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Grade 12 – Foundations for College Mathematics Mathematics

# TOPIC TITLE
1 Study Plan Study plan – Grade 12 – Foundations for College Mathematics
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.
2 Indices/Exponents Adding indices when multiplying terms with the same base
Objective: To add indices when multiplying powers that have the same base
3 Indices/Exponents Subtracting indices when dividing terms with the same base
Objective: To subtract indices when dividing powers of the same base
4 Indices/Exponents Multiplying indices when raising a power to a power
Objective: To multiply indices when raising a power to a power
5 Indices/Exponents Multiplying indices when raising to more than one term
Objective: To raise power products to a power
6 Indices/Exponents Terms raised to the power of zero
Objective: To evaluate expressions where quantities are raised to the power 0
7 Indices/Exponents Negative Indices
Objective: To evaluate or simplify expressions containing negative indices
8 Indices/Exponents Fractional Indices
Objective: To evaluate or simplify expressions containing fractional indices
9 Indices/Exponents Complex fractions as indices
Objective: To evaluate or simplify expressions containing complex fractional indices and radicals
10 Graphs part 2 The Exponential Function
Objective: To graph exponential curves whose exponents are either positive or negative
11 Series and sequences part 2 Compound Interest
Objective: To calculate the compound interest of an investment using A=P(1+r/100)^n
12 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
13 Series and sequences part 2 Time Payments
Objective: To calculate the payments required to pay off a loan
14 Measurement – Capacity The relationship between the common units of capacity: the litre and the millilitre
Objective: To convert L to mL and vice versa using 1000 mL = 1 L
15 Measurement – Capacity Converting between volume and capacity using kiloliters and liters
Objective: To know the formal units of measurement for volume and capacity for bigger objects
16 Measurement – Capacity Estimate, measure and compare the capacity of containers
Objective: To understand estimation and a way to go about it
17 Measurement – Capacity Converting between volume and capacity using milliliters and liters
Objective: To solve capacity problems involving mixed dimensional units
18 Measurement – Mass The Kilogram
Objective: To recognise which of two (or more) objects has the greater mass
19 Measurement – Mass The Gram
Objective: To calculate net mass in grams and solve shopping problems involving mass
20 Measurement – Advanced area Area of a Trapezium
Objective: To calculate the area of trapezia using A=(h/2)(a+b)
21 Measurement – Advanced area Area of a Rhombus
Objective: To calculate the area of a rhombus using diagonal products
22 Measurement – Advanced area Area of a Circle
Objective: To calculate the area of circles and sectors and to solve circle problems
23 Measurement – Advanced area Area of Regular Polygons and Composite Figures
Objective: To calculate area of composite figures and solve problems using correct formulae
24 Measurement – Advanced volume Finding the volume of prisms
Objective: To calculate the volume of prisms using V=Ah and solve volume problems
25 Measurement – Advanced volume Composite Solids
Objective: To calculate the volume of composite figures using appropriate formulae
26 Surface area Surface Area of a Cube/Rectangular Prism
Objective: To calculate the surface area of cubes and rectangular prisms
27 Surface area Surface Area of a Triangular/Trapezoidal Prism
Objective: To calculate the surface area of triangular and trapezoidal prisms
28 Surface area Surface Area of a Cylinder and Sphere
Objective: To calculate the surface area of cylinders and spheres
29 Surface area Surface Area of Pyramids
Objective: To calculate the surface area of pyramids
30 Surface area Surface Area of Composite Solids
Objective: To calculate the surface area of composite solids
31 Space Measure and classify angles
Objective: To classify and measure angles and calculate angles in a triangle
32 Trigonometry part 1 Trigonometric Ratios
Objective: To name the sides of a right-angled triangle and to determine the trig ratios of an angle
33 Trigonometry part 1 Using the Calculator
Objective: To determine trigonometric ratios using a calculator
34 Trigonometry part 1 Using the Trigonometric Ratios to find unknown length [Case 1 Sin]
Objective: To use the sine ratio to calculate the opposite side of a right-angled triangle
35 Trigonometry part 1 Using the Trigonometric Ratios to find unknown length [Case 2 Cosine]
Objective: To use the cosine ratio to calculate the adjacent side of a right-angle triangle
36 Trigonometry part 1 Using the Trigonometric Ratios to find unknown length [Case 3 Tangent Ratio]
Objective: To use the tangent ratio to calculate the opposite side of a right-angled triangle
37 Trigonometry part 1 Unknown in the Denominator [Case 4]
Objective: To use trigonometry to find sides of a right-angled triangle and the Unknown in denominator
38 Trigonometry part 1 Bearings: The Compass
Objective: To change from true bearings to compass bearings and vice versa
39 Trigonometry part 1 Angles of Elevation and Depression
Objective: To identify and distinguish between angles of depression and elevation
40 Trigonometry part 1 Trigonometric Ratios in Practical Situations
Objective: To solve problems involving bearings and angles of elevation and depression
41 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
42 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
43 Trigonometry part 1 The Sine Rule: Finding a Side
Objective: To find an unknown side of a triangle using the sine rule
44 Trigonometry part 1 The Sine Rule: Finding an Angle
Objective: To find an unknown angle of a triangle using the sine rule
45 Trigonometry part 2 Angles of Any Magnitude
Objective: To assign angles to quadrants and to find trigonometric values for angles
46 Trigonometry part 2 Trigonometric ratios of 0°, 90°, 180°, 270° and 360°
Objective: To find trigonometric ratios of 0, 90, 180, 270 and 360 degrees
47 Statistics part 1 Frequency distribution table
Objective: To construct a frequency distribution table for raw data and to interpret the table
48 Statistics part 1 Frequency histograms and polygons
Objective: To construct and interpret frequency histograms and polygons
49 Statistics part 1 Relative Frequency
Objective: To extend the frequency distribution table to include a relative frequency column
50 Statistics part 1 The Range
Objective: To determine the range of data in either raw form or in a frequency distribution table
51 Statistics part 1 The Mode
Objective: To find the mode from raw data and from a frequency distribution table
52 Statistics part 1 The Mean
Objective: To calculate means from raw data and from a frequency table using an fx column
53 Statistics part 1 The Median
Objective: To determine the median of a set of raw scores
54 Statistics part 1 Cumulative Frequency
Objective: To construct cumulative frequency columns, histograms and polygons
55 Statistics part 1 Calculating the Mean from a Frequency Distribution
Objective: To determine averages (mean, median and mode) from cumulative frequency polygons
56 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
57 Statistics part 2 Using the Calculator for Statistics
Objective: To find a mean, using a data set or a frequency distribution table and calculator.
58 Statistics part 2 Measures of Spread
Objective: To determine a range and use it in decision making
59 Statistics part 2 Standard deviation applications
Objective: To find a standard deviation, using a data set or a frequency distribution table and calculator
60 Statistics part 2 Measures of Spread: the interquartile range
Objective: To find the upper and lower quartiles and the interquartile range
61 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
62 Statistics part 1 The Scatter plot
Objective: To make a valid interpretation of data presented as a scatter plot
63 Exam Exam – Grade 12 – Foundations for College Mathematics
Objective: Exam