NATIONAL SENIOR CERTIFICATE GRADE 11 - Past Papers South ...

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NATIONAL SENIOR CERTIFICATE

GRADE 11

MATHEMATICS P1 NOVEMBER 2016

This question paper consists of 9 pages.

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Mathematics/P1

2 CAPS ? Grade 11

DBE/November 2016

INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions.

1.

This question paper consists of 10 questions.

2.

Answer ALL the questions.

3.

Number the answers correctly according to the numbering system used in this

question paper.

4.

Clearly show ALL calculations, diagrams, graphs et cetera that you have used in

determining your answers.

5.

Answers only will not necessarily be awarded full marks.

6.

You may use an approved scientific calculator (non-programmable and

non-graphical), unless stated otherwise.

7.

If necessary, round off answers to TWO decimal places, unless stated otherwise.

8.

Diagrams are NOT necessarily drawn to scale.

9.

Write neatly and legibly.

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Mathematics/P1

3 CAPS ? Grade 11

DBE/November 2016

QUESTION 1

1.1

Solve for x in each of the following:

1.1.1

3x2 5x 1 0 (leave youranswer correct to TWO decimal places)

(3)

1.1.2

x2 6x 8 0

(3)

1.1.3

4x 2x2 0

(4)

1.1.4

23x1 23x 12

(4)

1.1.5

x 1 3 x 4

(6)

1.2

Solve for x and y simultaneously:

3x y 2 0 and y x2 2x 8

(6)

1.3

Show that the roots of 3x2 (k 2)x 1 k are real and rational for all values of k.

(4)

[30]

QUESTION 2

2.1

Simplify fully, WITHOUT using a calculator:

5a2 .2a2

2.1.1

10a 10a1 .2

(5)

27m6 48m6

2.1.2

(3)

12m6

2.2

WITHOUT using a calculator, show that 2 8 2

(4)

1 2 8

[12]

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Mathematics/P1

4 CAPS ? Grade 11

DBE/November 2016

QUESTION 3

Consider the quadratic pattern: ? 9; ? 6 ; 1 ; 12 ; x ; ...

3.1

Determine the value of x.

(1)

3.2

Determine a formula for the nth term of the pattern.

(4)

3.3

A new pattern, Pn , is formed by adding 3 to each term in the given quadratic

pattern. Write down the general term of Pn in the form Pn an2 bn c.

(1)

3.4

Which term of the sequence found in QUESTION 3.3 has a value of 400?

(4)

[10]

QUESTION 4

4.1

Given the linear pattern: 18 ; 14 ; 10 ; ...

4.1.1

Write down the fourth term.

(1)

4.1.2

Determine a formula for the general term of the pattern.

(2)

4.1.3

Which term of the pattern will have a value of ? 70?

(2)

4.1.4

If this linear pattern forms the first differences of a quadratic pattern,

Qn, determine the first difference between Q509 and Q510.

(2)

4.2

A quadratic pattern has a constant second difference of 2 and T5 T17 29 .

4.2.1

Does this pattern have a minimum or maximum value? Justify the

answer.

(3)

4.2.2

Determine an expression for the nth term in the form

Tn an2 bn c.

(5)

[15]

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5 CAPS ? Grade 11

DBE/November 2016

QUESTION 5 Given: f(x) = ?2x2 + x + 6

5.1

Calculate the coordinates of the turning point of f.

(4)

5.2

Determine the y-intercept of f.

(1)

5.3

Determine the x-intercepts of f.

(4)

5.4

Sketch the graph of f showing clearly all intercepts with the axes and turning point.

(3)

5.5

Determine the values of k such that f(x) = k has equal roots.

(2)

5.6

If the graph of f is shifted two units to the right and one unit upwards to form h,

determine the equation h in the form y a(x p)2 q.

(3)

[17]

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