# Grade 12 – Foundations for College Mathematics – Canada

### 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 |