Grade 11 Mathematics: Question Paper 2 MARKS: 150 TIME: 3 ...

Mathematics(NSC)/Grade 11/ P2

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Grade 11 Mathematics: Question Paper 2

MARKS: 150

TIME: 3hours

QUESTION 1

1.1 A triangleisdrawnwithverticesA (0;2);B (4;5)andC (4;-4).

1.1.1 FindthelengthofAB.

(2)

1.1.2 FindtheequationofthelinethroughB andC.

(1)

1.1.3 FindtheequationofthelinethroughA andB.

(2)

1.1.4 FindtheinclinationofthelinethroughA andB.

(2)

1.2 W hatwillbethegradientofthelineperpendicularto3x 2 y 7 0?

(2)

1.3 Usingacalculatorfindthevaluesofthefollowingifx 42D and y 127,8D :

1.3.1 sin3x

(1)

1.3.2 cos2 (3x y)2

(2)

sin180D A

 1.4 Simplify: sin90D A

(3)

1.5 Findthesolutionto3tan2x 1 ontheintervalx [0,270DD]

(4)

1.6 Considerthediagram below:

P

7 cm

R

3040 5 cm

T 60 K

1.6.1 FindthelengthofKT.

(3)

1.6.2 FindthelengthofPT.

(3)

1.7 Draw,onthegraphpaperonyourdiagram sheet,aboxandwhiskerdiagram for asetofdatawiththefollowingcharacteristics:

o M edianis17 o Upperquartileis20 o Lowerquartileis11 o M aximum valueis30 o Rangeis20

(5)

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Mathematics(NSC)/Grade 11/ P2

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1.8 Find the volume of the right cone with slant height 13 mm and with radius of base 5 mm.

13

5

(3)

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QUESTION 2

Consider parallelogram ABCD with co-ordinates as shown in the diagram below.

A (0;20)

B (11;25)

D (10;0)

C (21;5)

2.1 List two properties that are true of a rectangle which are not true of all

parallelograms.

(2)

2.2 Find the lengths of AC and BD (leave your answers in surd form).

(4)

2.3 Find the gradients of AB and AD.

(4)

2.4 Is ABCD a rectangle? Give two detailed reasons using your answers from 2.2

and 2.3.

(2)

[12]

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Mathematics(NSC)/Grade 11/ P2

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QUESTION 3

A triangle with vertices A (3;5); B (8;4) and C (2;2) is drawn. A copy of this diagram appears on your diagram sheet.

6y A (3;5)

5

4

B (8;4)

3

2 1

-8 -7 -6 -5 -4 -3 -2 -1 -1

C (2;2)

x 12345678

3.1 Give the co-ordinates of the vertices of the image A' B'C' of ? ABC when it is

rotated 90 degrees anti-clockwise around the origin.

(5)

3.2 Complete the generalisation of this transformation:

(x; y) o(.......... ; ..........)

(2)

3.3 Find the equation of the perpendicular bisector of BB' .

(5)

3.4 Given that the equation of AA' is y =-4x, show that AA' and BB' intersect at the

centre of rotation.

(3)

3.5 Give the co-ordinates of the vertices of A'' B''C'' if it is the image of ?ABC

when it is rotated through an angle of 180?.

(3)

[18]

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QUESTION 4

Square PQRS has vertices with co-ordinates as shown in the diagram below. This diagram is reproduced on your diagram sheet. PQRS is to be enlarged by a scale factor of 3.

y 12 11 10 9 8 7 6 5 4 3 2P 1 (1;2)

12 -1 -2 -3

Q (4;4)

R (6;1) 345678 S (3;-1)

x 9 10 11 12 13 14 15 16 17 18

4.1 On the diagram sheet draw this enlargement and indicate the vertices P'Q' R'S'

and the co-ordinates of these vertices.

(7)

4.2 Calculate the length of a side of both PQRS and P'Q' R'S' and hence determine

the relationship between the increased length of the sides and the increased area

of the squares. Work in surd form.

(6)

[13]

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QUESTION 5

Throughout this question a calculator may not be used and all working must be clearly shown.

5.1 Simplify the following:

 - tanx.sin 90D x

tanx 180D

5.1.1

sin x

cos90D x

(6)

5.1.2 cos120D

tan 225D

(4)

5.2 Consider the equation: 2cos2 x cos x 0

5.2.1 Factorise the left hand side of the equation.

(1)

5.2.2 Find the general solution to the equation.

(5)

5.3 If sin 58D k , then find the following:

5.3.1 sin 238D

(2)

5.3.2 cos58D

(3)

[21]

QUESTION 6

Four learners are arguing about whose trigonometric expression best describes a particular situation.

Sipho

1 tan 2 T 1 tan 2 T

Ray 1 2sin 2 T

Lorraine 1 sinT

Vishnu 2cos2 T 1

6.1 They each substitute T 30D into their expression. They all get the same value.

What is it?

(1)

6.2 They each substitute T 50D . What value do they each get?

(4)

6.3 Using your knowledge of trigonometric identities, show that three of the

learners'expressions are exactly the same.

(7)

[12]

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