Download sin sin sin a b c A B C = = 2 cos ba c bc A = + -

4b1 Maths Homework
Set Wednesday 16/11/16. Due on or before Wednesday 23rd November 2016.
CALCULATORS WILL BE NEEDED
Study Support available after school on WEDNESDAY with Mr Watkins
(also MONDAY with Mr Davidson and THURSDAY with Miss Logan or Miss Mesouani)
If you don’t do homework properly, you will fail your maths exam. Harsh, but
true.
Make sure you try all the questions and ask me for help if you need to.
Not attempting one of the questions means you’ve not done the homework
properly.
Formulae Sheet
Sine rule:
a
b
c


sin A sin B sin C
Cosine rule:
a 2  b2  c 2  2bc cos A
Area of a triangle:
1
A  ab sin C
2
Standard deviation:
1)
s
n 1
2
where n is the sample size
Find the area of this
triangle. (2)
2)
3)
 (x  x )
Use the cosine rule to find the length BC
in this triangle. (3)
Use the sine rule to find the size of the
angle y in this triangle. (3)
4)
The diagrams below show 2 directed line segments a and b.
b
a
Using the squares in your jotter, draw the resultant of a + 3b . (3)
5)
The diagram below shows a square based pyramid of height 5 cm. Square
OABC has a side length of 4 cm. The coordinates of A are (4, 0, 0). C lies
on the y-axis.
z
D
y
C
B
x
O
A (4, 0, 0)
Write down the coordinates of C. (1)
6)
Three forces are acting on an object. Each force is represented by three
vectors a, b and c as given below.
5
 4
 
 
a   1 , b   5  ,
 
 
1
 2 
 3 
 
c 0 
 
 7 
Find the resultant force. (2)
7)
5
2
Calculate 2u  v .
8)
 4
.
3

 
Two vectors are given by u    and v  
(3)
A diamond ring costs £80 000. Its value appreciates by 2·5% each year.
Find the value of the ring after 6 years. (3)
9)
Find the area of this rectangle as either a topheavy fraction or a mixed
number: (2)
3
6 cm
5
4
2
cm
7
10)
In a sale, 35% is taken off the price of a camera.
In the sale, the camera costs £193·05.
What did it cost before the sale? (3)
11)
a) The price of vegetables in five supermarkets were 76p, 82p, 77p, 74p and
76p. Calculate the mean and standard deviation. (4)
b) The price of milk in five supermarkets had a mean price of 54p and a
standard deviation of 3·2. Make two valid statements comparing the price
of vegetables and the price of milk. (#2.2)