Grade 12 Technical Mathematics June Paper 2 and Memo:
Total: 100 Marks.
Contents of the exam paper contains the following details:
Question 1: Coordinates, gradients, angles of inclination, and parallel lines.
Question 2: Circle equations, tangent lines, and ellipse graphing.
Question 3:...
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
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through EFT, credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying this summary from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller SummariesSA. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy this summary for R50,00. You're not tied to anything after your purchase.