Year 11 – 9: Models of Growth Mathematics – Northern Territory (NT)
NT Year 11 – 9: Models of Growth Mathematics
| # | TOPIC | TITLE | |
|---|---|---|---|
| 1 | Study Plan | Study plan – Year 11 – 9: Models of Growth | |
| Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. | |||
| 2 | Coordinate Geometry-gradient | Gradient | |
| Objective: On completion of the lesson the student will be able to calculate the gradient of a line given its inclination, or angle to the positive direction of the x-axis; or its rise and run. | |||
| 3 | Coordinate Geometry-gradient | Gradient formula. | |
| Objective: On completion of the lesson the student will be able to calculate the gradient of a line given any two points on the line and also be capable of checking whether 3 or more points lie on the same line and what an unknown point will make to parallel lines. | |||
| 4 | Coordinate Geometry-straight line | The straight line. | |
| Objective: On completion of the lesson the student will be able to draw a line which is parallel to either axis and comment on its gradient, where that gradient exists. | |||
| 5 | Coordinate Geometry-slope, etc. | Lines through the origin. | |
| Objective: On completion of the lesson the student will be able to draw a line which passes through the origin of the form y=mx and comment on its gradient compared to the gradients of other lines through the origin and use the information to solve problems. | |||
| 6 | Coordinate Geometry-equation of line | General form of a line and the x and y Intercepts. | |
| Objective: On completion of the lesson the student will be able to change the equation of a straight line from the form, written as y=mx+c, into the general form and vice versa. | |||
| 7 | Coordinate Geometry-intercept | Slope intercept form of a line. | |
| Objective: On completion of the lesson the student will be able to find the slope and intercept given the equation and given the slope and intercept, derive the equation. | |||
| 8 | Coordinate Geometry-point slope | Point slope form of a line | |
| Objective: On completion of the lesson the student will understand how to derive the equation of a straight line given the gradient and a point on the line. | |||
| 9 | Co-ordinate Geometry-Two point formula | Two point formula: equation of a line which joins a pair of points. | |
| Objective: On completion of the lesson the student will be able to calculate the equation of a line given any two named points on the line. | |||
| 10 | Statistics | Scatter Diagrams | |
| Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these. | |||
| 11 | Logarithms-Power of 2 | Powers of 2. | |
| Objective: On completion of the lesson the student should be able to convert between logarithmic statements and index statements to the power of 2. | |||
| 12 | Logarithms-Equations and logs | Equations of type log x to the base 3 = 4. | |
| Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the number from which the logarithm evolves. | |||
| 13 | Logarithms-Equations and logs | Equations of type log 32 to the base x = 5. | |
| Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the base from which the number came. | |||
| 14 | Logarithms-Log laws | Laws of logarithms. | |
| Objective: On completion of the lesson the student will be familiar with 5 logarithm laws. | |||
| 15 | Logarithms-Log laws expansion | Using the log laws to expand logarithmic expressions. | |
| Objective: On completion of the lesson the student will be able to use the log laws to expand logarithmic expressions. | |||
| 16 | Logarithms-Log laws simplifying | Using the log laws to simplify expressions involving logarithms. | |
| Objective: On completion of the lesson the student will be able to simplify logarithmic expressions using the log laws. | |||
| 17 | Logarithms-Log laws numbers | Using the log laws to find the logarithms of numbers. | |
| Objective: On completion of the lesson the student will have an enhanced understanding of the use of the log laws and be able to do more applications with numerical examples. | |||
| 18 | Logarithms-Equations and logs | Equations involving logarithms. | |
| Objective: On completion of the lesson the student will be able to solve equations with log terms. | |||
| 19 | Logarithms-Logs to solve equations | Using logarithms to solve equations. | |
| Objective: On completion of the lesson the student will be able to use logarithms to solve index equations with the assistance of a calculator. | |||
| 20 | Logarithms-Change base formula | Change of base formula | |
| Objective: On completion of the lesson the student will have seen the change of base formula for logarithms and be capable of using it to change the logarithm of one base to another base. | |||
| 21 | Logarithms-Graph-log curve | The graph of the logarithmic curve | |
| Objective: On completion of the lesson the student will be able to draw a logarithmic curve to a given base and know the general properties of log curves. | |||
| 22 | Logarithms-Log curves | Working with log curves. | |
| Objective: On completion of the lesson the student will be able to solve problems with log curves | |||
| 23 | Exponential function | The exponential function. | |
