Summary Maths Paper 2 Notes

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