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Mathematics Paper 1Grade 11

November Examination 2018

DURATION: 3 hours EXAMINER: R. ObermeyerMARKS: 150 marks MODERATOR: A. JanischDate: 9 November 2018 External Moderator: I. Atteridge

INSTRUCTIONS:

See overleaf for Instructions. This paper consists of 18 pages (including cover) and an information sheet.

NAME: ____________________________________

ASSESSMENT

Question Level Tested Topic Time

AllocationPossible

markMark

obtainedSECTION A

1 1 – 4 Equations & Inequalities 28 mins 23

2 1 – 4 Exponents, Surds & Equations 14 mins 12

3 1 – 4 Number Patterns 7 mins 64 1 – 4 Functions 20 mins 175 1 – 4 Functions 8 mins 7

6 1 – 4 Financial Mathematics 7 mins 6

7 1 – 4 Probability 11 mins 9SECTION B

8 1 – 4 Equations & Number Systems 20 mins 17

9 1 – 4 Number Patterns 10 mins 8

10 1 – 4 Financial Mathematics 10 mins 8

11 1 – 4 Functions & Equations 10 mins 8

12 1 – 4 Functions 26 mins 2213 1 – 4 Probability 9 mins 7

TOTAL: 150PERCENTAGE:

Teacher’s Signature: ________________________

Controller’s Signature: _______________________

Moderator’s Signature: _______________________

Mathematics Paper 1 Grade 11November Examination 2018 Examiner: Ms. R. Obermeyer

Instructions

PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY

1. This question paper consists of 18 pages (including the cover page) and an information sheet. Please check that your question paper is complete.

2. Read the questions carefully.3. Answer ALL the questions on the question paper and hand this in at the end of the

examination. 4. Diagrams are not necessarily drawn to scale.5. You may use an approved non-programmable and non-graphical calculator, unless

otherwise stated.6. All necessary working details must be clearly shown.7. Leave all final answers to one decimal place unless otherwise stated.8. Ensure that your calculator is in DEGREE mode.9. It is in your own interest to write legibly and to present your work neatly.

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SECTION AQuestion 1

a) Solve for x:1) x (x−2 )=8 (3)

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2) (x−1)(x+4)≥6 (5)______________________________________________________________________________

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3) 6−2√x+2=x (7)______________________________________________________________________________

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b) Given: ( x−3 ) (2 x2−5 x−8 )=01) Give a rational value of x which satisfies the equation. (1)

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2) Determine the irrational roots of the equation. (4)______________________________________________________________________________

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c) Calculate the value of f (x) if f (x)= x2−4x−2

and x=21354699999. (3)

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Question 2

a) Simplify the following as far as possible without the use of a calculator:1) √32−√128+√18 (2)

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2) ( 1√5+ √55 )

2

(3)

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b) Solve for x without the use of a calculator:

1) ( x+2 )( x32−8)=0 (3)

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2) 3x+1+3x+3x−1=13 (4)______________________________________________________________________________

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Question 3

Given the following sequence: −15 ;−11;−7 ;… a) Determine the equation for the general term. (2)

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b) Determine the 26th term in the sequence. (1)______________________________________________________________________________

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c) For T n=173, determine n. (3)______________________________________________________________________________

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[6]Question 4

Consider the function: f (x)= −2x−2

+1

a) Calculate the coordinates of the y-intercept of f . (2)

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b) Calculate the coordinates of the x-intercept of f . (3)

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c) Sketch the graph of f on the grid below, showing clearly the asymptotes and the

intercepts with the axes. (4)

d) For which values of x is f (x)<0? (2)

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e) Calculate the average gradient of f between x=−2 and x=0. (4)

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f) Give the equation of the line of symmetry of f (x) which has a negative gradient. (2)

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[17]Question 5

Consider the functions: f (x)=( 12 )x

+1 and g(x )=9.

a) Verify algebraically that the point of intersection of f and g is (−3 ;9 ). (3)

