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Grade 11 – Foundation for College Mathematics Mathematics

# TOPIC TITLE
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
Objective: To find the solutions of quadratic equations presented as a product of factors
Objective: To solve quadratic equations requiring factorisation
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
Objective: To find the roots of a quadratic equation by using the quadratic formula
Objective: To solve problems which require finding the roots of a quadratic equation
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