| Objective: On completion of the lesson the student will be able to graph any equation in the form y equals a to the power x, where a is any positive real number apart from 1. | |||
| 24 | Log functions | Logarithmic functions. | |
| Objective: On completion of this lesson the student will be able to define basic logarithmic functions and describe the relationship between logarithms and exponents including graph logarithmic functions. The student will understand the relationship between logarit | |||
| 25 | Sequences and Series | General sequences. | |
| Objective: On completion of the lesson the student will be able to work out a formula from a given number pattern and then be able to find particular terms of that sequence using the formula. | |||
| 26 | Sequences and Series | Finding Tn given Sn. | |
| Objective: On completion of the lesson the student will understand the concept that the sum of n terms of a series minus the sum of n minus one terms will yield the nth term. | |||
| 27 | Arithmetic Progression | The arithmetic progression | |
| Objective: On completion of the lesson the student will be able to test if a given sequence is an Arithmetic Progression or not and be capable of finding a formula for the nth term, find any term in the A.P. and to solve problems involving these concepts. | |||
| 28 | Arithmetic Progression | Finding the position of a term in an A.P. | |
| Objective: On completion of the lesson the student will be able to solve many problems involving finding terms of an Arithmetic Progression. | |||
| 29 | Arithmetic Progression | Given two terms of A.P., find the sequence. | |
| Objective: On completion of the lesson the student will be able to find any term of an Arithmetic Progression when given two terms | |||
| 30 | Arithmetic Progression | Arithmetic means | |
| Objective: On completion of the lesson the student will be able to make an arithmetic progression between two given terms. This could involve finding one, two, or even larger number of arithmetic means. | |||
| 31 | Arithmetic Progression | The sum to n terms of an A.P. | |
| Objective: On completion of the lesson the student will understand the formulas for the sum of an Arithmetic Progression and how to use them in solving problems. | |||
| 32 | Geometric Progression | The geometric progression. | |
| Objective: On completion of the lesson the student will be able to test if a given sequence is a Geometric Progression or not and be capable of finding a formula for the nth term, find any term in the G.P. and to solve problems involving these concepts. | |||
| 33 | Geometric Progression | Finding the position of a term in a G.P. | |
| Objective: On completion of the lesson the student will understand how to find terms in a geometric progression and how to apply it different types of problems. | |||
| 34 | Geometric Progression | Given two terms of G.P., find the sequence. | |
| Objective: On completion of this lesson the student will be able to solve all problems involving finding the common ratio of a Geometric Progression. | |||
| 35 | Sequences and Series-Geometric means | Geometric means. | |
| Objective: On completion of the lesson the student will be able to make a geometric progression between two given terms. This could involve finding one, two, or even larger number of geometric means. | |||
| 36 | Sequences and Series-Sum of gp | The sum to n terms of a G.P. | |
| Objective: On completion of the lesson the student will understand the formulas and how to use them to solve problems in summing terms of a Geometric Progression (G.P). | |||
| 37 | Sequences and Series-Sigma notation | Sigma notation | |
| Objective: On completion of the G.P. lesson the student will be familiar with the sigma notation and how it operates. | |||
| 38 | Sequences and Series-Sum-infinity | Limiting sum or sum to infinity. | |
| Objective: On completion of the lesson the student will have learnt the formula for the limiting sum of a G.P., the conditions for it to exist and how to apply it to particular problems. | |||
| 39 | Sequences and Series-Recurring decimal infinity | Recurring decimals and the infinite G.P. | |
| Objective: On completion of the G.P. lesson the student will have understood how to convert any recurring decimal to a rational number. | |||
| 40 | Sequences and Series-Compound interest | Compound interest | |
| Objective: On completion of the G.P. lesson the student will understand the compound interest formula and how to use it and adjust the values of r and n, if required, for different compounding periods. | |||
| 41 | Sequences and Series-Superannuation | Superannuation. | |
| Objective: On completion of the lesson the student will understand the method of finding the accumulated amount of a superannuation investment using the sum formula for a G.P. | |||
| 42 | Sequences and Series-Time payments | Time payments. | |
| Objective: On completion of the lesson the student will have examined examples carefully and be capable of setting out the long method of calculating a regular payment for a reducible interest loan. | |||
| 43 | Sequences and Series | Applications of arithmetic sequences | |
| Objective: On completion of the lesson the student will be capable of problems involving practical situations with arithmetic series. | |||
