Mathematics Paper 1

2

HERZLIA SENIOR HIGH SCHOOL

MATHEMATICS PAPER 1

GRADE 11

FRIDAY 18TH NOVEMBER 2016

“If you will it, it is no legend”

MARKS: 125 TIME: 2 HOURS

INSTRUCTIONS AND INFORMATION

1. This question paper consists of 7 pages with 9 questions.

2. Answer ALL the questions.

3. Clearly show ALL calculations, diagrams and graphs that you have used in determining your answers.

4. It is in your own interest to write legibly and to present your work neatly.

5. An approved scientific calculator (non-programmable and non-graphical) may be used, unless stated otherwise.

6. If necessary, answers should be rounded off to TWO decimal places, unless stated otherwise.

7. Diagrams are NOT necessarily drawn to scale.

QUESTION 1

1.1 Solve for x in each of the following:

1.1.1 (2)

1.1.2 (6)

1.1.3 (2)

1.2 Given:

1.2.1 Solve for x if (correct to TWO decimal places). (3)

1.2.2 Hence, or otherwise, calculate the value of d for which

has equal roots. (3)

1.3 Solve for x and y simultaneously:

and (6)

[22]

QUESTION 2

2.1 Simplify the following WITHOUT using a calculator:

2.1.1 (3)

2.1.2 (3)

2.2 Solve for x in each of the following:

2.2.1 (4)

2.2.2 (5)

2.2.3 (3)

2.3 Given:

2.3.1 Show that P is rational if . (2)

2.3.2 For what value(s) of x will P be a real number? (2)

2.4 Calculate the sum of the digits of . (3)

[25]

QUESTION 3

ACDF is a rectangle with an area of cm2. B is a point on AC

and E is a point on FD such that ABEF is a square with sides of length

cm each.

Calculate the length of ED.

[5]

PLEASE TURN OVER

QUESTION 4

The sketch below shows the graph of .

A is the point of intersection of the asymptotes of f.

4.1 Write down the coordinates of A. (2)

4.2 Determine the coordinates of the x- and y-intercepts of f. (3)

4.3 The graph of f is reflected about the x-axis to obtain the graph of g.

Write down the equation of g in the form y = ……….. (2)

4.4 Write down the equation of the axis of symmetry of f that has a

negative gradient. (2)

4.5 Hence, or otherwise, determine the coordinates of a point that lies

on f in the fourth quadrant, which is closest to point A. (4)

4.6 Given:

4.6.1 Show that the points of intersection between f and h can be

found by solving the following equation:

(2)

4.6.2 Hence, find the x-values of these points of intersection. (3)

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PLEASE TURN OVER

QUESTION 5

Given:

5.1 Determine the coordinates of the y-intercept of h. (1)

5.2 Explain why h does not have an x-intercept. (2)

5.3 Draw a sketch graph of h, clearly showing all asymptotes, intercepts

with the axes and at least one other point on h. (3)

5.4 Describe the transformation from h to g if . (2)

[8]

QUESTION 6

Sketch the graph of if it is also given that:

·  is increasing on

· 

· 

·  has two distinct roots, one of them is positive and the other one is

negative

[4]

PLEASE TURN OVER

QUESTION 7

The graph of and the straight line g are sketched below.

A and B are the points of intersection of f and g. A is also the turning point

of f. The graph of f intersects the x-axis at B(3;0) and C. The axis of

symmetry of f is .

7.1 Write down the coordinates of C. (1)

7.2 Determine the equation of f in the form . (2)

7.3 Determine the range of f. (2)

7.4 Determine the equation of g in the form . (3)

7.5 For which values of x will:

7.5.1 (3)

7.5.2 (3)

7.6 For what values of p will have non-real roots? (3)

[17]

PLEASE TURN OVER

QUESTION 8

8.1 A tractor bought for R120000 depreciates to R11090,41 after 12 years

by using the reducing balance method. Calculate, as a percentage, the

rate of depreciation per annum. (The rate was fixed over the 12 years.) (4)

8.2 Calculate the annual effective interest rate, as a percentage, if interest is

9,8% p.a., compounded monthly. (2)

8.3 R80000 is invested in an account which offers the following:

·  7,5% p.a. compounded quarterly, for the first 4 years and thereafter

·  9,2% p.a. compounded monthly, for the next 3 years

Calculate the total amount of money that will be in the account at the

end of 7 years if no further transactions happen on the account. (4)

8.4 Exactly 8 years ago David invested R30000 in an account earning

6,5% per annum, compounded monthly.

8.4.1 How much will he receive if he withdrew his money today? (3)

8.4.2 David withdrew R10000 three years after making the initial

deposit and re-invested R10000 five years after making the

initial deposit.

Calculate the difference between the final amount David will

now receive after eight years and the amount he would have

received had there not been any transactions on the account

after the initial deposit. (5)

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PLEASE TURN OVER

QUESTION 9

A survey was carried out with 240 customers who bought food from a

fastfood outlet on a particular day. The outlet sells cheese burgers (C),

beef burgers (B) and vegetarian burgers (V). The Venn diagram below

shows the number of customers who bought different types of burgers

on the day.

9.1 How many customers did NOT buy burgers on the day? (1)

9.2 If a customer from this group is selected at random, determine

the probability that he/she:

9.2.1 Bought only a vegetarian burger (1)

9.2.2 Did not buy a cheese burger (2)

9.2.3 Bought a beef burger or a vegetarian burger (2)

9.3 If it is known that a certain customer did have a beef burger, what

is the probability that they also had a cheese burger? (2)

[8]

TOTAL : 125