TECH MATHS P2 ANSWER BOOK JUNE 2024 Afr+Engl hlayiso.com

LEARNER’S NAME/ NAAM VAN LEERDER: CLASS / KLAS: NATIONAL SENIOR CERTIFICATE/ NASIONALE SENIORSERTIFIKAAT GRADE/GRAAD 12 JUNE/JUNIE 2024 TECHNICAL MATHEMATICS P2/TEGNIESE WISKUNDE V2 SPECIAL ANSWER BOOK/SPESIALE ANTWOORDEBOEK HOD/HVD DISTRICT/DISTRIK PROVINCIAL/PROVINSIAAL QUESTION/VRAAG MARKS/PUNTE (Level 1 mod./Vlak 1 mod.) (Level 2 mod./Vlak 2 mod.) (Level 3 mod./Vlak 3 mod.) 1 2 3 4 5 6 7 8 9 10 11 TOTAL/TOTAAL This special answer book consists of 25 pages./ Hierdie spesiale antwoordeboek bestaan uit 25 bladsye.

2 TECHNICAL MATHEMATICS P2/TEGNIESE WISKUNDE V2 (EC/JUNE/JUNIE 2024) FOLLOW THESE INSTRUCTIONS CAREFULLY VOLG HIERDIE INSTRUKSIES NOUKEURIG 1. Answer ALL questions in the spaces 1. Beantwoord ALLE vrae in die ruimtes wat provided. voorsien is. 2. No pages may be torn from this answer 2. Geen bladsye mag uit hierdie book. ANTWOORDEBOEK geskeur word nie. 3. Answers must be written in black/blue 3. Skryf die antwoorde so duidelik moontlik ink as distinctly as possible. Do not write met swart/blou ink. Moenie in die kantlyn in the margins. skryf nie. 4. Indicate the questions you have 4. Dui die vrae wat jy beantwoord het aan op answered by drawing a circle around the die voorblad van die ANTWOORDEBOEK relevant numbers on the front cover of waar die punte aangebring is, deur ʼn the ANSWER BOOK where marks are kringetjie te trek om die nommers van die to be recorded. vrae wat jy beantwoord het. 5. Draw a line through any work/rough 5. Trek ʼn netjiese lyn deur enige werk/rofwerk work that must not be marked. wat nie nagesien moet word nie. 6. In the event that you use the additional 6. Ingeval jy die bykomende ruimte wat space provided: voorsien word, gebruik: 6.1 Write down the number of the 6.1 Skryf die nommer van die vraag neer. question. 6.2 Leave a line and rule off after your 6.2 Laat ʼn lyn oop en trek ʼn lyn na jou answer. antwoord. Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

(EC/JUNE/JUNIE 2024) TECHNICAL MATHEMATICS P2/TEGNIESE WISKUNDE V2 3 QUESTION/VRAAG 1 Solution/Oplossing Marks/ Punte 𝑦 A (15 ; 18) B (23 ; 5) 𝛼 𝛽 𝑥 O 1.1 (4) 1.2 (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

4 TECHNICAL MATHEMATICS P2/TEGNIESE WISKUNDE V2 (EC/JUNE/JUNIE 2024) Solution/Oplossing Marks/ Punte 1.3 (4) 1.4 (5) [16] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

(EC/JUNE/JUNIE 2024) TECHNICAL MATHEMATICS P2/TEGNIESE WISKUNDE V2 5 QUESTION/VRAAG 2 Solution/Oplossing Marks/ Punte 2.1 𝑦 𝑥 0 A(− 2 ; − 3) 2.1.1 (1) 2.1.2 (4) 2.1.3 (2) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

6 TECHNICAL MATHEMATICS P2/TEGNIESE WISKUNDE V2 (EC/JUNE/JUNIE 2024) Solution/Oplossing Marks/ Punte 2.2 (3) [10] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

(EC/JUNE/JUNIE 2024) TECHNICAL MATHEMATICS P2/TEGNIESE WISKUNDE V2 7 QUESTION/VRAAG 3 Solution/Oplossing Marks/ Punte 3.1 𝑦 A(a ; ξ3 ) 𝜃 𝑥 O 3.1.1 (3) 3.1.2 (1) 3.1.3 (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

8 TECHNICAL MATHEMATICS P2/TEGNIESE WISKUNDE V2 (EC/JUNE/JUNIE 2024) 3.2 (4) [11] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

(EC/JUNE/JUNIE 2024) TECHNICAL MATHEMATICS P2/TEGNIESE WISKUNDE V2 9 QUESTION/VRAAG 4 Solution/Oplossing Marks/ Punte 4.1 sin(180° − 𝜃) tan(180° + 𝜃)sin (270°) cos(360° − 𝜃) tan(180° − 𝜃) (6) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