| 44 | Exam | Exam – Year 11 – 9: Models of Growth | |
| Objective: Exam | |||
| # | TOPIC | TITLE | |
|---|---|---|---|
| 1 | Study Plan | Study plan – Year 11 – 10: Quadratic and other Polynomials | |
| Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. | |||
| 2 | Factors by grouping | Factors by grouping. | |
| Objective: On completion of the lesson the student will be able to complete the process given just two factors for the whole expression. | |||
| 3 | Difference of 2 squares | Difference of two squares | |
| Objective: On completion of the lesson the student understand the difference of two squares and be capable of recognising the factors. | |||
| 4 | Common fact and diff | Common factor and the difference of two squares | |
| Objective: On completion of the lesson the student will be aware of common factors and recognise the difference of two squares. | |||
| 5 | Quadratic trinomials | Quadratic trinomials [monic] – Case 1. | |
| Objective: On completion of the lesson the student will understand the factorisation of quadratic trinomial equations with all terms positive. | |||
| 6 | Factorising quads | Factorising quadratic trinomials [monic] – Case 2. | |
| Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative. | |||
| 7 | Factorising quads | Factorising quadratic trinomials [monic] – Case 3. | |
| Objective: On completion of the lesson the student will have an increased knowledge on factorising quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative. | |||
| 8 | Factorising quads | Factorising quadratic trinomials [monic] – Case 4. | |
| Objective: On completion of the lesson the student will understand how to factorise all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative. | |||
| 9 | Factorising quads | Factorisation of non-monic quadratic trinomials | |
| Objective: On completion of the lesson the student will be capable of factorising any quadratic trinomial. | |||
| 10 | Factorising quads | Factorisation of non-monic quadratic trinomials – moon method | |
| Objective: On completion of the lesson the student know two methods for factorisation of quadratic trinomials including the cross method. | |||
| 11 | Surds | Binomial expansions | |
| Objective: On completion of the lesson the student will be able to expand and simplify the squares of binomial sums and differences involving surds. | |||
| 12 | Surds | Conjugate binomials with surds | |
| Objective: On completion of the lesson the student will be able to expand and simplify conjugate binomial expressions involving surds. | |||
| 13 | Surds | Rationalising the denominator | |
| Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves surds. | |||
| 14 | Surds | Rationalising binomial denominators | |
| Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves binomial expressions. | |||
| 15 | Quadratic equations | Introduction to quadratic equations. | |
| Objective: On completion of the lesson the student will understand simple quadratic equations. | |||
| 16 | Quadratic equations | Quadratic equations with factorisation. | |
| Objective: On completion of the lesson the student will be able to find both roots of a quadratic equation by factorising. | |||
| 17 | Quadratic equations | Solving quadratic equations. | |
| Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations. | |||
| 18 | Quadratic equations | Completing the square | |
| Objective: On completion of the lesson the student will understand the process of completing the square. | |||
| 19 | Quadratic equations | Solving quadratic equations by completing the square | |
| Objective: On completion of the lesson the student will understand the reasoning behind completing the square. | |||
| 20 | Quadratic equations | The quadratic formula | |
| Objective: On completion of the lesson the student will be familiar with the quadratic formula. | |||
| 21 | Quadratic equations | Problem solving with quadratic equations | |
| Objective: On completion of the lesson the student will be able to express a problem as a quadratic equation and then solve it. | |||
| 22 | Quadratic equations | Solving simultaneous quadratic equations graphically | |
| Objective: On completion of the lesson the student will better understand why quadratic equations have two solutions and will be capable of solving quadratic equations and problems graphically.. | |||
| 23 | Geometry-parabola | The parabola: to describe properties of a parabola from its equation | |
| Objective: On completion of the lesson the student will be able to predict the general shape and important features of a parabola and then graph the parabola to check the predictions. | |||
| 24 | Functions and graphs | Quadratic polynomials of the form y = ax. + bx + c. | |
| Objective: On completion of the lesson the student will be able to predict the general shape of a parabola and verify the predictions by sketching the parabola. The student will also be introduced to the discriminant and the axis. | |||
| 25 | Functions and graphs | Graphing perfect squares: y=(a-x) squared | |
| Objective: On completion of the lesson the student will be able to analyse a curve and then check their work by graphing the curve. | |||
| 26 | Graphing roots | Graphing irrational roots | |
