TECHNICAL MATHEMATICS PAPER 1
GRADE 12
NATIONAL SENIOR CERTIFICATE
MEMORANDUM
NOVEMBER 2019
MARKING CODES | |
A | Accuracy |
AO | Answer only |
CA | Consistent accuracy |
M | Method |
R | Rounding |
NPR | No penalty for rounding |
NPU | No penalty for unit |
S | Simplification |
F | Correct formula |
SF | Substitution in correct formula |
MARKS: 150
These marking guidelines consist of 24 pages.
NOTE:
QUESTION 1
1.1.1 | p (x) = 2x2 - 8 OR | common factor A OR |
1.1.2 | p(x) = 2 (x - 2/9) (x + 2/9) = 0 OR | both values of CA OR |
1.2.1 | (3x -5)(x + 2) = -13 3x2 + x - 10 + 13 = 0 OR OR OR | standard form A √−35 = √35 i CA both x-values CA |
1.2.2 | (4 – x) (x + 3) < 0 OR (x – 4 ) (x + 3) > 0 x < -3 or x > 4 OR | both critical values A Accept Number Line (3) |
1.3 | y = 3x - 8 OR OR | substitution A S CA factors or formula CA both x-values CA both y-values CA OR substitution A standard form CA factors/ formula CA both y-values CA both x-values CA (6) |
1.4.1 | V = I x Z | dividing by A (1) |
1.4.2 | I = V | substitution CA (5) |
1.5 | 1 0 12 OR | M A OR [25] |
QUESTION 2
2.1.1 | G = √ p + 1 2 p -1 = 0 | p = ½ A |
2.1.2 | p +1 = 0 | p = -1 A |
2.2 | x2 - k + 4 = 5x 25 + 4k -16 ≥ 0 | standard form A (5) [7] |
QUESTION 3
3.1 | (- 2 4 √a3 )8 | 256 A |
3.2 | log2 (3x - 2) + log20,5 = 3 OR OR OR OR | log2 0, 5 =-1 A OR OR log property A correct value CA correct value CA OR correct value CA |
3.3 | log 0, 6 OR | exp. form A OR (5) |
3.4.1 | V = 2(cos 240° + i sin 240°) | Value of V 1) |
3.4.2 | V = 2(cos 240°+ i sin 240°) OR OR | CA from Q/3.4.1 OR |
3.5 | m + ni = 2(6 - 4i)- (- 7i) OR | value of m A OR |
QUESTION 4
4.1.1 | ( x - 5)( x + 3) = 0 | both values of A |
4.1.2 | q (x) = 12 - 2 OR | y = 0 A OR CA (2) AO: Full marks |
4.1.3 | x = 5 - 3 = 1 OR TP( 1 ; -16) OR | M CA OR OR |
4.1.4 | y = -2 | y = -2 |
4.1.5 | Graph: Graph q: | |
4.2.1 | d = -4 | value of A |
4.2.2 | h(x) = ax - 4 | substitution CA |
4.2.3 | h ( 0 ) = a0 - 4 OR h(0) = (0, 5)0 - 4 T ( 0 ; - 3) | x = 0 A |
4.2.4 | y∈ [ - 3 ; 0] OR - 3 ≤ y ≤ 0 | range CA (1) |
4.2.5 | p ( x ) = -√ 9 - x2 | equation of CA equation of CA (2) AO: Full marks |
4.2.6 | 0 < x ≤ 3 OR x ∈ (0 ; 3) | endpoints A [25] |
QUESTION 5
5.1.1 | R11 000 | new value A (1) |
5.1.2 | A = R5 500 P = R11 000 n = 5 i = ? | SF CA AO: Full marks (3) |
5.2 # | A = P( 1 + i )n OR | SF A OR |
5.3 | Value of the investment after initial deposit: Value of the investment after adding R95 000 : Value of the investment after change in interest rate: Yes she has accumulated sufficient funds. OR OR OR OR 2 years: A = R490705, 2026 (1+ 7.5 %)4 x 12 OR A2 = R95 000 ( 1+ 0, 067)2x4 | SF A value of i and n A OR M A OR M SF A OR OR NOTE: 1) Max. 4 marks if Simple Interest is used.
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QUESTION 6
6.1 | f ( x ) = 5 - ½ x | definition A AO: ONLY 1 mark | |
No penalty for notation in the remaining questions | |||
6.2.1 | f ( x ) = a3 - 0, 5x3 - x-1 | derivative of a3 A | |
6.2.2 | x½ A | ||
6.3.1 | xy + 2x3 = 7x6 | M A | |
6.3.2 | y = 7x5 - 2x2 | 35x4 CA | |
6.4.1 | P(300) = 0,8(300)2 - 200(300) | profit A (1) | |
6.4.2 | P(x) = 0,8 x2 - 200x OR | factors M A OR AO: Full marks (2) | |
6.4.3 | P(x) = 0,8 x2 - 200x | derivative A [22] |
QUESTION 7
7.1 | g ( x ) = 9x + 18 OR | 0 = 9x + 18 A | ||
7.2 | f ( x) = ( x + 2)( x - 3)( x - 3) OR OR | repeated factor A OR d = 18 A OR d = 18 | ||
7.3 | f ( x ) = x3 - 4x2 - 3x + 18 | f / (x ) CA f / (x ) = 0 CA factors/formula CA correct value of x CA R coordinates CA (5) | ||
7.4.1 | y = 500 OR y ≈ 18, 52 27 | equation CA | ||
7.4.2 | x > - 2 OR x ∈ ( - 2 ; ∞) | correct inequality A (1) | ||
7.4.3 | - 1 < x < 3 OR x ∈ (-1/3 ; 3) | critical values CA [15] |
QUESTION 8
8.1 | h = ( 66 - 2x - x) cm | height A (1) |
8.2 | V (in cm3 ) = πr 2h + ½ (4/3πr3) | F A |
8.3 | V( in cm3 ) = 66πx2 - 7/3πx3 | derivative CA correct value of x CA (4) |
8.4 | V(in cm3) = 66πx2 - 7πx 3 | SF CA NPR (2) [10] |
QUESTION 9
9.1.1 | ∫mxpdx | C A OR |
9.1.2 | - 2x1 + C CA (4) | |
9.2 | area notation using integral A correct positive value of the bounded area CA OR area notation using integral A OR area notation using integral A [12] | |
TOTAL:150 |