Grade 12 Paper 2 June 2014 Memorandum

Question 11.1.1

TRUE 1

1.1.2

False (SD = 6,51) 1

1.1.3

False 1

1.2.1

False: Data is skewed to the left 1

1.2.2

False: Median is 15 1

1.2.3

False: Q1−1,5×IQR=10−1,5×8 = −2

2

1.3.1

40 1

1.3.2

Median = 30 mins 1

1.3.3

(40−28)/40×100=30%Or (40−27)/40×100=32,5%

2

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2.1 negative linear correlation for bothor A decrease in carb or calorie intake results in an increase in weight loss(NOTE this is NOT and inversely proportion relationship)

2

2.2 y = 213,353−2,566x (note answer must be to 3 dec places)

3

2.3 r = −0,8499=−0,850 12.4 1000 = −5,6426x +1631,5

x =111,916kg2

2.5 No – a person would not be able to lose 111,91kg/6 = 18,65kg on average per month

2

2.6 Low Carb diet is more reliableThe correlation coefficient is strong and negative compared to the other which is weak and negative

2

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Question 33.1.1

ABCD is a parallelogram with adjacent sides equal and therefore it is a rhombusOR show diagonals are perpendicular

4

3.1.2 D (4; 6) 23.1.3

5

3.2.1 M = (2; −1 ) 23.2.2 ∴m(perpendicular bisector) =

4

3.2.3 E(4; k) A(−1; 1)B(6; 4)&

4

[21]

Question 4

4.1.1 3

4.1.2 4

4.1.3

3

4.2.1 2

4.2.2 3

4.2.3 3

[18]

Question 55.1.1 15.1.2 2

5.1.3 3

5.2 6

5.3.1 5

5.3.2 Undefined if 3

[20]

Question 66.1 a = −1 and b = 2 2

6.2 3

6.3 4

6.4 2[11]

Question 77.1

or

4

7.2

6

[10]

Question 8

8.1 DEC = E2 = x tan chord thm (2 marks each S/R)

EDC = D2 = x angles opp equal sides (EC=DC)

AED = E1 = x alternate to D2 AB // DC

BCD = C1+2 = x ext angle E1 of cyclic quad DEBC = int

opp

A = x corresponding to CDF AB // DC

10

8.2 B = 180°− x opp angle cyclic quad

D1+2=180°− x angles or str line

A = C1+2 = x proved above∴ 2 pairs of opposite angles of quadrilateral equal∴ ABCD is a parallelogram

OR

FCD = C1+2 = x proved but these are alternate angles ∴ BC // AD

And AB // DC ( given)∴ 2 pairs of opposite sides of quadrilateral parallel∴ ABCD is a parallelogram

3

[13]

Question 99.1 3

9.2

4

9.3

3

[10]

Question 1010.1

6

10.2

10.2.1

7

10.2.2

3[16]

Question 11

11.1 Draw OT AB ∴ OT bisects AB (radius perpendicular to chord, bisects chord)

or

3

11.2

Area of the shaded region : Area of triangle

5

[8]