St Stithians College 11 Papers/St Stithians... · Web viewRead all questions carefully and pay attention to the mark allocation of each. Answer all questions on the question paper

November Examinations 2018

MATHEMATICS DEPARTMENT

GRADE 11 PAPER 1

Time: 3 hours Total: 150 marks

Examiner: Mr E. Stolk (BC) Moderator: Mr P. Statham

PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY:

1. This question paper consists of 28 pages. Please check that your question

paper is complete.

2. A separate green information sheet with formulae has been provided to you.

3. Read all questions carefully and pay attention to the mark allocation of each.

4. Answer all questions on the question paper in the spaces provided.

5. Clearly show ALL calculations, diagrams, graphs, etc. which you have used in

determining your answers.

6. Answers only will NOT necessarily be awarded full marks.

7. You may use an approved scientific calculator (non-programmable and non-

graphical), unless otherwise stated.

8. If necessary, round off your answers to TWO decimal places, unless stated

otherwise.

9. Diagrams are NOT necessarily drawn to scale.

10. Write neatly and legibly.

11. PLEASE WRITE YOUR NAME AND CIRCLE THE NAME OF YOUR

TEACHER ON THE BACK PAGE.

SECTION A

QUESTION 1:

Solve each of the following for , leaving your answer in surd form if necessary:

(a) (4)

(b) (5)

[9]

© ST STITHIANS COLLEGE MATHEMATICS DEPARTMENT Page 2 of 28

QUESTION 2:

(a) Simplify each of the following without using a calculator:

(1) (4)

(2) (4)


(b) If and , express in terms of and . (4)

and , express [12]

EXTRA WORKING SPACE:


QUESTION 3:

Given the sequence: 5 ; 11 ; 19 ; 29 ; …

(a) Determine the next two terms of the sequence. (1)

41 ; 55

(b) Determine the general formula that generates the sequence. (4)

(c) Which term will have a value of 181? (3)

(d) Using the sequence above, determine a formula for the first differencesof the terms. (2)

[10]


QUESTION 4:

(a) Ayanda’s uncle buys him a car for R200 000. It is expected to depreciate on the reducing balance method at a rate of 15% p.a.

(i) Ayanda will buy the car from his uncle at its book value in 5 years’ time. What will the car be worth in 5 years’ time? (2)

(ii) The cost of a new car is expected to increase at an inflation rate of 6,5% p.a. What will the cost of a new car be in 5 years’ time? (3)

(iii) Ayanda’s uncle deposits an amount into a savings account now so that he will have enough money to replace the car in 5 years’ time. The account earns interest of 11% p.a. compounded monthly. What amount does he deposit into the account if he uses the money from the sale of the old car towards the purchase of the new car?


(b) What is the nominal interest rate p.a. compounded quarterly if the effective interest rate is 9,5% p.a.?

[11]



QUESTION 5:

The diagram represents the graphs of and .Points and are the -intercepts of and point is the -intercept.The -intercept of is at point , and the -intercept is at point .The graphs intersect at points and as shown:

(a) Determine the length of . (4)


x

y

R

Q

T

P

gf

F

Z

A

C

L B

(b) Determine the coordinates of point . (5)

(c) Given that and with on and on ,

determine the length of . (4)

[13]


QUESTION 6:

Given the functions: and

(a) Write down the domain of . (1)

(b) Write down the range of . (1)

(c) How must the graph of be shifted so that it lies on top of . (2)

5 units to the left

2 units down

(d) Determine the equation of the line of symmetry of that has a positive gradient. (2)


(e) On the set of axes below, draw the graph of indicating clearly all asymptotes and intercepts with the axes. (4)

−6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10 11

−6

−5

−4

−3

−2

−1

1

2

3

4

5

6

x

y

[10]


QUESTION 7:

A group of 110 pupils were asked how they spend their leisure time. Three activities were surveyed – pupils who do some form of Arts and Culture (A&C), those who do some form of Sporting Activity (SpA) and those who Socialise with Friends (SwF).

The Venn diagram below represents the results of the survey:

(a) Determine the value of x . (2)

(b) How many pupils did some form of Sporting Activity and Socialised with Friends? (1)


n(S) = 110

2

SwF

SpAA&C

40

x + 8x

75

3

9

(c) Find the probability that a pupil chosen at random only did some form of Arts and Culture.

