Ocr Core 2 Review Sheet Page 2
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1
2Use Pascal’s triangle to give the coefficients and remember that the powers drop for the x’s
n
st
n-1
nd
n
and increase for the y’s. (e,g from x
for the 1
term to x
y for the 2
etc to end with y
.)
Easiest to write out sequence using x and y’s then substitute in the actual terms afterwards
remembering to apply the power to the whole expression.
n )x
n )x
n )y
n ) =
n )x
n
n
n-1
n-2
2
n
n
(x+y)
= (
+ (
y + (
y
= … +(
where (
C
=
n!
r
1
2
n
r
0
n
(If want rth term of the nth row of Pascal’s triangle use
C
)
r!(n – r)!
r
Use the formula booklet for full formula and just substitute in numbers.
Trigonometry
Tangent Curve
Cosine Curve
Sine Curve
1.5
1.5
10
1
1
5
0.5
0.5
0
0
45 90
180
270
360
0
45 90
180
270
360
45 90
180
270
360
-0.5
-0.5
-5
-1
-1
-10
-1.5
-1.5
Sine
Repeats every 360º. Supplementary angle at 180º - θ.
Cosine
Repeats every 360º. Supplementary angle at 360º - θ
Tangent
Repeats every 180º.
2
2
Tan θ = sin θ
sin
θ + cos
θ = 1
cos θ
If finding sin 2 θ then let 2 θ = α and find solution for α then ½ your answers.
Remember that range of possible values for α is twice as big (e.g. 0 < θ < 360º becomes
0 < α < 720º) as will halve the solutions as θ = α ÷ 2.
Radians
2
2 π = 360º
Arc Length s = r θ Area of sector A = ½ r
θ (Must be in radians)
π = 180º
Often better to calculate angle in degrees then change to a fraction of π especially when
using trigonometry.
Integration
Opposite of differentiation.
n
n+1
∫ x
dx =
1
x
+ c
If there is a coefficient in front of the x, then it just stays their
n+1
and multiples the answer. C = arbitrary constant.
If you know a point on the curve, then can integrate the gradient formula f ’(x) to find the
formula for the function and use coordinates to find the constant c.
Integrating a function also finds the area beneath the curve between 2 points and is a
definite integral. If the limits are x=3 and x = 1 then integrate with respect to x and substitute
in the 2 x values (3 and 1) and subtract.
If 2 curves and want area between them, can find the areas under each separately then
subtract or subtract the equations first, then integrate and substitute in.
Trapezium Rule
Used if you cannot integrate the function. Split curve up into separate trapeziums of equal
width and find approximate area for each. Number of intervals (separate trapeziums will be
given.) Area of a trapezium = ½ h (y
+ y
) where h = x
– x
.
0
1
1
0
Can use the formula area = ½ h{(y
+ y
) + 2( y
+ y
+ … + y
)} where h = x
– x
and
0
n
1
2
n-1
n
0
n = number of intervals. (x
and x
are the upper and lower limits).
n
n
0
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