Datum / Date: SEPTEMBER 2024
Tyd / Time: 3 hours
Punte / Marks: 150
Graad / 12
Grade:
Vak / Subject: Technical Mathematics
Vraestel 1
/Paper:
Naam en Van / Name and
Surname:
General instructions for the writing of exams:
1. Quickly scan through your entire paper.
2. Read the question twice before you begin.
3. Make sure to answer ALL questions.
4. Write neatly and legibly.
If you struggle too much with a question, move on to the next one and return
5
once you have answered all the other questions.
6. If the question calls for a longer answer, plan before you start writing.
7. For any answer longer than 1-2 words, always write in full sentences.
8. Make sure every point you make refers to the central question.
9. Use correct grammar, spelling, and punctuation to the best of your ability.
If you make a mistake, cross it out clearly with a single, neat line and write
10.
the correct answer instead.
Number the answers correctly according to the numbering system used in
11.
this question paper.
12. Present your answers according to the instructions for each question.
Good luck with your exam!
Topics covered in this paper:
Algebraic Equations and Inequalities • Calculus
Geometry and Area Calculations • Financial Mathematics
Formulas and Subject Manipulation • Projectile Motion
Number Systems • Integration
Logarithms and Exponentials
Complex Numbers
Functions and Graphs
Quadratic Functions
Bl / Pg www.summariessa.co.za Opsteller / CHR SMI
Author:
Graad / Vak / TECHNICAL Datum / Date:
12 SEPT 2024
Grade: Subject: MATHEMATICS
, Discriminants and Nature of Roots
QUESTION 1
1.1 Solve for x
1.1.1 −2 x ( x +a ) ( 3− x ) =0 (3)
1.1.2 2 x=6−x2 (4)
1.1.3 5 x ( x−2)≤ 0 (3)
1.2 The total area represented by die building premises given below is
21 units2 . The equation b=2 a=−7 represents the relationship of the
sides of the two squares.
Solve for x and y (dimensions of two squares) if:
y−2 x=−7 x 2+ xy+ y 2=21 (7)
1.3 The formula below represents the moment of inertia (E), with mass (M)
and length (L).
1 2
E= ML
12
1.3.1 Make L the subject of the formula. (2)
1.3.2 Calculate the value of L, if E=8.3 ×10−2 kg . m2 and M =1.6 ×10 3 kg .
(2)
1.4 Express 36 as a binary number. (2)
[23]
Bl / Pg www.summariessa.co.za Opsteller / CHR SMI
Author:
Graad / Vak / TECHNICAL Datum / Date:
12 SEPT 2024
Grade: Subject: MATHEMATICS
, QUESTION 2
2.1 Simplify the following WITHOUT the use if a calculator. (Show ALL
calculations.)
( )
−1
√ b3
2.1.1 −1 (3)
2
b
2.1.2 log 2 0.125−2 log 5 √ 5+log 4 1 (4)
2.1.3 ( √ 3− √ 2 )2 (2)
2.2 Solve for x
1
2.2.1 log x 125+ log 4 64−log 3 = log 2 128 (4)
3
2.2.2 21−2 x −243=0 (3)
2.3 The current in amps, A, of an alternating current (AC) circuit is given by:
4.5 ∟30 ° A .WITHOUT using a calculator, express the given current in
rectangular form.
(5)
2.4 Solve for x and y if:
7+i
x +iy= (5)
2−i
[26]
Bl / Pg www.summariessa.co.za Opsteller / CHR SMI
Author:
Graad / Vak / TECHNICAL Datum / Date:
12 SEPT 2024
Grade: Subject: MATHEMATICS
Tyd / Time: 3 hours
Punte / Marks: 150
Graad / 12
Grade:
Vak / Subject: Technical Mathematics
Vraestel 1
/Paper:
Naam en Van / Name and
Surname:
General instructions for the writing of exams:
1. Quickly scan through your entire paper.
2. Read the question twice before you begin.
3. Make sure to answer ALL questions.
4. Write neatly and legibly.
If you struggle too much with a question, move on to the next one and return
5
once you have answered all the other questions.
6. If the question calls for a longer answer, plan before you start writing.
7. For any answer longer than 1-2 words, always write in full sentences.
8. Make sure every point you make refers to the central question.
9. Use correct grammar, spelling, and punctuation to the best of your ability.
If you make a mistake, cross it out clearly with a single, neat line and write
10.
the correct answer instead.
Number the answers correctly according to the numbering system used in
11.
this question paper.
12. Present your answers according to the instructions for each question.
Good luck with your exam!
Topics covered in this paper:
Algebraic Equations and Inequalities • Calculus
Geometry and Area Calculations • Financial Mathematics
Formulas and Subject Manipulation • Projectile Motion
Number Systems • Integration
Logarithms and Exponentials
Complex Numbers
Functions and Graphs
Quadratic Functions
Bl / Pg www.summariessa.co.za Opsteller / CHR SMI
Author:
Graad / Vak / TECHNICAL Datum / Date:
12 SEPT 2024
Grade: Subject: MATHEMATICS
, Discriminants and Nature of Roots
QUESTION 1
1.1 Solve for x
1.1.1 −2 x ( x +a ) ( 3− x ) =0 (3)
1.1.2 2 x=6−x2 (4)
1.1.3 5 x ( x−2)≤ 0 (3)
1.2 The total area represented by die building premises given below is
21 units2 . The equation b=2 a=−7 represents the relationship of the
sides of the two squares.
Solve for x and y (dimensions of two squares) if:
y−2 x=−7 x 2+ xy+ y 2=21 (7)
1.3 The formula below represents the moment of inertia (E), with mass (M)
and length (L).
1 2
E= ML
12
1.3.1 Make L the subject of the formula. (2)
1.3.2 Calculate the value of L, if E=8.3 ×10−2 kg . m2 and M =1.6 ×10 3 kg .
(2)
1.4 Express 36 as a binary number. (2)
[23]
Bl / Pg www.summariessa.co.za Opsteller / CHR SMI
Author:
Graad / Vak / TECHNICAL Datum / Date:
12 SEPT 2024
Grade: Subject: MATHEMATICS
, QUESTION 2
2.1 Simplify the following WITHOUT the use if a calculator. (Show ALL
calculations.)
( )
−1
√ b3
2.1.1 −1 (3)
2
b
2.1.2 log 2 0.125−2 log 5 √ 5+log 4 1 (4)
2.1.3 ( √ 3− √ 2 )2 (2)
2.2 Solve for x
1
2.2.1 log x 125+ log 4 64−log 3 = log 2 128 (4)
3
2.2.2 21−2 x −243=0 (3)
2.3 The current in amps, A, of an alternating current (AC) circuit is given by:
4.5 ∟30 ° A .WITHOUT using a calculator, express the given current in
rectangular form.
(5)
2.4 Solve for x and y if:
7+i
x +iy= (5)
2−i
[26]
Bl / Pg www.summariessa.co.za Opsteller / CHR SMI
Author:
Graad / Vak / TECHNICAL Datum / Date:
12 SEPT 2024
Grade: Subject: MATHEMATICS