(d) Determine the probability that a pupil chosen at random enjoyed Socialising with Friends and did some form of Arts and Culture but did no Sporting Activity.

[5]


[70 marks]


SECTION B

QUESTION 8:

(a) Shown below is an image of the Gateway Arch in St Louis, Missouri. It could be superimposed onto a set of axes, where each unit would represent 1 metre in reality. The arch is 192m tall and the legs, which are in the same horizontal plane,

are 120m apart. Points and are the bases of the arch. Point is the turning point of the arch:

https://www.travelpulse.com/news/destinations/st-louis-gateway-arch-to-welcome-new-museum.html

Determine the coordinates of point C . (4)


B

C

A

THIS PAGE IS INTENTIONALLY BLANK


(b) The graph below represents the functions and .

The graph of has -intercepts at and and a -intercept

at . The graph of passes through the origin and the point :

(i) Determine the values of . (5)


f

x

y

f

g

C

BA

(ii) Calculate the values of . (4)

(iii) Write down the value(s) of for which . (3)

(iv) Write down the value(s) of for which will have no real roots. (4)

[20]


QUESTION 9:

(a) Study the following pattern:

12 3

4 5 67 8 9 10

(i) How many numbers are in row 100? (1)

100

(ii) What is the first number in row 100? (4)

(iii) Will row 100 have a middle term (like the 5 in row 3)? (1)

No, middle term only in odd rows.

(b) If the following sequence is quadratic, determine the value of :4 ; 9 ; ; 37 ; … (4)

[10]


QUESTION 10:

(a) Thabang invests a sum of money for 6 years. He earns interest at a rate of 10% p.a. compounded monthly for the first 2 years and 11,5% p.a. compounded quarterly for the remaining 4 years. After 3 years he deposits a further R2 500 into the account. His money grows to a total of R35 000 over the 6-year period. How much did Thabang invest initially? (8)

(b) What is the effective annual rate over a 4-year period if the nominal rate for the first 3 years is 8,5% p.a. compounded monthly and then 9,75% p.a. compounded daily for the last year?

[13]


T0 T1 T6T4T3T2 T5

QUESTION 11:

(a) Xia and Yvonne collect buttons. Xia only collects buttons with 2 holes and Yvonne only collects buttons with 4 holes. Xia has 10 more buttons than Yvonne. The total number of holes found in all their buttons is 110.

How many buttons do they have altogether? (4)

(b) If and , find one numerical value for . (4)

[8]


QUESTION 12:

(a) For which value(s) of will the equation have non-real (imaginary) roots? (5)

(b) Solve for if . (6)

[11]


QUESTION 13:

Given:

(a) Complete the square of the expression and write it in the form in terms of p. (3)

(b) Hence prove that for all values of . (2)

[5]


x

y

QUESTION 14:

(a) Matthew goes fishing for trout. The probability that he will catch a male trout is 0,47 if the temperature is below 15℃. If the temperature is above 15℃, the probability he will catch a male trout drops to 0,33. The weather forecast for Saturday says the probability of the temperature being below 15℃ is 20%. What is the probability that Matthew will catch a female trout on Saturday?(Assume he will catch a fish which will be either male or female)

(b) Given: , and .If are independent events, determine the value of . (5)


F

F

M

80%

20%

47%

53%

33%

67%

M

(c)

https://marketingd2d.com/flags-mall/super-flags/american-flags/usaflagsofallsizes

The American flag consists of thirteen equally-spaced horizontal red and white stripes, with a blue rectangle in the canton (the top left-hand corner) bearing 50 small white 5-pointed stars.

What is the probability that, if I randomly shine a laser pointer at the flag, I will be pointing at a spot that is within a red part of the flag?

(3)

[13]

[80 marks]


Blue Rectangle

White stripe

Red stripe







MARK RECORD SHEETFOR OFFICIAL USE ONLY

NAME OF LEARNER:

NAME OF TEACHER: KAUR MAGWEGWE SCHAERER JUDD

Algebra Sequences & Series Finance Functions Probability

1 / 9

2 / 12

3 / 10

4 / 11

5 / 13

6 / 10

7 / 5

8 / 20

9 / 10

10 / 13

11 / 8

12 / 11

13 / 5

14 / 13

TOTAL / 45 / 20 / 24 / 43 / 18

TOTAL / 150 %


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St Stithians College 11 Papers/St Stithians... · Web viewRead all questions carefully and pay attention to the mark allocation of each. Answer all questions on the question paper