Download S4 HOMEWORK 5A 1. 2. (a) Simplify i) ii) (b) Express without

S4 HOMEWORK 5A
1.
The number of Golden Eagles in Scotland has increased by 17.5%
over the last ten years. If there are now 987 Golden Eagles, how
many were there ten years ago?
2.
3.
i)
2x  14
x  4x  21
1
5

2
3x 12x
(a)
Simplify
ii)
(b)
Express without brackets
(c)
Change the subject of the formula to n
(a)
Solve the equation
(b)
A sequence of numbers can be grouped and added together
as shown.
2
1 3 2 
(3)
(3,3)
2
(2)
nE  T(r  Rn)
(4)
(1)
2n  32
The sum of 2 numbers:
(1 + 2) = 4 - 1
The sum of 3 numbers:
(1 + 2 + 4) = 8 - 1
The sum of 4 numbers: (1 + 2 + 4 + 8) = 16 – 1
(1)
Find a similar expression for the sum of 5 numbers.
(c)
4.
Find a formula for the sum of the first n numbers of this sequence.
(2)
The diagram shows the position of a student as she views the top of
a tower.
T
From position A, the angle of
elevation to T at the top of the tower
is 69O.
The distance AB is 17.4 metres and
the height of the student to eye level
is 1.5 metres.
Find the height of the tower.
B
(4)
5.
A sensor in a security system covers
a horizontal area of the shape of a
sector of a circle of radius 15m.
The area of the sector is 200 square
metres.
Find the length of the arc of the
(4)
sector.
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