Ocr Core 2 Review Sheet
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2
Sine and Cosine Rules
Area of a triangle = ½ x base x height = ½ a b sin C where C is angle between a and b
Sin A = Sin B = Sin C or even
a
=
b
=
c _
a
b
c
Sin A
Sin B
Sin C
a² = b² + c² – 2bc cos A Can swap letters around but angle A, B or C must be between
the lengths you know.
Logarithms
x
f(x) = b
where b = base, x = exponent.
x
y = b
and x = log
y
If using base 10 then can use calculator but otherwise
b
work out mentally. e.g If 2 = log
y then y = 3² = 9
3
x
Or x = log
64 then 64 = 4
so x = 3.
4
log (pq) = log p + log q
Split number into factor pairs then use this rule to simplify.
log (p/q) = log p – log q Split number into 2 divisible numbers then use this rule.
x
log (p
) = x log p
Useful when want x so log both sides then rearrange. Can use
calculator as log
10
Factors and remainders
If f(x) has (x – 3) is a factor, then f(3) = 0.
No remainder.
3
2
2
If f(3x
– 2x
+ x – 18) and x – 2 is a factor, then (x –2)(ax
+ bx + c) = 0
and compare coefficients to find a, b and c then solve for the quadratic.
If don’t know any factors, experiment with numbers to find one then do as above.
If not a factor, then substitute in, what’s left is the remainder.
3
2
3
2
e.g Is (x – 4) a factor of (3x
– 2x
+ x –6), f(4) = 3 x 4
- 2 x 4
+ 4 – 6 = 158 (remainder)
3
2
2
then (3x
+ 2x
+ x –6) = (x-4) (ax
+ bx + c) + R. Compare coefficients to find a, b and c.
This expression is the quotient.
Sequences
If goes up or down in steps of d = Arithmetic
If goes up by a common multiplier, e.g x 2, x 3 etc then Geometric
Arithmetic
U
= a + (r-1)d where d is common difference, a = first term, r = term number.
r
Can add common difference or subtract to move up or down the sequence.
L = a + (n-1)d
sum S = ½ n ( a + L)
or
S = ½ n (2a + (n – 1)d)
Geometric
Has a common multiplier called common ratio.
nd
st
U
= r U
where r = common ratio ( 2
term / 1
term or any other pairing) (term to term
i+1
i
formula)
i-1
U
= a r
where a = first term. (position to term formula)
i
th
Could use 4
term then i becomes 4 less as new starting point. e.g If r = 2 and U
= 8, then
4
th
8 – 4 – 1
3
8
term U
= 8 x 2
= 8 x 2
= 64.
8
Could find a by working backwards then use formula as normal.
n
Sum S
= a ( 1 – r
) and if n tends to infinity, then S
tends to
a
n
n
1 – r
1 – r
Binomial Theorem
n
Used to expand (x + y)
where n is a positive integer.
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