Date: SEPTEMBER 2025
Time: 1 ½ HOURS
Marks: 60
Grade: 11
Subject: MATHEMATICS
Question paper: 1
Name and Surname:
Instructions and Information
1. This question paper consists of 4 questions with a total of 60 marks.
2. All questions are compulsory.
3. Number your answers according to the numbering system used in the question
paper.
4. Show all necessary calculations and steps. Answers without the correct
workings may not be awarded full marks.
5. Use a non-programmable, non-graphical calculator where necessary.
6. Diagrams are not necessarily drawn to scale.
7. An approved mathematical instrument set may be used.
8. Round off answers to two decimal places, unless otherwise stated.
9. Manage your time carefully. Use the mark allocation as a guide to how long you
should spend on each question.
10. Write neatly and ensure that your answers are clearly indicated.
Topics covered in this test
• Algebra
• Patterns and Sequences
• Functions and Graphs
• Trigonometry
• Analytical Geometry
• Probability
• Statistics
• Financial Mathematics
• Euclidean Geometry
• Mensuration (Surface Area and Volume)
Pg 1/ 6 www.summariessa.co.za Author: CHR SMI
Grade: 11 Subject: Mathematics Date: SEPTEMBER 2025
, QUESTION 1
1.1 A security company uses a sensor system to detect intruders. Two
independent sensors, X and Y, are installed – one at the main entrance and
the other at the back gate. If someone breaks in, the probability that the
person is detected by sensor X is 0.45 and the probability that the person
is detected by sensor Y is 0.65.
1.1.1 If there is an intruder, what is the probability that the intruder will be
detected by at least one sensor? (3)
1.1.2 Determine the probability that the intruder will not be detected at all.
(2)
1.2 At a certain college, a survey was conducted among 110 students about their
subject choices. The Venn diagram shows the results of the survey in terms
of:
o Natural Sciences (N)
o Accounting (R)
o Mathematics (W)
1.2.1 Show that .𝑥 = 8 (2)
Pg 2/ 6 www.summariessa.co.za Author: CHR SMI
Grade: 11 Subject: Mathematics Date: SEPTEMBER 2025
Time: 1 ½ HOURS
Marks: 60
Grade: 11
Subject: MATHEMATICS
Question paper: 1
Name and Surname:
Instructions and Information
1. This question paper consists of 4 questions with a total of 60 marks.
2. All questions are compulsory.
3. Number your answers according to the numbering system used in the question
paper.
4. Show all necessary calculations and steps. Answers without the correct
workings may not be awarded full marks.
5. Use a non-programmable, non-graphical calculator where necessary.
6. Diagrams are not necessarily drawn to scale.
7. An approved mathematical instrument set may be used.
8. Round off answers to two decimal places, unless otherwise stated.
9. Manage your time carefully. Use the mark allocation as a guide to how long you
should spend on each question.
10. Write neatly and ensure that your answers are clearly indicated.
Topics covered in this test
• Algebra
• Patterns and Sequences
• Functions and Graphs
• Trigonometry
• Analytical Geometry
• Probability
• Statistics
• Financial Mathematics
• Euclidean Geometry
• Mensuration (Surface Area and Volume)
Pg 1/ 6 www.summariessa.co.za Author: CHR SMI
Grade: 11 Subject: Mathematics Date: SEPTEMBER 2025
, QUESTION 1
1.1 A security company uses a sensor system to detect intruders. Two
independent sensors, X and Y, are installed – one at the main entrance and
the other at the back gate. If someone breaks in, the probability that the
person is detected by sensor X is 0.45 and the probability that the person
is detected by sensor Y is 0.65.
1.1.1 If there is an intruder, what is the probability that the intruder will be
detected by at least one sensor? (3)
1.1.2 Determine the probability that the intruder will not be detected at all.
(2)
1.2 At a certain college, a survey was conducted among 110 students about their
subject choices. The Venn diagram shows the results of the survey in terms
of:
o Natural Sciences (N)
o Accounting (R)
o Mathematics (W)
1.2.1 Show that .𝑥 = 8 (2)
Pg 2/ 6 www.summariessa.co.za Author: CHR SMI
Grade: 11 Subject: Mathematics Date: SEPTEMBER 2025
