Mathematics 30 June 1999 Grade 12 Diploma Exam

Mathematics 30 Formula Sheet
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Page
The following information may be useful in writing this examination.
• The roots of the quadratic equation ax 2 + bx + c = 0 are
x =
–b ± √ b 2 – 4ac
2a
• The distance between two points (x 1
, y 1
) and (x 2
, y 2
) is
d = √ (x 2
– x 1
) 2 + (y 2
– y 1
) 2
Quadratic Relations
• e =
PF
PD
Fold and tear along perforation.
Trigonometry
• arc length a = rθ • csc A =
• sin 2 A + cos 2 A = 1 • sec A =
• 1 + tan 2 A = sec 2 A • cot A =
• 1 + cot 2 A = csc 2 A
• sin(A + B) = sin A cos B + cos A sin B
• sin(A – B) = sin A cos B – cos A sin B
1
sin A
1
cos A
cos A
sin A
Permutations and Combinations
• n
P r
=
n!
• n
C r
=
n!
(n – r)!
r!(n – r)!
• cos(A + B) = cos A cos B – sin A sin B
• cos(A – B) = cos A cos B + sin A sin B
• In the expansion of (x + y) n , the general term is t k + 1
= n
C k
x n – k y k
Sequences and Series
• t n
= a + (n – 1)d • t n
= ar n – 1
n[2a + (n – 1)d ]
a(r
• S n
= • S n
= n – 1)
, r ≠ 1
2
r – 1
a + t rt
• S n
= n n
• S n
= n
– a
r – 1
, r ≠ 1
2
Exponential and Logarithmic Functions
• log a
mn = log a
m + log a
n
m
• log a n
= log a
m – log a
n
• log a
m n = n log a
m