1.
(a)
correct substitution into formula for E(X)
(A1)
e.g. 0.05 240
E(X) =12
(b)
A1
2
N2
evidence of recognizing binomial probability (may be seen in part (a)
(M1)
240
15
225
e.g. 15 (0.05) (0.95) , X ~ B(240,0.05)
P(X =15) = 0.0733
(c)
A1
2
N2
P(X 9)
1.
(a)
correct end points
(A1)(A1)
max = 27, min = 4
range = 23
(b)
Graph 3
A1
3
N3
A2
2
N2
[5]
2.
(a)
fx = 1(2) + 2(4) + . + 7(4), fx = 146 + 5x (seen anywhere)
fx
evidence of substituting into mean =
f
A1
(M1)
correct equation
146 5 x
e.g. 34 x = 4.5, 1
1.
A box holds 240 eggs. The probability that an egg is brown is 0.05.
(a)
Find the expected number of brown eggs in the box.
(2)
(b)
Find the probability that there are 15 brown eggs in the box.
(2)
(c)
Find the probability that there are at least 10 bro
Topic5VectorsDay3student
December09,2013
VECTORS IN SPACE
To be able to work in 3 space, we will set up a grid so that we can discuss points &
vectors
We have our origin as well as 3 mutually perpendicular axes called the xaxis, yaxis
and the zaxis
We wil
Topic5VectorsDay5Vectoreqofaline
December11,2013
VECTOR EQUATION OF A LINE
Linear Equations have been written as:
(1) y = mx + b
(2) y y1 = m(x x1)
(3) Ax + By + C = 0
(slopeintercept form)
(pointslope form)
(standard form)
But now with our look at vec
1.
6
0
6
The circle shown has centre O and radius 6. OA is the vector , OB is the vector
0
5
and OC is the vector,
11 .
y
C
B
(a)
O
A
x
Verify that A, B and C lie on the circle.
(3)
(b)
Find the vector AC .
(2)
(c)
Using an appropriate scal
1.
A scientist has 100 female fish and 100 male fish. She measures their lengths to the nearest cm.
These are shown in the following box and whisker diagrams.
(a)
Find the range of the lengths of all 200 fish.
(3)
(b)
Four cumulative frequency graphs are
Topic5VectorsDay4Student
December10,2013
PARALLELISM
Two nonzero vectors are parallel if and only if one is a scalar multiple of the
other.
If a is parallel to b , then there exists a scalar k such that
|k| is the modulus of k, where |a| is the length of
1.
OA = 6
A is on the circle
(A1)
OB = 6
(a)
B is on the circle.
(A1)
C is on the circle.
(A1)
5
OC
11
= 25 11
=6
(b)
AC OC OA
5 6
=
11 0
1
=
11
(c)
cos OAC
6 1
.
0 11
=
6 1 11
6
=
6 12
=
1
2 3
(M1)
(A1)
AO AC
AO AC
3
6
6 2 ( 12