equalities; Inequalities; Division
of Polynomials
1125
Fractions and Operations: Negative Exponents; Rational Numbers; Simplifying Fractional
Expressions; Multiplication of Fractions; Division of Fractions; Least Common Denominator;
Adding, and Subtracting Fractions. Fractions and Equations: Complex Fractions; Synthetic
Division; Fractional Equations; Fractional Inequalities; Applied Problems. Rational Numbers as
Decimals: Decimals; Scientific Notation; Approximations
1126
First-Degree Functions: Relations; Functions; Inverse of a Relation; Linear Equations;
Relations and Slope; Linear Inequalities; Direct Variation. Second-Degree Functions: Quadratic
Functions; Axis of Symmetry and the Vertex; Minimum and Maximum Points; Completing the
Square; Axis of Symmetry and the Vertex from y = a (x - h )2 + k. Further Considerations
Level 3 Mathematics with Calculus
1127
Radicals: Square Roots; Roots of Radicals; Rational and Irrational Numbers. Operating with Radicals:
Products and Quotients; Sums and Differences; Simplification of Radicals; Rationalizing Denominators;
Radicals and Exponents; Radicals and Equations. Radicals Within Radicals; Complex Numbers: Pure
Imaginary Numbers; imaginary and Real Numbers; Complex Conjugates and Division
1128
Quadratic Equations: Solving Quadratics by Factoring; Fractional Equations and Quadratics; Solving
Quadratics by Completing the Square. Quadratic Solutions: The Quadratic Formula; The Discriminant and
Solutions; Quadratic Coefficients. Polynomial Functions: Evaluating, Polynomial Functions; Synthetic
Substitution; Remainder Theorem; Factor Theorem
1129
Quadratic Relations: Distance Formula; Circles: Centre at Origin; Circles: Centre at (h, k). The Parabola,
Ellipse, and Hyperbola: Parabolas: Vertex at Origin; Sketching the Graph of a Parabola; Parabolas: Vertex at (h,
k); Quadratic Equations in Parabolic Form; Ellipses: Centre at Origin; Hyperbolas: Centre at Origin. Quadratic
Systems: Quadratic-Linear Systems; Quadratic-Quadratic Systems
1130
Exponential Functions: Review of Laws of Exponents; Irrational Exponents; Inverse of y = ax. Logarithms:
Meaning of a Logarithm; Logarithmic Properties; Common Logarithms; Mantissa and Characteristic; Interpolation;
Antilogarithms. Computations and Logarithms: Computations; Logarithmic Equations
SM 11
Introduction to differentiation: focusing on tangents and secants, limits and continuity, theorems and points of
discontinuity. The derivative of a function and differentiation from first principles. Differentiation rules relating
to a constant, a power, a constant times a function, the sum of two functions and the difference of two
functions.
SM 12 Sketching Graphs, Students will work with linear functions including simultaneous equations with practical
examples, modeling linear functions including break even analysis, polynomial functions including quadric functions
and modeling them, higher order simultaneous equations.
A study of cubic functions will be covered, including their modeling, quartic functions, and rational functions,
including rectangular hyperbola. The unit concludes with inverse functions and their graphs.
SM 13
Trigonometric Graphs, This unit covers trigonometric functions including angles in different quadrants;
trigonometric functions with a negative angle including sine, cosine and tangent. Section 2 covers graphing
trigonometric functions, the unit circle and the tangent, changing the parameters including dilation, translation, and
reflection. The student will also sketch trigonometric functions, including phase shift, identifying functions, domain
and range and applications of this work.
SM 14 Applications of Derivatives, This unit involves interpretation and application of the derivative both algebraically and
geometrically. Particle motion in a straight line is examined with attention given to position, velocity and
acceleration. Application of differentiation and of rates of change is treated. Students study the equation of the
tangent, the equation of the normal and the angle between two curves. The unit also covers increasing and
decreasing functions, the nature of stationary values including the second derivative test, greatest and least values
and points of inflection and applications of the derivative.
SM 15 Differentiation Rules, Relevant concepts of continuity limits are dealt with including convergent and divergent
sequences, the limit of a function, including limit theorems, the derivative of a function including polynomials, rules
for differentiation including the second derivative, and piecewise-defined functions. The chain rule, product rule,
and quotient rule assist with further differentiation of more complex functions.
SM 16 Antidifferentiation, The student will study antidifferentiation including indefinite integrals and the family of curves,
integrating the sum of difference of functions, definite integrals including properties of definite integrals, areas
bounded by a curve including the mid-point and trapezoid rules, and the calculation of area including the area
between a curve and the y-axis.
