Gr. 12
Technical Mathematics
Formal test – Term 2
Total: 1 00 points Time: 3 hours
Learner's name: _________________________________ Gr. 12: __________.
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
Question 1: Coordinates, gradients, angles of inclination, and parallel lines.
Question 2: Circle equations, tangent lines, and ellipse graphing.
Question 3: Trigonometric identities, angles, and simplification.
Question 4: Area calculations and geometric properties in real-world contexts.
Question 5: Simplification and proof of trigonometric identities.
Question 6: Properties of circles and segments, similar triangles, and mid-ordinate
rule.
Question 7: Circular motion, angular velocity, and sector area calculations.
,SECTION A
QUESTION 1
In the diagram below, KLM is a triangle with vertices K(2 ; 2), and L ( d ; 4) and M (-10 ; -4). P is the
center of KLM.
The equation of the straight line LM is y−x =6given by
The angle formed by Lm and the x−¿ axis is β .
1.1 Given the equation of straight line LM as y−x =6. Write down the numerical value
of the gradient of LM. (1)
1.2 Determine:
1.2.1 The size of β , the angle of inclination of LM. (2)
1.2.2 The numerical value of d (2)
1.2.3 The coordinates of P. (2)
1.3 1.3.1 Write down the gradient of the straight line parallel to straight line LM. (1)
1.3.2 Next, determine the equation of the straight line parallel to LM and
passing through point K. (2)
[10]
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 12 June Paper 2
, QUESTION 2
The diagram below shows a circle with equation x 2+ y 2=13and a tangent line touching point
Q (2 ; 3).
2.1.1 Determine the gradient of OQ. (2)
2.1.2 Next, or otherwise, determine the equation of the tangent in the form y=…
(3)
2.2 Given:
2 2
x y
+ =1
9 4
Sketch the given graph, clearly showing all intercepts with the axes. (3)
[8]
3| 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 12 June Paper 2
Technical Mathematics
Formal test – Term 2
Total: 1 00 points Time: 3 hours
Learner's name: _________________________________ Gr. 12: __________.
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
Question 1: Coordinates, gradients, angles of inclination, and parallel lines.
Question 2: Circle equations, tangent lines, and ellipse graphing.
Question 3: Trigonometric identities, angles, and simplification.
Question 4: Area calculations and geometric properties in real-world contexts.
Question 5: Simplification and proof of trigonometric identities.
Question 6: Properties of circles and segments, similar triangles, and mid-ordinate
rule.
Question 7: Circular motion, angular velocity, and sector area calculations.
,SECTION A
QUESTION 1
In the diagram below, KLM is a triangle with vertices K(2 ; 2), and L ( d ; 4) and M (-10 ; -4). P is the
center of KLM.
The equation of the straight line LM is y−x =6given by
The angle formed by Lm and the x−¿ axis is β .
1.1 Given the equation of straight line LM as y−x =6. Write down the numerical value
of the gradient of LM. (1)
1.2 Determine:
1.2.1 The size of β , the angle of inclination of LM. (2)
1.2.2 The numerical value of d (2)
1.2.3 The coordinates of P. (2)
1.3 1.3.1 Write down the gradient of the straight line parallel to straight line LM. (1)
1.3.2 Next, determine the equation of the straight line parallel to LM and
passing through point K. (2)
[10]
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 12 June Paper 2
, QUESTION 2
The diagram below shows a circle with equation x 2+ y 2=13and a tangent line touching point
Q (2 ; 3).
2.1.1 Determine the gradient of OQ. (2)
2.1.2 Next, or otherwise, determine the equation of the tangent in the form y=…
(3)
2.2 Given:
2 2
x y
+ =1
9 4
Sketch the given graph, clearly showing all intercepts with the axes. (3)
[8]
3| 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 12 June Paper 2
