Graad/Grade 11 Maart/March

Toets/Test Totaal/Total: 60 punte/marks

Eksaminator: Tyd/Time: 1 uur/hour

Moderator:

INSTRUKSIES INSTRUCTIONS

1. Beantwoord ALLE vrae.2. Sakrekenaars mag gebruik word.3. Dit is tot jou eie voordeel om netjies en volledig

te werk.4. Rond alle antwoorde af tot 2 desimale syfers.5. Trek ‘n lyn na elke vraag.6. Geniet die vraestel.

1. Answer ALL questions.2. Calculators may be used.3. It is to your advantage to work neatly and show

all workings.4. Round off all answers to two decimal places.5. Draw a line after each question.6. Enjoy the paper.

Vraag 1/Question 1

1.1 Los op vir x/Solve for x:

1.1.1 (2 x+1 ) (3 x−5 )=0 (2)

1.1.2 5 x2−8=x (4)

1.1.3 x−√5+x=7 (5)

1.2 Gegee/Given:

( x+2 ) (x−3 )←3x+2

1.2.1 Los op vir x as ( x+2 ) (x−3 )←3x+2

Solve for x if ( x+2 ) (x−3 )←3x+2 (4)

1.2.2 Vervolgens, of andersins, bepaal die som van al die heelgetalle wat die uitdrukking

x2+2x−8<0 sal bevredig.

Hence, or otherwise, determine the sum of all the integers which will satisfy the expression x2+2 x−8<0 (2)

1.3 Los op vir x en y in die gegewe vergelykings.

Solve for x and y simultaneously in the given equations.

3y=81x+ 1 en/and y=x2−6x−20 (7)

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Vraag 2/Question 2

2.1 Vereenvoudig sonder die gebruik van ‘n sakrekenaar.

Simplify without using a calculator.

¿ (4)

2.2 Gegee/Given:

4x−1+4x+ 1

17.12x

2.2.1 Vereenvoudig die uitdrukking volledig/Simplify the expression completely. (3)

2.2.2 Indien 3−x=4 t , druk 4x−1+4x+1

17.12x in terme van t uit.

If 3−x=4 t , express in terms of t 4x−1+4x+1

17.12x(1)

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Vraag 3/Question 3

3.1 Die oplossing van ‘n kwadratiese vergelyking is x=3±√4−8 p4

. Bepaal die waarde(s)

van p sodat:

The solution of a quadratic equation is ¿ 3±√4−8 p4

. Determine the value(s) of p if:

3.1.1 die vergelyking gelyke wortels het/the equation has equal roots. (2)

3.1.2 die vergelyking nie-reële wortels het/the equation have non-real roots. (2)

3.2 Beskou die getalpatroon/Given the number pattern:

-6; 1; 14; 33

3.2.1 Bepaal die algemene term van die ry/Determine the general term of the pattern. (4)

3.2.2 Bepaal of 1270 ‘n term van die getalpatroon is.

Determine if 1270 is a term of the number pattern. (4)

3.3 ‘n Gegewe kwadratiese patroon T n=an2+bn+c het T 2=T 4=0 en ‘n 2de

verskil van 12. Bepaal die waarde van die derde term van die patroon.

A given quadratic pattern T n=an2+bn+c has T 2=T 4=0 and a 2nd difference of 12.

Determine the value of the third term of the pattern. (2)

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Vraag 4/Question 4

In die volgende diagram is C(k; 5), A(-4;1) en F(k; p) die hoekpunte van ∆CAF . B(-1; -5) is die middelpunt van AF en CF is parallel aan die y-as.

In the following diagram is C(k; 5), A(-4; 1) and F(k; p) the vertices of ∆CAF . B(-1; -5) is the midpoint of AF and CF is parallel to the y-axis.

4.1 Bepaal/Determine:

4.1.1 die waardes van k en p/the values of k and p. (2)

4.1.2 die lengte van AB/the length of AB. (2)

4.1.3 die vergelyking van AF/the equation of AF. (3)

4.1.4 die vergelyking van die middelloodlyn van AF.

the equation of the perpendicular bisector of AF. (3)

4.2 As D(k; y) ‘n punt op CF is sodat BD∥ AC, bepaal die waarde van y.

If D is a point on CF with BD∥ AC, determine the value of y. (4)

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