A seventeen years old learner is expected to be able to:
- Understand limiting process intuitively.
- Evaluate the limit algebraically. Discover the steps to find the one sided limits. Apply factoring and simplifying the function to find the limit.
- Identify the limits from the graph of the function or tables of data
- Recognize the asymptotes from the graph.
- Discover the asymptotic behavior in terms of limits involving infinity
- Understand continuity and identify the different types of discontinuities.
- Investigate the continuity in terms of limits
- Understand derivative graphically, numerically and analytically. Recognize that slope of the curve is derivative of the function at certain point.
- Interpret derivative as instantaneous rate of change
- Discover derivative of a function using limit.
- Discover the relation between differentiability and continuity
- Knowledge of derivatives of basic functions including power, exponential, logarithmic, trigonometric and inverse trigonometric function.
- Investigate the derivative rule for sum, product and quotient of functions. Recognize chain rule and implicit differentiation
- Understand that second derivative is the derivate of derivate of a function. Discover that higher order derivatives can be evaluated using the concept of second derivative.
- Apply Rolle’s Theorem and mean value theorem to find the point c between the interval. Apply L’hopital’s rule to find the limit.
- Apply derivative in finding the equation for tangent and normal line of the curve.
- Equate the derivative to zero and solve to find the critical points. Use the critical points to identify the absolute extreme of the function
- Use second derivative to find the concavity of the curve.
- Interpret derivative as a rate of change in varied applied contexts including velocity, speed, acceleration, maximizing or minimizing cost or area etc.
- Recognize integration as the opposite of the derivative
- Discover the integration rules using derivative rule.
- Apply fundamental theorem of calculus to find definite integral
- Apply integral to find the equation of the curve from the tangent line or velocity from acceleration etc.
- Apply definite integral to investigate the area under or between curves and volume of revolution.
- Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.
- Sketch the complex number on argand diagram.
- Perform multiplication and division in complex number by converting into trigonometric form. Use De Moivre’s rule to find the higher powers. Find the nth root of the complex number in trigonometric form.
- Differentiate between polar coordinates and rectangular coordinates. Use modulus and argument to convert polar equation into rectangular equation and vice versa.
- Represent data on the coordinate plane (bar chart, histograms, and frequency polygon) or as pie chart. .
- Apply statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (standard deviation) of two or more different data sets. Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
- Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).
- Recognize that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
- Recognize the conditional probability of A given B as P(A and B)/P(B), and deduce independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
- Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.
- Discover the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.
- Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model. Discover that in mutually exclusive event P(A and B) will be zero.
- Apply fundamental counting principle, permutations and combinations to compute probabilities of compound events and solve problems.