| 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 |
