Achievement Standards for Mathematical Methods T Courses Technology, its selection and appropriate use, is an integral part of all the following descriptors. A student who achieves the A grade typically, A student who achieves the B grade typically, A student who achieves the C grade typically, A student who achieves the D grade typically, A student who achieves the E grade typically, Knowledge demonstrates very high level of proficiency in the use of mathematical facts, techniques and formulae demonstrates high level of proficiency in the use of mathematical facts, techniques and formulae demonstrates some proficiency in the use of mathematical facts, techniques and formulae studied demonstrates limited use of mathematical facts, techniques and formulae studied Demonstrates very limited use of mathematical facts, techniques and formulae studied Application Selects, extends and applies appropriate mathematical modelling and problem solving techniques Selects and applies appropriate mathematical modelling and problem solving techniques. With direction, applies a mathematical model. Solves most problems Solves some mathematical problems independently Solves some mathematical problems with guidance Reasoning Uses mathematical reasoning to develop logical arguments in support of conclusions, results and/or decisions; justifies procedures Uses mathematical reasoning to develop logical arguments in support of conclusions, results and/or decisions Uses some mathematical reasoning to develop logical arguments Uses some mathematical reasoning to develop simple logical arguments Uses limited reasoning to justify Communication Is consistently accurate and appropriate in presentation of mathematical ideas in different contexts Is generally accurate and appropriate in presentation of mathematical ideas in different contexts Presents mathematical ideas in different contexts Presents some mathematical ideas Presents some mathematical ideas with guidance
t1 = a, tn+1 = rtn for n ≥ 1 and where r is the constant ratio Partial sums of a sequence (Series) The sequence of partial sums of a sequence t1,…, ts, … is defined by Sn = t1 + …+ tn Partial sum of an arithmetic sequence (Arithmetic series) The partial sum Sn of the first n terms of an arithmetic sequence with first term a and common difference d. a, a + d, a + 2d,……, a + (n – 1)d,… is Sn = (a + tn) = (2a + (n – 1)d) where tn is the nth term of the sequence. The partial sums form a sequence with Sn+1 = Sn + tn and S1 = t1 Partial sums of a geometric sequence (Geometric series) The partial sum Sn of the first n terms of a geometric sequence with first term a and common ratio r, a, ar, ar2,……, arn – 1,… is Sn = , r ≠ 1. The partial sums form a sequence with Sn+1 = Sn + tn and S1 = t1. Introduction to differential calculus Gradient (Slope) The gradient of the straight line passing through points and is the ratio . Slope is a synonym for gradient. Secant A secant of the graph of a function is the straight line passing through two points on the graph. The line segment between the two points is called a chord. Tangent line The tangent line (or simply the tangent) to a curve at a given point can be described intuitively as the straight line that "just touches" the curve at that point. At where the tangent meets the curve the curve meet, the curve has "the same direction" as the tangent line. In this sense it is the best straight-line approximation to the curve at the point . Linearity property of the derivative The linearity property of the derivative is summarized by the equations: for any constant and Local and global maximum and minimum