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MATHEMATICS
EXAM PAPER 1
EXAMINATOR: Me S. Kotze
MODERATOR: Me L. Havenga
GRADE 11
June 2013
TOTAL: 120
Time: 2h30min
Instructions
Answer on the folio paper
Write with a blue or black pen
Round off answers to 2 decimal places where necessary
Leave a line open between your answers
Neat and legible work will count in your favour
Question 1
[27]
Simplify without using a calculator.
1.1
1.2
1.3
1.4
22𝑥 −2𝑥
(2)
2𝑥 −1
(3 − √2)(3 + √2)
3(𝑥 4 𝑦 −4 )²
2(𝑥𝑦 2 )²
÷
(2)
(𝑥𝑦)−3
(5)
(3𝑥 −2 𝑦 4 )2
(3𝑥)−2
(3)
3𝑥 −3
1.5
√3(√3 + √6) + √2 (Leave answer in root form)
(3)
1.6
Prove that 2𝑥+1 + 3. 2𝑥 = 5. 2𝑥
(2)
1.7
√75−√27
√12
(5)
1.8
22013 −6.22011
(5)
4 1010
1
Question 2
[30]
Solve for 𝒙:
2.1
𝑥² − 𝑥 = 3
2.2
√2𝑥 + 5 − 𝑥 + 5 = 0
(6)
2.3
−𝑥(𝑥 − 9) ≤ 14
(4)
2.4
𝑥 ½ = 18
(2)
2.5
1 + 𝑥−2 + 𝑥−1 = 0
2.6
2𝑥 − (√2)
𝑥+1
(till 1 desimal number)
(5)
2
𝑥+8
(6)
+ 64 = 0
(7)
[16]
Question 3
3.1
Solve for 𝑥 and 𝑦 simultaneously:
𝑥𝑦 + 6 = 0
3.2
Determine the nature of the roots of
3.3
For which values of 𝑘 will the roots of the equation 𝑘𝑥 2 + 2𝑘𝑥 = −3
and
𝑥 + 3𝑦 + 3 = 0
𝑥² = 2(𝑥 + 1)
be equal if k ≠ 0?
(5)
(5)
[14]
Question 4
4.1
(6)
A Quadratic sequence second term is equal to 1, the third term is equal to -6 and the fifth
term is equal to -14.
4.1.1 Determine the second difference of this quadratic sequence.
(5)
4.1.2 Now continue to determine the first term of this sequence.
(2)
4.2
The sequence 4; 9; x; 37; …. is a quadratic sequence.
4.2.1 Determine the value of x.
(3)
4.2.2 Now continue to determine the general term of this sequence.
(4)
2
[6]
Question 5
5
The sketch of the sequence shows tile patterns. Each one is form by the previous pattern
(black tiles) with the gray surrounding tiles.
5.1
Two sequences is form. Firstly there is the amount of squares that is being added to each
new pattern (the grey squares). Secondly there is the total amount of squares that forms
the pattern. Write down the first six terms of each pattern.
(6)
[12]
Question 6
Consider the graph of the functions:
p x   2 x 2  x  3
qx  2x  3
^y
D
F
A
G
H
E
O
B
C
3
>x
6.1
Determine the distance of AB.
(2)
6.2
Determine the coordinates of C, the turning point of the parabola.
(4)
6.3
Determine the coordinates of D en E, the intercepts of the two graphs.
(6)
Question 7
[15]
−6
Consider the function 𝑓(𝑥) = 𝑥−3 − 1
7.1
Write down the asymptotes of f.
(2)
7.2
Draw a sketch graph of f on the attach graph paper.
Clearly indicate all intercepts with the axes.
(6)
7.3
For which values of 𝑥 will 𝑓(𝑥) > 0.
(2)
7.4
Determine the average gradient between the points x = -2 and x = 0
(5)
TOTAL 120
4