| 1 |
Study Plan |
Study plan – Grade 11 – Foundation for College Mathematics |
| Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. |
| 2 |
Algebra – Products and factors |
Larger Expansions |
| Objective: To expand and simplify the product of a binomial and a trinomial |
| 3 |
Algebra – Products and factors |
Highest Common Factor |
| Objective: To factorise an expression by identifying and extracting the highest common factor |
| 4 |
Algebra – Products and factors |
Factors by Grouping |
| Objective: To factorise a four-term expression by grouping |
| 5 |
Algebra – Products and factors |
Difference of Two Squares |
| Objective: To factorise differences of two squares |
| 6 |
Algebra – Products and factors |
Common factor and the difference of two squares |
| Objective: On completion of the lesson the student will be aware of common factors and recognize the difference of two squares. |
| 7 |
Algebra – Products and factors |
Quadratic Trinomials (monic): Case 1 |
| Objective: On completion of the lesson the student will understand the factorization of quadratic trinomial equations with all terms positive. |
| 8 |
Algebra – Products and factors |
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. |
| 9 |
Algebra – Products and factors |
Quadratic Trinomials (monic): Case 3 |
| Objective: On completion of the lesson the student will have an increased knowledge on factorizing quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative. |
| 10 |
Algebra – Products and factors |
Quadratic Trinomials (monic): Case 4 |
| Objective: On completion of the lesson the student will understand how to factorize all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative. |
| 11 |
Algebra – Products and factors |
Factorisation of nonmonic quadratic trinomials |
| Objective: To factorise nonmonic quadratic trinomials using the ‘X’ method |
| 12 |
Algebra – Products and factors |
Factorisation of nonmonic quadratic trinomials: Moon method |
| Objective: To factorise nonmonic quadratic trinomials using the ‘Moon’ method |
| 13 |
Algebra – Products and factors |
Sum and Difference of Two Cubes |
| Objective: To factorise the sum and difference of two cubes |
| 14 |
Algebra – Products and factors |
Simplifying algebraic fractions |
| Objective: To simplify algebraic fractions by factorisation and cancellation |
| 15 |
Graphs part 1 |
The parabola: to describe properties of a parabola from its equation |
| Objective: To describe properties of a parabola from its equation and sketch the parabola |
| 16 |
Graphs part 1 |
Quadratic Polynomials of the form y = ax^2 + bx + c |
| Objective: To describe and sketch parabolas of the form y = x^2 + bx + c |
| 17 |
Graphs part 1 |
Graphing perfect squares: y=(a-x) squared |
| Objective: To describe and sketch parabolas of the form y = (x – a)^2 |
| 18 |
Graphs part 1 |
Graphing irrational roots |
| Objective: To determine the vertex (using -b/2a), and other derived properties, to sketch a parabola |
| 19 |
Graphs part 1 |
Solving Simultaneous Equations graphically |
| Objective: To solve simultaneous equations graphically |
| 20 |
Algebra – Quadratic equations |
Introduction to Quadratic Equations |
| Objective: To find the solutions of quadratic equations presented as a product of factors |
| 21 |
Algebra – Quadratic equations |
Solving Quadratic Equations with Factorisation |
| Objective: To solve quadratic equations requiring factorisation |
| 22 |
Algebra – Quadratic equations |
Solving Quadratic Equations |
| Objective: To solve quadratic equations that need to be changed into the form ax^2 + bx + c = 0 |
| 23 |
Algebra – Quadratic equations |
Completing the square |
| Objective: To complete an incomplete square |
| 24 |
Algebra – Quadratic equations |
Solving Quadratic Equations by Completing the Square |
| Objective: To solve quadratic equations by completing the square |
| 25 |
Algebra – Quadratic equations |
The Quadratic Formula |
| Objective: To find the roots of a quadratic equation by using the quadratic formula |
| 26 |
Algebra – Quadratic equations |
Problem solving with quadratic equations |
| Objective: To solve problems which require finding the roots of a quadratic equation |
| 27 |
Algebra – Quadratic equations |
Solving Simultaneous Quadratic Equations Graphically |
| Objective: To determine points of intersection of quadratic and linear equations |
| 28 |
Graphs part 2 |
Graphing complex polynomials: quadratics with no real roots |
| Objective: To graph quadratics that have no real roots, hence don’t cut the x-axis |
| 29 |
Uniform motion |
The Speed Formula |
| Objective: To calculate speed, distance or time using speed = distance/time |
| 30 |
Uniform motion |
Using Subscripted Variables |
| Objective: To use subscripted variables to solve motion problems |
| 31 |
Uniform motion |
