Date: SEPTEMBER 2025
Time: 1 ½ HOURS
Marks: 75
Grade: 11
Subject: TECHNICAL MATHEMATICS
Question paper: 1
Name and Surname:
INSTRUCTIONS AND INFORMATION
1. Read all the questions carefully before you begin.
2. Answer ALL the questions.
3. Write down all answers clearly and neatly.
4. Show all calculations and steps in full to earn partial merit.
5. Use a non-programmable calculator where necessary.
6. All answers must, where applicable, be rounded to the required number of decimal
places.
7. You may use a dark pencil or blue/black pen.
8. For questions that require graphs or sketches, clearly mark all critical values (for
example, maximum, minimum, intercepts and asymptotes).
9. If a diagram is provided, use it as indicated and do not change any given
measurements.
10. The total for the paper is 75 marks.
Main topics
1. Trigonometric calculations and identities
2. Functions and graphs (trigonometric functions)
3. Proofs and simplification of identities
4. Geometry in the plane (2D problems with triangles and rectangles)
5. Circular geometry and radial calculations (Ferris wheel problem)
6. Financial mathematics (growth, decay, compound interest, inflation)
Pg 1/ 6 www.summariessa.co.za Author: CHR SMI
Grade: 11 Subject: Technical Mathematics Date: SEPTEMBER 2025
, QUESTION 1:
If 𝐴̂ = 34°en 𝐵̂= 22,6°, determine the numerical value of the following, correct to
TWO decimal places:
1.1.1 𝑠𝑖𝑛 𝐴 + 𝑐𝑜𝑠 𝐵 (1)
1
1.1.2 .𝑠𝑒𝑐²(𝐴 − 𝐵) (2)
𝐾(−6; −3)lies on the Cartesian plane and has an angle, 𝛼with the positive 𝑥-axis.
Use the diagram to calculate the value of:
1.1.3. The radius, 𝑟, in simplified square root form. (3)
1.1.4 √5 𝑠𝑖𝑛 𝛼 − 2 𝑡𝑎𝑛 𝛼 (2)
1.1.5 𝑐𝑜𝑠𝑒𝑐 𝛼 + 3 𝑡𝑎𝑛² 𝛼 (3)
5
1.2 Given sentence 2𝑥 + 3 = 2 𝑤𝑎𝑎𝑟 2𝑥 ∈ [0°; 360°],determines all possible
values for 𝑥. (4)
[15]
Pg 2/ 6 www.summariessa.co.za Author: CHR SMI
Grade: 11 Subject: Technical Mathematics Date: SEPTEMBER 2025
Time: 1 ½ HOURS
Marks: 75
Grade: 11
Subject: TECHNICAL MATHEMATICS
Question paper: 1
Name and Surname:
INSTRUCTIONS AND INFORMATION
1. Read all the questions carefully before you begin.
2. Answer ALL the questions.
3. Write down all answers clearly and neatly.
4. Show all calculations and steps in full to earn partial merit.
5. Use a non-programmable calculator where necessary.
6. All answers must, where applicable, be rounded to the required number of decimal
places.
7. You may use a dark pencil or blue/black pen.
8. For questions that require graphs or sketches, clearly mark all critical values (for
example, maximum, minimum, intercepts and asymptotes).
9. If a diagram is provided, use it as indicated and do not change any given
measurements.
10. The total for the paper is 75 marks.
Main topics
1. Trigonometric calculations and identities
2. Functions and graphs (trigonometric functions)
3. Proofs and simplification of identities
4. Geometry in the plane (2D problems with triangles and rectangles)
5. Circular geometry and radial calculations (Ferris wheel problem)
6. Financial mathematics (growth, decay, compound interest, inflation)
Pg 1/ 6 www.summariessa.co.za Author: CHR SMI
Grade: 11 Subject: Technical Mathematics Date: SEPTEMBER 2025
, QUESTION 1:
If 𝐴̂ = 34°en 𝐵̂= 22,6°, determine the numerical value of the following, correct to
TWO decimal places:
1.1.1 𝑠𝑖𝑛 𝐴 + 𝑐𝑜𝑠 𝐵 (1)
1
1.1.2 .𝑠𝑒𝑐²(𝐴 − 𝐵) (2)
𝐾(−6; −3)lies on the Cartesian plane and has an angle, 𝛼with the positive 𝑥-axis.
Use the diagram to calculate the value of:
1.1.3. The radius, 𝑟, in simplified square root form. (3)
1.1.4 √5 𝑠𝑖𝑛 𝛼 − 2 𝑡𝑎𝑛 𝛼 (2)
1.1.5 𝑐𝑜𝑠𝑒𝑐 𝛼 + 3 𝑡𝑎𝑛² 𝛼 (3)
5
1.2 Given sentence 2𝑥 + 3 = 2 𝑤𝑎𝑎𝑟 2𝑥 ∈ [0°; 360°],determines all possible
values for 𝑥. (4)
[15]
Pg 2/ 6 www.summariessa.co.za Author: CHR SMI
Grade: 11 Subject: Technical Mathematics Date: SEPTEMBER 2025
