SUBJECT Mathematics PAPER AP Maths Paper 1 GRADE 12 DATE 3 July 2018 EXAMINER Mr Benecke MARKS 200 NAME Memo MODERATOR Mrs Povall TEACHER DURATION 2 hours QUESTION NO DESCRIPTION MAXIMUM MARK ACTUAL MARK 1 Algebra 43 2 Limits 23 3 Split Graphs 29 4 Trigonometry 10 5 Differentiation 20 6 Graphs 25 7 Absolute Graphs 11 8 Integration 22 9 Newton-Raphson 7 10 Application 10 TOTAL 200
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SUBJECT AP Maths Paper 1 Mathematics PAPER GRADE 12 …
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SUBJECT Mathematics PAPER AP Maths Paper 1
GRADE 12 DATE 3 July 2018
EXAMINER Mr Benecke MARKS 200
NAME Memo MODERATOR Mrs Povall
TEACHER DURATION 2 hours
QUESTION NO
DESCRIPTION MAXIMUM MARK
ACTUAL MARK
1 Algebra 43
2 Limits 23
3 Split Graphs 29
4 Trigonometry 10
5 Differentiation 20
6 Graphs 25
7 Absolute Graphs 11
8 Integration 22
9 Newton-Raphson 7
10 Application 10
TOTAL 200
Grade 12 2 of 19 Mathematics Paper AP Maths Paper 1
QUESTION 1 43 MARKS
a) Solve for 𝑥:
1) 𝑥 = |2| (1)
𝑥 = 2
2) |𝑥| = 2 (1)
𝑥 = ±2
3) |𝑥 + 3| = 1 +12
|𝑥+3| (7)
𝐿𝑒𝑡 𝑘 = |𝑥 + 3|
𝑘 = 1 +12
𝑘
𝑘2 − 𝑘 − 12 = 0
(𝑘 − 4)(𝑘 + 3) = 0
|𝑥 + 3| = 4 or |𝑥 + 3| = −3
N/A
𝑥 + 3 = 4 or −𝑥 − 3 = 4
𝑥 = 1 or 𝑥 = −7
Grade 12 3 of 19 Mathematics Paper AP Maths Paper 1
4) 1𝑥. 2𝑥. 3𝑥 = 4 (4)
6𝑥 = 4
𝑥 = log6 4
𝑥 = 0,77
5) 𝑥2
4≥ 1 (5)
𝑥2
4−
4
4≥ 0
𝑥2−4
4≥ 0
(𝑥 + 2)(𝑥 − 2) ≥ 0
𝑥 ≤ −2 𝑜𝑟 𝑥 ≥ 2
6) 𝑥3√𝑥−1
2𝑥−3≤ 0 (6)
1 ≤ 𝑥 <3
2
Grade 12 4 of 19 Mathematics Paper AP Maths Paper 1
b) One root of the equation 𝑧3 + 𝑧 + 𝑘 = 0 is 1 − 2𝑖, find all the other roots. (9)
(1 − 2𝑖)3 + (1 − 2𝑖) + 𝑘 = 0
(−3 − 4𝑖)(1 − 2𝑖) + 1 − 2𝑖 + 𝑘 = 0
−3 + 6𝑖 − 4𝑖 − 8 + 1 − 2𝑖 + 𝑘 = 0
𝑘 = 10
𝑧 = 1 + 2𝑖 𝑖𝑠 𝑎𝑙𝑠𝑜 𝑎 𝑟𝑜𝑜𝑡
(𝑧 − 1 − 2𝑖)(𝑧 − 1 + 2𝑖) = 𝑧2 − 2𝑧 + 5
(𝑧2 − 2𝑧 + 5)(𝑧 + 2) = 0
𝑧 = −2 𝑖𝑠 𝑎 𝑟𝑜𝑜𝑡
Grade 12 5 of 19 Mathematics Paper AP Maths Paper 1