10 TECHNICAL MATHEMATICS P2/TEGNIESE WISKUNDE V2 (EC/JUNE/JUNIE 2024) 4.2 1 + cos 𝐵 (cosec B − cot 𝐵)2 = 1 − cos 𝐵 (6) [12] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

(EC/JUNE/JUNIE 2024) TECHNICAL MATHEMATICS P2/TEGNIESE WISKUNDE V2 11 QUESTION/VRAAG 5 Solution/Oplossing Marks/ Punte 5.1 (1) 5.2 (1) 5.3 (8) 5.4.1 (2) 5.4.2 (2) [14] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

12 TECHNICAL MATHEMATICS P2/TEGNIESE WISKUNDE V2 (EC/JUNE/JUNIE 2024) QUESTION/VRAAG 6 Solution/Oplossing Marks/ Punte 6.1 (1) 6.2 B 48 𝑚 1C 2  A 7 9 D 6.2.1 (2) 6.2.2 (2) 6.2.3 (4) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

(EC/JUNE/JUNIE 2024) TECHNICAL MATHEMATICS P2/TEGNIESE WISKUNDE V2 13 Solution/Oplossing Marks/ Punte 6.2.4 (2) 6.2.5 (3) [14] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

14 TECHNICAL MATHEMATICS P2/TEGNIESE WISKUNDE V2 (EC/JUNE/JUNIE 2024) QUESTION/VRAAG 7 Solution/Oplossing Marks/ Punte Q S 12 1 2 T 21 34 𝑥 1 2 2 1 3 P O 7.1 (6) 7.2 (5) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

(EC/JUNE/JUNIE 2024) TECHNICAL MATHEMATICS P2/TEGNIESE WISKUNDE V2 15 Solution/Oplossing Marks/ Punte 7.3 (3) [14] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

16 TECHNICAL MATHEMATICS P2/TEGNIESE WISKUNDE V2 (EC/JUNE/JUNIE 2024) QUESTION/VRAAG 8 Solution/Oplossing Marks/ Punte Q 1 P ∥ 3 2 1 2 34 𝑥 ∥ T 2 2 3 1 3 1 V R S 8.1 (8) 8.2 (1) 8.3 (5) [14] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

(EC/JUNE/JUNIE 2024) TECHNICAL MATHEMATICS P2/TEGNIESE WISKUNDE V2 17 QUESTION/VRAAG 9 Solution/Oplossing Marks/ Punte P C A D Q ∣ ∣ R B 9.1 (3) 9.2 (3) 9.3 (6) [12] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

18 TECHNICAL MATHEMATICS P2/TEGNIESE WISKUNDE V2 (EC/JUNE/JUNIE 2024) QUESTION/VRAAG 10 Solution/Oplossing Marks/ Punte 10.1 (2) 10.2 (5) 10.3 (3) 10.4 (3) 10.5 (2) [15] Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

(EC/JUNE/JUNIE 2024) TECHNICAL MATHEMATICS P2/TEGNIESE WISKUNDE V2 19 QUESTION/VRAAG 11 Solution/Oplossing Marks/ Punte 11.1 FIGURE/FIGUUR A FIGURE/FIGUUR B E C D 11.1.1 (3) 11.1.2 (3) 11.1.3 (3) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

20 TECHNICAL MATHEMATICS P2/TEGNIESE WISKUNDE V2 (EC/JUNE/JUNIE 2024) Solution/Oplossing Marks/ Punte 11.2 (5) Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

(EC/JUNE/JUNIE 2024) TECHNICAL MATHEMATICS P2/TEGNIESE WISKUNDE V2 21 Solution/Oplossing Marks/ Punte 11.3 7 cm 6,5 cm 𝑥 5 cm 7,5 cm 6 cm 4 cm 3 cm (4) [18] TOTAL/TOTAAL: 150 Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

22 TECHNICAL MATHEMATICS P2/TEGNIESE WISKUNDE V2 (EC/JUNE/JUNIE 2024) Additional Space/Addisionele Ruimte Marks/ Punte Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

(EC/JUNE/JUNIE 2024) TECHNICAL MATHEMATICS P2/TEGNIESE WISKUNDE V2 23 Additional Space/Addisionele Ruimte Marks/ Punte Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

24 TECHNICAL MATHEMATICS P2/TEGNIESE WISKUNDE V2 (EC/JUNE/JUNIE 2024) Additional Space/Addisionele Ruimte Marks/ Punte Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief

(EC/JUNE/JUNIE 2024) TECHNICAL MATHEMATICS P2/TEGNIESE WISKUNDE V2 25 Additional Space/Addisionele Ruimte Marks/ Punte Copyright reserved/Kopiereg voorbehou Please turn over/Blaai om asseblief