Grade 12 Mathematics Paper 3 (LO1, LO3 & LO4 - Optional) Record Exam 2009 MEMO Page 1 of 3
Record Exam 2009
Grade 12Mathematics Paper 3 (LO1, LO3 & LO4 - Optional)
Date:Time: 2 hTotal: 100
MEMO
QUESTION 1
1.1.1(3)
1.1.2Geometric(1)
1.1.3(2)
1.2.1509(1)
1.2.2 and (3)[10]
QUESTION 2
2.1(3)
2.2 Not: positively skewed (R) median (21-30) = 24.5, median < mean(4) [7]
QUESTION 3
3.1 If the price was R190000 (mean + 1×standard deviation) then the percentile rank would be: 0.1+0.5+1.4+4.6+9.1+14.5+19.8+19.8+14.5 = 84.3% This means that 84% of the cars sold last month were sold for R190000 or less (4)
3.2 14.5+19.8+19.8+14.5=68.6% 68.6% of the cars were sold between R140000 and R190000 so Mr. Tladi was correct. (4) [8]
QUESTION 4
4.1 No, in total, but not necessarily individually(2)
4.2 Kabelo 400/5 = R80 (Nathan 800/20 = R40; Thabo 500/8 = R62.50)(2)
4.3 Average y-axis Bars 80, 40, 62.5(4) [8]
Average
spent (R)
K N T
QUESTION 5
5.1x-label y-labelpoints plotted clearly(4)
5.2r = 0.915Positive- very strong(3)
5.3straight line show dotted line at 87% - approximately 84%(3)
5.4(3)[13]
QUESTION 6
6.1 Number of events = 1 × 1 × 21 × 10 × 9 × 8 = 15120
Total number of choices = 21 × 21 × 21 × 10 × 10 × 10 = 9 261000
Probability (5)
6.2 (4)
6.3.1 Children: 7! Grandparents: 2! Parents: 6×1×4×1×2×1
number = 7!2!48 = 483840(5)
6.3.2 Children: 7! Men left/right: Grandparents: 1×1 Parents: 3×1×2×1×1×1
P = (7!6)2/7!2!48 = 1/4 (4)[18]
QUESTION 7:
7.1.1subtended by diameter A’s Δ =180°(4)
7.1.2 tan chord(2)
7.2.1opp A’s cyclic quad(2)
7.2.2ext A cyclic quad (2)[10]
QUESTION 8:
8.1(3)
8.2 KX = XB, KL//XD midpoint theorem. KX = XB and KL//XD BC = 2 BD(5)[8]
QUESTION 9:
9.1In ABDAFE: is common, subtended by diameters AC and BE 3rd angle ABD /// AFE (A,A,A) (4)
9.2 tan-chord vertical opposite (3)
9.3 & corresponding, FE//BC alternating, FE//BC tan-chord (6)
9.4 and BFE /// CBA(5)[18]