2016
REA’S NOTES
GRADE 12 FINAL EXAM
3 HOURS
150 MARKS
Table of Contents
Statistics.......................................................................................................................................................................................................1
Analytical Geometry ..............................................................................................................................................................................6
Trigonometry ............................................................................................................................................................................................9
Euclidean Geometry and Measurement .................................................................................................................................... 14
NB: Euclidean Geometry Formal Proofs .............................................................................................................................. 27
NB & not on formula sheet
[MATHEMATICS
PAPER II]
Study Notes
, Statistics
Grade 11 Revision
Best Fit Curves
Relating Two Measures
use a scatter plot
Positive Correlation Negative Correlation
Correlation
Strong
Correlation
Weak
No Correlation
points which do not fit line of best fit are called outliers
the point must be on line of best fit
there should be on average the same number of points below line as above
best fit curve can be straight line, quadratic, exponential
r is the correlation factor, can be number or percentage
Straight Line (2: ) & Exponential (6: ): Calculator Options
regression coefficient A
regression coefficient B
correlation coefficient r
estimated value of x
estimated value of y
Quadratic (3: ): Calculator Options
regression coefficient A
regression coefficient B
coefficient of x2
estimated value of x
estimated value of y
1 Statistics | Mathematics Paper II | Rea’s Notes
, Univariate Numerical Data
Ungrouped/Discreet data
ungrouped data working with single variables or frequencies of single variables
Measures of central tendency
for normal data:
mean average
for frequency tables:
mode most common; most popular
Dispersion
range
interquartile range (box in box and whisker)
semi interquartile range
Ways of displaying data
frequency diagrams raw data tally frequency
0
1
stem & leaf plot ascending
2
3
bar graphs discrete quantitative data spaces between columns
histograms continuous data intervals – joined
pie charts similar to bar graphs pictorially
uses midpoints of intervals
frequency polygons based on histogram grounded 1 interval before & 1 interval after
Five Point Summary / Box and Whisker Plot
min minimum value smallest/lowest value in range
25% of values between min & Q1
Q1 lower quartile found in position
25% of values between Q1 & M
M median found in position
25% of values between M & Q3
Q3 upper quartile found in position
25% of values between Q3 & max
max maximum value largest/highest value in range
Skewed and Symmetrical Data
it is correct/right to be happy/positive
symmetrical data is balanced on either side of median
data spread more to right of median
skewed to right / positively skewed median is near start of data set
for B&W: right box is fatter
data spread more to left of median
skewed to left / negatively skewed median is near end of data set
for B&W: left box is fatter
2 Statistics | Mathematics Paper II | Rea’s Notes
REA’S NOTES
GRADE 12 FINAL EXAM
3 HOURS
150 MARKS
Table of Contents
Statistics.......................................................................................................................................................................................................1
Analytical Geometry ..............................................................................................................................................................................6
Trigonometry ............................................................................................................................................................................................9
Euclidean Geometry and Measurement .................................................................................................................................... 14
NB: Euclidean Geometry Formal Proofs .............................................................................................................................. 27
NB & not on formula sheet
[MATHEMATICS
PAPER II]
Study Notes
, Statistics
Grade 11 Revision
Best Fit Curves
Relating Two Measures
use a scatter plot
Positive Correlation Negative Correlation
Correlation
Strong
Correlation
Weak
No Correlation
points which do not fit line of best fit are called outliers
the point must be on line of best fit
there should be on average the same number of points below line as above
best fit curve can be straight line, quadratic, exponential
r is the correlation factor, can be number or percentage
Straight Line (2: ) & Exponential (6: ): Calculator Options
regression coefficient A
regression coefficient B
correlation coefficient r
estimated value of x
estimated value of y
Quadratic (3: ): Calculator Options
regression coefficient A
regression coefficient B
coefficient of x2
estimated value of x
estimated value of y
1 Statistics | Mathematics Paper II | Rea’s Notes
, Univariate Numerical Data
Ungrouped/Discreet data
ungrouped data working with single variables or frequencies of single variables
Measures of central tendency
for normal data:
mean average
for frequency tables:
mode most common; most popular
Dispersion
range
interquartile range (box in box and whisker)
semi interquartile range
Ways of displaying data
frequency diagrams raw data tally frequency
0
1
stem & leaf plot ascending
2
3
bar graphs discrete quantitative data spaces between columns
histograms continuous data intervals – joined
pie charts similar to bar graphs pictorially
uses midpoints of intervals
frequency polygons based on histogram grounded 1 interval before & 1 interval after
Five Point Summary / Box and Whisker Plot
min minimum value smallest/lowest value in range
25% of values between min & Q1
Q1 lower quartile found in position
25% of values between Q1 & M
M median found in position
25% of values between M & Q3
Q3 upper quartile found in position
25% of values between Q3 & max
max maximum value largest/highest value in range
Skewed and Symmetrical Data
it is correct/right to be happy/positive
symmetrical data is balanced on either side of median
data spread more to right of median
skewed to right / positively skewed median is near start of data set
for B&W: right box is fatter
data spread more to left of median
skewed to left / negatively skewed median is near end of data set
for B&W: left box is fatter
2 Statistics | Mathematics Paper II | Rea’s Notes
