MATHEMATICS PAPER 1 Grade 11 November 2016

[Pages:15]MATHEMATICS PAPER 1 Grade 11

November 2016

Examiner/s Moderator/s Marks Time IInstructions:

JS, CS, LP

LP, CS, JS, GK

150

3 hours

Answers to 1 dp unless otherwise stated. Circle the name of your teacher. Show all necessary working out.

NAME

Q1 Q6 Q11 Q16

Teacher: GK CSw LP JSt

Q2

Q3

Q4

Q5

Q7

Q8

Q9

Q10

Q12

Q13

Q14

Q15

/150

Grade 11 Examinations, November 2016

SECTION A 90 Marks

Question 1 [6 marks] Solve for x in terms of m: (a) 3x2 = m

(b) (mx + 1)(x ? m) = 0

(c) ? 2x < 4 ? 10m

Question 2 [19 marks] Solve for x: (a) ?3(3x + 1)(x ? 4) < 0

MATHEMATICS PAPER 1

(b) 2x x 1 1

Page 1 of 14

(2) (2) (2)

(3) (5)

Grade 11 Examinations, November 2016

(c)

1 2

4x

(d) 2x + 2 + 2x = 20

MATHEMATICS PAPER 1

(e) Solve for x and y: 2x ? y = 8 and x2 ? xy + y2 = 19

Page 2 of 14

(2)

(3)

(6)

Question 3 [7 marks]

(a) Simplify and write as a single fraction

3x1 3x

3k 12

k.3x 3x.22 k 2 16

(5)

Grade 11 Examinations, November 2016

(b)

Simplify

52x 1

5x 1

MATHEMATICS PAPER 1

Page 3 of 14

(2)

Question 4 [2 marks] If B = x 5 , determine the values of x for which:

x2

(a) B is undefined

(1)

(b) B is non-real

(1)

Question 5 [16 marks]

(a) Given the arithmetic series :

2 + 9 + 16 + . . . . . (to 251 terms).

(1) Write down the formula for the n th term in the series.

(2)

(2) Calculate the 251st term of the series.

(1)

(3) Express the series in sigma notation.

(1)

(4) Calculate the sum of the series.

(2)

Grade 11 Examinations, November 2016

MATHEMATICS PAPER 1

(5) How many terms in the series are divisible by 4?

(b)

In a converging geometric series S

40 3

and

T2

5 2

;

calculate the possible value(s) of the first term.

Page 4 of 14

(3)

(7)

Question 6 [10 marks]

Given the function fx 4.2x1 1

(a) State the equation of the asymptote.

(1)

(b) State the domain and range of the function.

(2)

(c) Determine the equation of gx if gx is formed when fx is reflected over the x-axis. (2)

(d) Determine the equation of hx if hx is formed when fx is shifted 2 units right and 3

units down.

(2)

Grade 11 Examinations, November 2016

MATHEMATICS PAPER 1

(e) In the space below, using your own axes, make a neat sketch graph of fx.

Show all intercepts and asymptotes.

Page 5 of 14

(3)

Question 7 [17 marks]

Sketched on the axis below are the functions fx and gx. A and B are the x-intercepts of the

functions. C is the common y-intercept of the two functions. D is one of the points of intersection of

the two functions. The point ( 3 ; 1,5) lies on fx

f

g

(a) State the equations of the asymptotes of fx.

(2)

Grade 11 Examinations, November 2016

(b) Determine the equation of fx.

MATHEMATICS PAPER 1

Page 6 of 14

(3)

(c) Determine the equation of the axis of symmetry with a positive gradient of fx.

(2)

(d) Hence determine the coordinates of A and C.

(3)

(e) Given that gx passes through the point of intersection of the asymptotes of fx, show

that gx 2x 3 .

(2)

Grade 11 Examinations, November 2016

(f) Determine the co-ordinates of D.

MATHEMATICS PAPER 1

Page 7 of 14

(5)

Question 8 [13 marks]

The graphs of fx x2 7x 8 and gx 3x 24 are sketched below.

The graphs intersect at B and C. A and B are the x-intercepts of f(x). S, T and R are on the same vertical straight line.

y

g S

C

A O

T

R

B

x

f

(a) Determine the length of AB.

(3)

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