GRADE 12 MATHEMATICS PAPER 1 MEMO

FRIDAY 29TH AUGUST 2014

TOTAL : 150 MARKS

QUESTION 1

1.1.1

ü

ü

or ü (3)

1.1.2

ü

ü

ü or ü (4)

1.1.3

ü

ü -2 5/2 üü (4)

1.1.4

Let

ü

ü

or ü

or ü

No solution ü

ü (6)

1.2

ü

Subs into

ü

ü

ü

or ü

or ü (6)

1.3

ü

ü (2)

1.4.1

ü

ü

(2)

1.4.2

ü

But

ü (2)

[29]

QUESTION 2

2.1 ü (1)

2.2 ü (1)

2.3 ; ; ; …

ü

ü (2)

2.4

ü

ü

ü

ü

OR (4)

2.5 ü

ü

or

But

ü

OR

ü

ü

or

But

ü (3)

2.6

ü (1)

[12]

QUESTION 3

3.1 ü

ü

ü

ü

(4)

3.2 ü

ü

ü

When ü ,

Smallest ü (5)

3.3

ü

ü

ü (3)

3.4 ü

ü

Length of rectangle ü

OR

üü

ü

Length of rectangle (3)

[15]

QUESTION 4

4.1 üü

Subs B

ü

ü

(4)

4.2 üü OR (2)

4.3 F üü (2)

[8]

QUESTION 5

since and

ü y-intercept positive

ü TP above x-axis ü TP right of y-axis ü min TP and shape

[4]

QUESTION 6

and

6.1 Subs into

ü

ü

(2)

6.2 üü (2)

6.3

ü

ü (2)

6.4

ü x-interecpt ü shape – increasing ü one other point (3)

6.5 OR (1)

6.6

üü (2)

6.7

ü

ü ; (2)

[14]

QUESTION 7

7.1 üü ü

ü

...

years ü (5)

7.2.1 ü

ü (2)

7.2.2 ü

ü (2)

7.2.3 ü

ü

ü

ü

ü (5)

[14]

QUESTION 8

8.1

ü

ü

ü

ü

ü (5)

8.2

ü

ü (2)

8.3

ü

Subs

ü

ü (3)

8.4 and

ü

ü (parallel tangents)

ü

ü

or ü (5)

[15]

QUESTION 9

and

9.1 P

P

(2)

9.2 P P

P

or P

P

(5)

9.3 P

P

P

or or P

Subs into

P

(5)

9.4 P (1)

9.5 P or P (2)

[15]

QUESTION 10

10.1 ü

ü

ü (3)

10.2 Area PQRS ü

Area PQRS

Area PQRS (1)

10.3 üü

ü

ü

ü (5)

[9]

QUESTION 11

11.1 P(A or B) = P(A) + P(B)

0,81 = P(A) + 2P(A) ü

0,81 = 3P(A)

P(A) = 0,27 ü

P(B) = 2(0,27)

P(B) = 0,54 ü (3)

11.2.1

ü first tier üüü second tier (4)

11.2.2

ü (1)

11.2.3 üü

ü (3)

[11]

QUESTION 12

12.1 ü (1)

12.2 ü (1)

12.3 ü OR ü (2) [4]