Grade 12 / A P Mathematics / 3 hours
Ex: SC / Memorandum / 300 marks
Section A – Algebra and Calculus
Question 1
1.1
(4)
1.2
or
(since )(6)
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Question 2
2.1If , which is divisible by
Assume is divisible by
Prove is divisible by
Proof:
which is divisible by since each term is divisible by
But is divisible by if , therefore true if , etc. (12)
2.2Width
(12)
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Question 3
3.13.1.1
or
or (4)
3.1.2
or
or or no solution(5)
3.1.3
or
or or no solution(5)
3.23.2.1(2)
3.2.23.2.2(a)
(4)
3.2.2(b)
(4)
3.2.2(c)
(4)
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Question 4
4.14.1.1
If :
If :
(8)
4.1.2
(8)
4.2 and
and (8)
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Question 5
, and
5.1
(5)
5.2
:
(6)
5.3
If If
(5)
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Question 6
and
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Question 7
7.17.1.1
(4)
7.1.2
(4)
7.2
(10)
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Question 8
8.1.
Let
(4)
8.28.2.1 ()
(4)
8.2.2(2)
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Question 9
9.19.1.1
(8)
9.1.2Let
(8)
9.1.3Let and
(10)
9.29.2.1
point of intersection
(8)
9.2.2
(6)
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Question 10
units2
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Question 11
11.1
or (9)
11.2
(4)
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Section B – Matrices and Graph Theory
Question 12
12.112.1.1Rotate 90° clockwise about the origin.(3)
12.1.2Stretch scale factor , invariant axis.(3)
12.212.2.1(2)
12.2.2(2)
12.2.3(2)
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Question 13
13.1
(6)
13.2
(4)
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Question 14
14.1
(10)
14.2
(10)
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Question 15
15.1EB; EH; AB; HI; AD; DG; EF; FC(8)
15.2 km(2)
15.3(4)
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Question 16
16.1 minutes(12)
16.2A; D; F; I; J(2)
16.3
(6)
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Question 17
17.1Odd nodes: A; G; H; B
AG + HB = 90 + 210 = 300
AH + GB = 150 + 210 = 360
AB + GH = 180 + 165 = 345
Double AG and HB
Length = m(10)
17.217.2.1(2)
17.2.2(2)
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Question 18
18.118.1.1(2)
18.1.2(2)
18.1.3(2)
18.2(4)
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TOTAL MARKS: 300
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