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b) Determine the equation of h if h(x )=f (−x ). (2)

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c) Determine the equation of p if p(x )=f (2x )−1. (2)

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[7]Question 6

Sheldon invests R 140 000. He is quoted a nominal interest rate of 8,2% per annum compounded monthly.

a) Calculate the effective interest rate per annum correct to FIVE decimal places. (3)______________________________________________________________________________

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b) Calculate the value of Sheldon’s investment if he invested the money for 4 years. (3)______________________________________________________________________________

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Question 7

A total of 300 boys from two different schools, R and W, are questioned about their winter sport.

a) Calculate the values of the letters marked a to f. (6)______________________________________________________________________________

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b) Is a boy’s preference for playing sport independent of the school he attends? Support your answer with calculations. (3)

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SECTION B

Question 8

a) Given: 2x+2x+2=−5 y+101) Express 2x in terms of y. (3)

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2) Solve for x if y=158 . (3)

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b) Given: A=√2 x+1x2−2 x

1) For which value(s) of x is A undefined? (3)______________________________________________________________________________

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2) For which value(s) of x is A non-real? (2)______________________________________________________________________________

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c) In 2012, Sipho ran a marathon race of 48 km. At the end he was very disappointed with his average speed during the race and decided to train very hard in order to improve for the next race in 2013. He calculated that if he increased his speed by 4 km/h during the 2013 race, he should complete the race in a time that is one hour less than in 2012. Calculate Sipho’s speed during the 2013 race. (6)

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Question 9

A quadratic pattern has a second term equal to 6, a third term equal to 11 and a fifth term equal to 27.

a) Calculate the second difference of this quadratic pattern. (6)______________________________________________________________________________

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b) Hence, or otherwise, calculate the first term of the pattern. (2)______________________________________________________________________________

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Question 10

A company buys a delivery truck for R 420 000. The truck depreciates at an annual rate of 15% p.a. reducing balance, while inflation averages 6,8% p.a.At the end of the first and fourth year the company invests R 80 000 into a sinking fund in order to replace the delivery truck.The interest rate on the sinking fund is 11% p.a compounded monthly.What is the surplus or shortfall in the sinking fund if the company wishes to buy a new truck at the end of 5 years after selling the old truck at its book value?______________________________________________________________________________

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Question 11

a) Make a freehand sketch of y=a x2+bx+c, where a>0 , b>0 , c<0 and a x2+bx+c=0 has TWO solutions. (4)

b) The volume of a box with a rectangular base is 3 072 cm3. The lengths of the sides are x ,2 xand 3 x respectively. Calculate the length of the shortest side. (4)

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Question 12

The figure below represents the graphs of the following functions:

f (x)=−2x2−4 x+16 and g(x )=8x+5

+6

a) Determine the coordinates of A, B, C, D and E. (8)______________________________________________________________________________

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Mathematics Paper 1 Grade 11November Examination 2018 Examiner: Ms. R. Obermeyer______________________________________________________________________________

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b) Write f (x) in the form a (x−p)2+q. Hence, give the co-ordinates of M, the turning point of f (x). (6)

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c) Write down the equations of the vertical and horizontal asymptotes of g. (2)______________________________________________________________________________

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d) Write down the range of f . (2)______________________________________________________________________________

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e) Determine the new equation of g if it is translated 3 units to the right and 2 units down. (2)______________________________________________________________________________

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f) Give the values of x where f (x) . g (x)<0. (2)______________________________________________________________________________

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Question 13A group of 80 athletes were asked which of the 3 sprints events (100m, 200m and 400m) they intended to enter at the next inter-House Athletics meeting.

21 entered none of these events

6 entered all three events

10 entered the 100m and 200m

11 entered the 200m and 400m

Of the 21 who entered the 100m, 10 entered nothing else

27 entered the 400m

a) Represent the above situation using a Venn diagram. (4)

b) How many athletes entered the 200m event? (1)

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c) What is the probability that an athlete, selected at random, is entered in at least 2

events of the three events? (2)

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