Uniform Motion With Equal Distances |
| Objective: To solve motion problems where distances are equal |
| 32 |
Uniform motion |
Uniform Motion Adding the Distances |
| Objective: To solve motion problems where total distance travelled is given |
| 33 |
Uniform motion |
Uniform Motion With Unequal Distances or Time |
| Objective: To solve motion problems where either distance or time are different |
| 34 |
Uniform motion |
Uniform Motion Problems Where the Rate is Constant |
| Objective: To solve miscellaneous motion problems where the rate is constant |
| 35 |
Uniform motion |
Vertical Motion under gravity: Object Dropped from Rest |
| Objective: To calculate velocity, time and distance for vertically falling objects dropped from rest |
| 36 |
Uniform motion |
Vertical Motion under gravity: Initial Velocity not Zero |
| Objective: To calculate velocity, time and distance for vertical motion with initial velocity not zero |
| 37 |
Indices/Exponents |
Adding indices when multiplying terms with the same base |
| Objective: To add indices when multiplying powers that have the same base |
| 38 |
Indices/Exponents |
Subtracting indices when dividing terms with the same base |
| Objective: To subtract indices when dividing powers of the same base |
| 39 |
Indices/Exponents |
Multiplying indices when raising a power to a power |
| Objective: To multiply indices when raising a power to a power |
| 40 |
Indices/Exponents |
Multiplying indices when raising to more than one term |
| Objective: To raise power products to a power |
| 41 |
Indices/Exponents |
Terms raised to the power of zero |
| Objective: To evaluate expressions where quantities are raised to the power 0 |
| 42 |
Indices/Exponents |
Negative Indices |
| Objective: To evaluate or simplify expressions containing negative indices |
| 43 |
Indices/Exponents |
Fractional Indices |
| Objective: To evaluate or simplify expressions containing fractional indices |
| 44 |
Indices/Exponents |
Complex fractions as indices |
| Objective: To evaluate or simplify expressions containing complex fractional indices and radicals |
| 45 |
Logarithms |
Powers of 2 |
| Objective: To convert between logarithm statements and indice statements |
| 46 |
Graphs part 2 |
The Exponential Function |
| Objective: To graph exponential curves whose exponents are either positive or negative |
| 47 |
Series and sequences part 1 |
The Geometric Progression |
| Objective: To find the common ratio of a given geometric progression |
| 48 |
Series and sequences part 1 |
Finding the position of a term in a G.P. |
| Objective: To find the place of a term in a given geometric progression |
| 49 |
Series and sequences part 1 |
Given two terms of G.P. find the sequence |
| Objective: To find the first term given two terms of a geometric progression |
| 50 |
Series and sequences part 2 |
Geometric Means |
| Objective: To find geometric means of a and b and insert geometric means between 2 endpoints |
| 51 |
Series and sequences part 2 |
The sum to n terms of a G.P. |
| Objective: To find the sum of n terms of a sequence |
| 52 |
Series and sequences part 2 |
Sigma notation |
| Objective: To evaluate progressions using sigma notation |
| 53 |
Series and sequences part 2 |
Limiting Sum or Sum to Infinity |
| Objective: To find the limiting sum of a sequence |
| 54 |
Series and sequences part 2 |
Recurring Decimals and the Infinite G.P. |
| Objective: To express recurring decimals as a G.P. and to express the limiting sum as a fraction |
| 55 |
Series and sequences part 2 |
Compound Interest |
| Objective: To calculate the compound interest of an investment using A=P(1+r/100)^n |
| 56 |
Series and sequences part 2 |
Superannuation |
| Objective: To calculate the end value of adding a regular amount to a fund with stable interest paid over time |
| 57 |
Series and sequences part 2 |
Time Payments |
| Objective: To calculate the payments required to pay off a loan |
| 58 |
Space |
Recognise nets for prisms, pyramids, cubes and cones |
| Objective: To match a net with a solid and determine whether a given net forms a solid |
| 59 |
Space |
Viewing 3-D Shapes |
| Objective: To recognise what a solid looks like when viewed from a given direction |
| 60 |
Measurement – Advanced area |
Area of a Circle |
| Objective: To calculate the area of circles and sectors and to solve circle problems |
| 61 |
Measurement – Advanced area |
Area of Regular Polygons and Composite Figures |
| Objective: To calculate area of composite figures and solve problems using correct formulae |
| 62 |
Measurement – Advanced volume |
Finding the volume of prisms |
| Objective: To calculate the volume of prisms using V=Ah and solve volume problems |
| 63 |
Measurement – Advanced volume |
Volume of a Cylinder and Sphere |
