S T S T I T H I A N S C O L L E G E

D e p a r t m e n t s o f M a t h e m a t i c s

GRADE 11

END-OF-YEAR EXAMINATION – PAPER 1(COMMON PAPER)

DATE:November 2016

TIME:3 hours

TOPICS:Probability, Algebra & Equations,

Finance, Functions, Patterns

TOTAL MARKS:150

EXAMINER:Mr. M Ancillotti

MODERATOR:Mr. P Statham

MEMO

SECTION A

QUESTION 1: [18]

1.1. Solve for in each of the following equations and inequalities:

1.1.1.

(3)

1.1.2.

(5)

1.1.3.

(4)

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1.2. Solve for x and y in the following equations:

(6)

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QUESTION 2: [24]

2.1. If it is given that ; Determine a value of k for which the value of x will be:

2.1.1. Rational and unequal (1)

2.1.2. Irrational and unequal (1)

2.1.3. Rational and equal (1)

2.1.4. Non-real (1)

2.2. Given that For which value(s) of k will the equation have equal roots? (5)

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2.3. Simplify the following expression:

(3)

2.4. Solve for x in each of the following equations:

2.4.1.

(4)

2.4.2.

(5)

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2.5. Show that can be written as (3)

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QUESTION 3: [6]

In a small town, 70% of the population received an anti-Ebola injection and 77% of thepopulation did not contract Ebola later that year. 54% of the population who received the injection did not develop Ebola.

Consider the following geometric diagram (contingency table) illustrating the above information:

3.1. Complete the diagram / table by calculating the values of a to d. (2)

3.2. Determine, using suitable calculations, whether “Receiving an anti-Ebolainjection” and “NOT contracting Ebola” are independent events. (4)

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INJECTION NO INJECTION

NO EBOLA 54 23 77

EBOLA 16 7 23

70 30 100

QUESTION 4: [10]

4.1. There are 360 learners in a school. 160 learners play Netball, 200 learners playHockey and 40 play both sports.

4.1.1. Draw a Venn diagram to represent this information. (3)

4.1.2. Calculate the probability that a learner chosen at random plays Hockeyor Netball. (1)

4.1.3. Calculate the probability that a learner chosen at random plays only oneof the sports. (1)

4.2. Using a tree diagram or otherwise, determine the probability that Tracey calls fora taxi and it arrives on time. (5)

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40

Netball

Hockey

120 (160-40) 160 (200-40)

40 (360-120-40-160)

QUESTION 5: [14]

5.

5.1. Given the function

5.1.1. Determine the y-intercept of . (2)

5.1.2. Determine the turning point of . (2)

5.2. Consider the graph of sketched below:

On the diagram of the graph given on your ANSWER SHEET, sketch accurate graphs of each of the following functions and label each graph clearly:

5.2.1. (2)

5.2.2. (2)

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5.3. The line with the equation intersects the graph of at two points, where x = 1 and x = 1.

Determine the values of a and b. (6)

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SECTION B

QUESTION 6: [7]

The graphs of and are sketched.

6.6.1. Determine the range of . (2)

6.2. On the diagram of the graphs given on your ANSWER SHEET, show the valueof x for which . Label the x-value using the letter P. (1)

6.3. If , determine the value of x. (2)

6.4. Determine the value of k for which has 3 different real roots. (2)

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QUESTION 7: [18]

Consider the sketch showing the graphs of and .

7.7.1. Determine the equation of by finding the values for , and . (4)

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7.2. Show that b = 2, m = 1 and n = 2. (7)

7.3. Determine the equation of the axis of symmetry of which has a positivegradient. (3)

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7.4. ED is a line parallel to the y-axis, with point E on the x-axis, point C on

and point D on . If the length of CD is units, find the length of OE. (4)

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QUESTION 8: [15]

8.8.1. Calculate the original price of an IPad if the depreciated value after 5 years is

R1 200 and the rate of depreciation is 13% per annum based on the reducingbalance method. (3)

8.2. Matt buys a car for R500 000 on an agreement in which he will repay it viamonthly instalments over a period of 5 years. Interest is charged at 18% p.a. compounded monthly.

8.2.1. Calculate the annual effective interest rate of the loan. (3)

8.2.2. At the end of 2 years, the market value of Matt’s car has reduced toR304 200. Determine the annual rate of depreciation according to thestraight line method. (3)

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8.3. Mario invests a certain sum of money for five years. He receives interest of12% p.a. compounded monthly for the first two years, and thereafter the interestrate changes to 14% p.a. compounded semi-annually. Half way through the finalyear of his investment, Mario needs to replace his car tyres, so he withdrawsR5 000 from his investment account.

If Mario’s investment has grown to a total of R75 000 at the end of the five-yearperiod, calculate how much money Mario invested initially. (6)

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QUESTION 9: [14]

Find the formula for the general term of each of the following sequences:

9.9.1.

(3)

9.2.

(2)

9.3. Given the sequence:

9.3.1. Write down the value of the next term. (1)

9.3.2. Determine an expression for the nth term of the sequence. (4)

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9.3.3. What is the value of the first term of the sequence that is greater than275? (4)

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QUESTION 10: [12]

10.

10.1. The first four terms of a quadratic sequence are:

Determine the value(s) of m. (6)

10.2. For the quadratic pattern given, how many coins do you need to make upa shape that contains 10 coins on a side? (6)

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QUESTION 11: [12]

11.

11.1. Given that and the minimum value of is 12.

Determine the value(s) of p. (6)

11.2. The equations of two parabolas are and .

Prove that these two curves must intersect for all real values of c. (6)

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END OF EXAMINATION

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