ADJUSTED MEMORANDUM
JUNE EXAMINATION 2025
GRADE 12
MATHEMATICS
TASK 5.1
PAPER 1/2
TIME: 3 hours TOTAL: 150
Page 1 of 15
, June Examination 2025
G12 ~ Mathematics
ADJUSTED MEMORANDUM
ANSWER / ANTWOORD MG / MR M/P L/V
QUESTION / VRAAG 1
6𝑥𝑥 2 − 5𝑥𝑥 = 4 SF (penalise if =0
6𝑥𝑥 2 − 5𝑥𝑥 − 4 = 0 not shown /
(2𝑥𝑥 + 1)(3𝑥𝑥 − 4) = 0 penaliseer indien =0
1 4 nie gewys nie) F
𝑥𝑥 = − 2 or / of 𝑥𝑥 = A
3
A
OR / OF
1.1.1 4 1
6𝑥𝑥 2 − 5𝑥𝑥 − 4 = 0 OR / OF
−(−5) ± �(−5)2 − 4(6)(−4)
𝑥𝑥 = SF
2(6)
CFS
1 4
𝑥𝑥 = − 2 or / of 𝑥𝑥 = A
3
A
𝑥𝑥 2 − 3𝑥𝑥 − 5 = 0 CFS
−(−3) ± �(−3)2 − 4(1)(−5)
𝑥𝑥 = A
2(1) A
1.1.2 3 1
𝑥𝑥 = −1,193 or / of 𝑥𝑥 = 4,193
Penalise only ONCE for rounding /
Penaliseer slegs EEN keer vir afronding
�2(𝑥𝑥 − 3) + 15 = 𝑥𝑥 + 12 Isolate square root
/ isoleer wortel
�2(𝑥𝑥 − 3) = 𝑥𝑥 + 12 − 15 Square BOTH
2 sides / Kwadreer
��2(𝑥𝑥 − 3)� = (𝑥𝑥 − 3)2
BEIDE kante
1.1.3 SF 4 3
2(𝑥𝑥 − 3) = 𝑥𝑥 2 − 6𝑥𝑥 + 9
BA
𝑥𝑥 2 − 8𝑥𝑥 + 15 = 0
(𝑥𝑥 − 5)(𝑥𝑥 − 3) = 0
𝑥𝑥 = 5 or / of 𝑥𝑥 = 3
5𝑥𝑥 (𝑥𝑥 + 2) < 0 5𝑥𝑥 > 0
5𝑥𝑥 > 0 𝑥𝑥 + 2 < 0
1.1.4 CV 4 4
∴ (𝑥𝑥 + 2) < 0 N
𝑥𝑥 < −2 OR / OF 𝑥𝑥 ∈ (−∞; −2)
Page 3 of 15 © Impaq
JUNE EXAMINATION 2025
GRADE 12
MATHEMATICS
TASK 5.1
PAPER 1/2
TIME: 3 hours TOTAL: 150
Page 1 of 15
, June Examination 2025
G12 ~ Mathematics
ADJUSTED MEMORANDUM
ANSWER / ANTWOORD MG / MR M/P L/V
QUESTION / VRAAG 1
6𝑥𝑥 2 − 5𝑥𝑥 = 4 SF (penalise if =0
6𝑥𝑥 2 − 5𝑥𝑥 − 4 = 0 not shown /
(2𝑥𝑥 + 1)(3𝑥𝑥 − 4) = 0 penaliseer indien =0
1 4 nie gewys nie) F
𝑥𝑥 = − 2 or / of 𝑥𝑥 = A
3
A
OR / OF
1.1.1 4 1
6𝑥𝑥 2 − 5𝑥𝑥 − 4 = 0 OR / OF
−(−5) ± �(−5)2 − 4(6)(−4)
𝑥𝑥 = SF
2(6)
CFS
1 4
𝑥𝑥 = − 2 or / of 𝑥𝑥 = A
3
A
𝑥𝑥 2 − 3𝑥𝑥 − 5 = 0 CFS
−(−3) ± �(−3)2 − 4(1)(−5)
𝑥𝑥 = A
2(1) A
1.1.2 3 1
𝑥𝑥 = −1,193 or / of 𝑥𝑥 = 4,193
Penalise only ONCE for rounding /
Penaliseer slegs EEN keer vir afronding
�2(𝑥𝑥 − 3) + 15 = 𝑥𝑥 + 12 Isolate square root
/ isoleer wortel
�2(𝑥𝑥 − 3) = 𝑥𝑥 + 12 − 15 Square BOTH
2 sides / Kwadreer
��2(𝑥𝑥 − 3)� = (𝑥𝑥 − 3)2
BEIDE kante
1.1.3 SF 4 3
2(𝑥𝑥 − 3) = 𝑥𝑥 2 − 6𝑥𝑥 + 9
BA
𝑥𝑥 2 − 8𝑥𝑥 + 15 = 0
(𝑥𝑥 − 5)(𝑥𝑥 − 3) = 0
𝑥𝑥 = 5 or / of 𝑥𝑥 = 3
5𝑥𝑥 (𝑥𝑥 + 2) < 0 5𝑥𝑥 > 0
5𝑥𝑥 > 0 𝑥𝑥 + 2 < 0
1.1.4 CV 4 4
∴ (𝑥𝑥 + 2) < 0 N
𝑥𝑥 < −2 OR / OF 𝑥𝑥 ∈ (−∞; −2)
Page 3 of 15 © Impaq
