Gr. 11
Technical Mathematics – Paper 1
Formal test – Term 2
Total: 100 points Time: 2 hours
Learner's name: _________________________________ Gr. 11: __________.
Instructions and information:
This paper consists of two questions, answer both questions.
The use of a calculator is not permitted.
No Tip – Ex may be used.
Show all the steps needed to arrive at the answer.
Strength!!
Content covered in this paper
Algebra and logarithms
Solve equations and applications
Function analysis
Rational functions
Circle and hyperbola
, QUESTION 1
1.1 Simplified, the complete WITHOUT the use of a calculator.
0
1.1.1 ( 5 √3 3−x 5 ) (2)
1
1.1.2 x 2 (3−x ) (3)
1.1.3 ( √ 3−3 )( √ 3−3 ) (3)
1 1
5 3
1.1.4 log 2 32 + log 2 27 (6)
0
log 2 6 +¿ log 7 x ¿
√
x−1 x+1
3 −7.3
1.2 Given: y= x
6.9 x
( )
1
1 −31 x
1.2.1 Prove that y= × (6)
3 9
1.2.2 Next, show that for y ∈real numbers then are x € even numbers. (2)
1.3 Consider binary numbers X =1000002andY =1112
1.3.1 Write X and Y in decimal form. (2)
1.3.2 Next, determine (X - Y) in binary form. (2)
[26]
QUESTION 2
2.1 Solve for x ∈ R, WITHOUT using a calculator:
1
2.1.1 5 = 32 (4)
( x )3
2.1.2 √ x+5−x=3 (6)
2.1.3 log x 3=−1 (3 )
2.1.4 log a (x−8)−¿ log a 24=−log a (x +2) ¿ (7)
2.2 Show that:
2| P a g e www.summariessa.co.za T e c h n i c a l M a t h e m a ti c s
Grade 11 June Paper 1
Technical Mathematics – Paper 1
Formal test – Term 2
Total: 100 points Time: 2 hours
Learner's name: _________________________________ Gr. 11: __________.
Instructions and information:
This paper consists of two questions, answer both questions.
The use of a calculator is not permitted.
No Tip – Ex may be used.
Show all the steps needed to arrive at the answer.
Strength!!
Content covered in this paper
Algebra and logarithms
Solve equations and applications
Function analysis
Rational functions
Circle and hyperbola
, QUESTION 1
1.1 Simplified, the complete WITHOUT the use of a calculator.
0
1.1.1 ( 5 √3 3−x 5 ) (2)
1
1.1.2 x 2 (3−x ) (3)
1.1.3 ( √ 3−3 )( √ 3−3 ) (3)
1 1
5 3
1.1.4 log 2 32 + log 2 27 (6)
0
log 2 6 +¿ log 7 x ¿
√
x−1 x+1
3 −7.3
1.2 Given: y= x
6.9 x
( )
1
1 −31 x
1.2.1 Prove that y= × (6)
3 9
1.2.2 Next, show that for y ∈real numbers then are x € even numbers. (2)
1.3 Consider binary numbers X =1000002andY =1112
1.3.1 Write X and Y in decimal form. (2)
1.3.2 Next, determine (X - Y) in binary form. (2)
[26]
QUESTION 2
2.1 Solve for x ∈ R, WITHOUT using a calculator:
1
2.1.1 5 = 32 (4)
( x )3
2.1.2 √ x+5−x=3 (6)
2.1.3 log x 3=−1 (3 )
2.1.4 log a (x−8)−¿ log a 24=−log a (x +2) ¿ (7)
2.2 Show that:
2| P a g e www.summariessa.co.za T e c h n i c a l M a t h e m a ti c s
Grade 11 June Paper 1