SM 19 Trigonometric, Exponential and Logarithmic Functions This unit deals with trigonometric functions including special
angles and trigonometric identities, trigonometric derivatives including product and quotient rule and applications of
trigonometric derivatives, derivatives of exponential functions, and the exponential function. The student also deals
with indices and logarithms, derivatives of logarithmic functions, the integration of trigonometric and exponential
functions and the integration of 1/x.
SM 20 Applications of the Integral, Attention will be given to areas between two curves, volumes of revolution
including rotations about the x and y axis, rates of changes including total changes from given rates of
changes and related rates and differential equations. Attention will also be given to growth and decay and
applications of exponential derivatives.
Level 3 Mathematics with Statistics
1127
Radicals: Square Roots; Roots of Radicals; Rational and Irrational Numbers. Operating with Radicals:
Products and Quotients; Sums and Differences; Simplification of Radicals; Rationalizing Denominators;
Radicals and Exponents; Radicals and Equations. Radicals Within Radicals; Complex Numbers: Pure
Imaginary Numbers; imaginary and Real Numbers; Complex Conjugates and Division
1128
Quadratic Equations: Solving Quadratics by Factoring; Fractional Equations and Quadratics; Solving
Quadratics by Completing the Square. Quadratic Solutions: The Quadratic Formula; The Discriminant and
Solutions; Quadratic Coefficients. Polynomial Functions: Evaluating, Polynomial Functions; Synthetic
Substitution; Remainder Theorem; Factor Theorem
1129
Quadratic Relations: Distance Formula; Circles: Centre at Origin; Circles: Centre at (h, k). The Parabola,
Ellipse, and Hyperbola: Parabolas: Vertex at Origin; Sketching the Graph of a Parabola; Parabolas: Vertex at (h,
k); Quadratic Equations in Parabolic Form; Ellipses: Centre at Origin; Hyperbolas: Centre at Origin. Quadratic
Systems: Quadratic-Linear Systems; Quadratic-Quadratic Systems
1130
Exponential Functions: Review of Laws of Exponents; Irrational Exponents; Inverse of y = ax. Logarithms:
Meaning of a Logarithm; Logarithmic Properties; Common Logarithms; Mantissa and Characteristic; Interpolation;
Antilogarithms. Computations and Logarithms: Computations; Logarithmic Equations
SM 11
Introduction to differentiation: focusing on tangents and secants, limits and continuity, theorems and points of
discontinuity. The derivative of a function and differentiation from first principles. Differentiation rules relating
to a constant, a power, a constant times a function, the sum of two functions and the difference of two
functions.
SM 12 Sketching Graphs, Students will work with linear functions including simultaneous equations with practical
examples, modeling linear functions including break even analysis, polynomial functions including quadric functions
and modeling them, higher order simultaneous equations.
A study of cubic functions will be covered, including their modeling, quartic functions, and rational functions,
including rectangular hyperbola. The unit concludes with inverse functions and their graphs.
SM 13
Trigonometric Graphs, This unit covers trigonometric functions including angles in different quadrants;
trigonometric functions with a negative angle including sine, cosine and tangent. Section 2 covers graphing
trigonometric functions, the unit circle and the tangent, changing the parameters including dilation, translation, and
reflection. The student will also sketch trigonometric functions, including phase shift, identifying functions, domain
and range and applications of this work.
SM 17 Probability, This unit examines the introduction to set notation and probability theory, the probability of an event,
developing sample spaces including lattice and tree diagrams, complementary and mutually exclusive events, and
the addition law of probability. The student will also study independent events, the multiplication law of probability,
and conditional probability.
SM 18 Discrete Probability Distributions, Students will focus on random variables including a review of probability,
probability distribution of discrete random variables, graphing probability distributions, expected values including
commercial ones, and expected value theorems including variance and standard deviation. Focus will also be on
the binomial probability distribution, parameters and their effects, and expected values and standard deviation.
SM 21 The Normal Distribution, This study incorporates continuous probability distributions, the normal distribution
including the properties of the normal distribution curve, probabilities less than 0.5, applications, solving the
impossible and confidence limits.
SM 22 Hypothesis Testing, This final unit deals with identifying a hypothesis, the statistical hypothesis, testing the null
hypothesis and the sign test. In the testing of a hypothesis the student will deal with acceptable level of error,
levels of significance and binomial distribution. Confidence intervals and upper and lower confidence limits are
also treated.