GRADE 11

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NATIONAL

SENIOR CERTIFICATE

GRADE 11

MATHEMATICS PAPER 1

COMMON TEST

AMAJUBA DISTRICT

JULY 2021

MARKS:

75

TIME:

1? hours

This question paper consists of 5 pages, including the cover page and instructions.

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Gr. 11 Mathematics

Common Test July 2021

Amajuba District

INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions.

1.

This question paper consists of 5 questions.

2.

Answer ALL the questions.

3.

Clearly show ALL calculations, diagrams, graphs, etc. which you have used in

determining your answers.

4.

Answers only will NOT necessarily be awarded full marks.

5.

You may use an approved scientific

non-graphical), unless stated otherwise.

6.

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

otherwise.

7.

Diagrams are NOT necessarily drawn to scale.

8.

Write neatly and legibly.

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Gr. 11 Mathematics

Common Test July 2021

Amajuba District

QUESTION 1

1.1

Solve for x:

1.1.1

1

x(3 ? x) ? 0

2

1.1.2

5x2 = 3x + 4

1.1.3

x ? 2x ? 1 ? 2

(4)

1.1.4

x 2 ? 15 ? 2 x

(3)

(2)

(correct to two decimal places)

1.2

Solve for x and y simultaneously: 2 x ? y ? 7 and x 2 ? xy ? y 2 ? 21 .

1.3

Given that ? =

(4)

(6)

¡Ì2? + 7

??5

For which values of ? will ? be a real number?

(3)

[22]

QUESTION 2

2.1

2.2

2.3

Solve for x without the use of a calculator :

If

9 x ?1 ? 6.3 2 x

( 3)

4 x ?1

? 3 a , determine the value of a.

Solve for x if 3x ? 8 ? 32 ? x

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43??1

8?

= 22??

(3)

(3)

(4)

[10]

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Gr. 11 Mathematics

Common Test July 2021

Amajuba District

QUESTION 3

3.1

Which term of the sequence 23 ; 21 ; 19 ; ¡­ will be equal to ¨C 47?

3.2

Consider the following quadratic number pattern: 1 ; 4 ; 11 ; 22 ; 37 ; ¡­

3.3

(4)

3.2.1

Determine the formula for the general term ( Tn ) of this pattern.

(4)

3.2.2

Determine the value of the 20th term of the first difference sequence for this

quadratic number pattern.

(3)

In the quadratic number pattern 4 ; ? ; ? ; ?11 ; ¡­ the first three first differences between

?

terms are 2? ? 4; ? ? 3 and 2 ? 1.

Determine:

3.4

3.2.1 the value of ?.

(3)

3.2.2 the second difference.

(2)

3.2.3 the values of x and ?.

(2)

Given the number pattern: 2 ; 4 ; 8 ; 16 ¡­

3.4.1

Is this pattern linear, quadratic or exponential?

(1)

3.4.2

Write down the general term ( Tn ) of this pattern.

(1)

[20]

QUESTION 4

Given: g ? x ? ?

?3

?6

x?2

4.1

Determine the intercepts of g with the axes.

(4)

4.2

Write down the equations of the asymptotes of g.

(2)

4.3

Draw the graph of g on your answer sheet. Show clearly the intercepts with the axes

as well as the asymptotes.

(3)

4.4

Write down the range of h if h( x) ? ? g ( x) .

(1)

4.5

Determine the equation of the axis of symmetry of g that has a negative x-intercept.

(2)

[12]

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Gr. 11 Mathematics

Common Test July 2021

Amajuba District

QUESTION 5

S(1 ; 18) is the turning point of the graph of f ( x) ? ax 2 ? bx ? c .

P and T are the x-intercepts of f.

The graph of g ( x) ? ?2 x ? 8 has an x-intercept at T.

R is a point of intersection of f and g.

y

S(1 ; 18)

f

R

g

P

T

x

0

5.1

Calculate the coordinates of T.

(2)

5.2

Determine the equation of f in the form y ? a ( x ? p ) 2 ? q .

(4)

5.3

If the coordinates of R are (?1 ; 10), use the graphs to determine for which values

of x:

5.3.1

f ?x ? ? g ?x ?

(2)

5.3.2

f ?x ?.g ?x ? ? 0

(3)

[11]

TOTAL: 75

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