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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