| Objective: To solve problems and calculate volumes of cylinders and spheres and parts of each |
| 64 |
Measurement – Advanced volume |
Volume of Pyramids and Cones |
| Objective: To calculate the volumes of pyramids and cones |
| 65 |
Measurement – Advanced volume |
Composite Solids |
| Objective: To calculate the volume of composite figures using appropriate formulae |
| 66 |
Trigonometry part 1 |
Angles of Elevation and Depression |
| Objective: To identify and distinguish between angles of depression and elevation |
| 67 |
Trigonometry part 1 |
Trigonometric Ratios in Practical Situations |
| Objective: To solve problems involving bearings and angles of elevation and depression |
| 68 |
Trigonometry part 1 |
The Cosine Rule to find an unknown side [Case 1 SAS] |
| Objective: To complete the cosine rule to find a subject side for given triangles |
| 69 |
Trigonometry part 1 |
The Sine Rule to find an unknown side: Case 1 |
| Objective: To complete the cosine rule to find a subject angle for given triangles |
| 70 |
Trigonometry part 1 |
The Sine Rule: Finding a Side |
| Objective: To find an unknown side of a triangle using the sine rule |
| 71 |
Trigonometry part 1 |
The Sine Rule: Finding an Angle |
| Objective: To find an unknown angle of a triangle using the sine rule |
| 72 |
Graphs – Basic |
Column Graphs |
| Objective: To read and interpret column graphs |
| 73 |
Graphs – Basic |
Line Graphs |
| Objective: To read and interpret line graphs |
| 74 |
Graphs – Basic |
Pie and Bar Graphs |
| Objective: To read and interpret pie and bar graphs |
| 75 |
Statistics part 1 |
Frequency distribution table |
| Objective: To construct a frequency distribution table for raw data and to interpret the table |
| 76 |
Statistics part 1 |
Frequency histograms and polygons |
| Objective: To construct and interpret frequency histograms and polygons |
| 77 |
Statistics part 1 |
Relative Frequency |
| Objective: To extend the frequency distribution table to include a relative frequency column |
| 78 |
Statistics part 1 |
The Range |
| Objective: To determine the range of data in either raw form or in a frequency distribution table |
| 79 |
Statistics part 1 |
The Mode |
| Objective: To find the mode from raw data and from a frequency distribution table |
| 80 |
Statistics part 1 |
The Mean |
| Objective: To calculate means from raw data and from a frequency table using an fx column |
| 81 |
Statistics part 1 |
The Median |
| Objective: To determine the median of a set of raw scores |
| 82 |
Statistics part 1 |
Cumulative Frequency |
| Objective: To construct cumulative frequency columns, histograms and polygons |
| 83 |
Statistics part 1 |
Calculating the Mean from a Frequency Distribution |
| Objective: To determine averages (mean, median and mode) from cumulative frequency polygons |
| 84 |
Statistics part 2 |
Calculating mean, mode and median from grouped data |
| Objective: To identify class centres, get frequency counts and determine mean, mode and median values |
| 85 |
Statistics part 2 |
Using the Calculator for Statistics |
| Objective: To find a mean, using a data set or a frequency distribution table and calculator. |
| 86 |
Statistics part 2 |
Measures of Spread |
| Objective: To determine a range and use it in decision making |
| 87 |
Statistics part 2 |
Standard deviation applications |
| Objective: To find a standard deviation, using a data set or a frequency distribution table and calculator |
| 88 |
Statistics part 2 |
Applications of Standard Deviation |
| Objective: To use standard deviation as a measure of deviation from a mean |
| 89 |
Statistics part 2 |
The Normal Distribution |
| Objective: To use the standard deviation of a normal distribution to find a percentage of scores within ranges |
| 90 |
Statistics part 2 |
Measures of Spread: the interquartile range |
| Objective: To find the upper and lower quartiles and the interquartile range |
| 91 |
Statistics part 1 |
Stem and Leaf Plots along with Box and Whisker Plots |
| Objective: To derive statistics from data represented as stem & leaf or box & whisker plots |
| 92 |
Statistics part 1 |
The Scatter plot |
| Objective: To make a valid interpretation of data presented as a scatter plot |
| 93 |
Probability |
Simple events |
| Objective: To find the probability of events using sample space and event set (E) and P(E) = n(E)/n(S) |
| 94 |
Probability |
Rolling a pair of dice |
| Objective: To find the probability of selected events when two dice are rolled |
| 95 |
Probability |
Experimental probability |
| Objective: To find the experimental probabilities of an experimental trial |
| 96 |
Probability |
Experimental probability |
| Objective: To use tree diagrams to determine sample spaces and compound probabilities |
| 97 |
Exam |
Exam – Grade 11 – Foundation for College Mathematics |
| Objective: Exam |