| Objective: On completion of the lesson the student will be able to solve any polynomial which has real roots, whether they are rational or irrational. | |||
| 27 | Coordinate geometry | Solve by graphing | |
| Objective: On completion of the lesson students will use the slope intercept form of a line to create graphs and find points of intersection. | |||
| 28 | Graphing-polynomials | Graphing complex polynomials: quadratics with no real roots | |
| Objective: On completion of the lesson the student will be able to determine whether a quadratic has real or complex roots and then graph it. | |||
| 29 | Sum/diff 2 cubes | Sum and difference of two cubes. | |
| Objective: On completion of the lesson the student will be cognisant of the sum and difference of 2 cubes and be capable of factorising them. | |||
| 30 | Graphing-cubic curves | Graphing cubic curves | |
| Objective: On completion of this lesson the student will be able to graph a cubic given its equation or derive the equation of a cubic given its graph or other relevant information. | |||
| 31 | Logarithms-Complex numbers | Imaginary numbers and standard form | |
| Objective: On completion of the lesson the student will use the a+bi form of complex numbers for addition and subtraction. | |||
| 32 | Logarithms-Complex numbers | Complex numbers – multiplication and division | |
| Objective: On completion of the lesson the student will use the a+bi form of complex numbers for multiplication and division. | |||
| 33 | Logarithms-Complex numbers | Plotting complex number and graphical representation | |
| Objective: On completion of the lesson the student will use the argand diagram to assist in the addition and subtraction of complex numbers. | |||
| 34 | Algebra-polynomials | Introduction to polynomials | |
| Objective: On completion of the lesson the student will understand all the terminology associated with polynomials and be able to judge if any algebraic expression is a polynomial or not. | |||
| 35 | Algebra-polynomials | The sum, difference and product of two polynomials. | |
| Objective: On completion of the lesson the student will be able to add subtract and multiply polynomials and find the degrees of the answers. | |||
| 36 | Algebra-polynomials | Polynomials and long division. | |
| Objective: On completion of the lesson the student will understand the long division process with polynomials. | |||
| 37 | Remainder theorem | The remainder theorem. | |
| Objective: On completion of the lesson the student will understand how the remainder theorem works and how it can be applied. | |||
| 38 | Remainder theorem | More on remainder theorem | |
| Objective: On completion of the lesson the student will understand the remainder theorem and how it can be applied to solve some interesting questions on finding unknown coefficients of polynomials. | |||
| 39 | Factor theorem | The factor theorem | |
| Objective: On completion of the lesson the student will be able to use the factor theorem and determine if a term in the form of x minus a is a factor of a given polynomial. | |||
| 40 | Factor theorem | More on the factor theorem | |
| Objective: On completion of the lesson the student will fully understand the factor theorem and how it can be applied to solve some questions on finding unknown coefficients of polynomials. | |||
| 41 | Factor theorem | Complete factorisations using the factor theorem | |
| Objective: On completion of the lesson the student will be able to factorise polynomials of a higher degree than 2 and to find their zeros. | |||
| 42 | Polynomial equations | Polynomial equations | |
| Objective: On completion of the lesson the student will be capable of solving polynomial equations given in different forms. | |||
| 43 | Graphs, polynomials | Graphs of polynomials | |
| Objective: On completion of the lesson the student will understand how to graph polynomials using the zeros of polynomials, the y intercepts and the direction of the curves. | |||
| 44 | Roots quad equations | Sum and product of roots of quadratic equations | |
| Objective: On completion of the lesson the student will understand the formulas for the sum and product of roots of quadratic polynomials and how to use them. The student will understand how to form a quadratic equation given its roots. | |||
| 45 | Roots quad equations | Sum and product of roots of cubic and quartic equations | |
| Objective: On completion of the lesson the student will be able to do problems on the sum and products of roots of cubic and quartic equations. | |||
| 46 | Approx roots | Methods of approximating roots | |
| Objective: On completion of the lesson the student will be capable of finding approximate roots of polynomial equations using half the interval method. The student will be able to make a number of applications of this rule within the one question. | |||
| 47 | Newton’s approx | Newton’s method of approximation | |
| Objective: On completion of the lesson the student will be able to use Newton’s method in finding approximate roots of polynomial equations and be capable of more than one application of this method. | |||
| 48 | Exam | Exam – Year 11 – 10: Quadratic and other Polynomials | |
| Objective: Exam | |||
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