Maths higher Paper 1 2001
Please note the marks shown here are not the official marking scheme this
will not be confirmed for about 2 weeks! They should however give you a good
idea as to your actual mark.
The solutions we hope are as accurate as possible; let us know of any errors.
Question 1
(1)(A)
This was basically an identity
just multiply it out and set the like powers of x equal to each other.
Solution a = 2, b= -10. (10
marks)
(B)
Sub in x = 1, x= -2 to find m and n. (20)
Solution, m
= -5, n= 1.
© This is the standard factor theorem
question.
(10 marks)
Now replace q by p in the divisor to get
(10)
Question 2:
This is the usual simultaneous equations
question.
Solution
X= 1,y = 1: x = -3, y = -3. (10 marks)
B (I)
<-1/3 (10)
(ii)
(Notice it really
the difference of two squares) (10)
C.
(20)
Question (3)
U = 1/5(3+4i). /u/=1 (10)
(ii)
(20 marks)
C
(i)
(10 marks)
(ii)
(10)
Question (4)
(i)
(10) B
(10,10)
C (i)
(20)
Question5:
(a)
The first term is -7 r = -3. (The common
ratio) (10)
(b)
X = 4
(10)
(ii) K = 4 or –4 (10)
©
De
Moivres Theorem, probably the worst kept secret of the exam.
Standard
proof by induction made easier by the fact that you were only asked the proof
for natural numbers
Question 6.
(a)
(10 marks)
b 
The first principals
is a standard proof. (10,10 marks)
C
(i)
(20 marks)
Question
7:
(a)
The second approximation of the root is
4/5. (10
marks)
(b)
(10,10,)
© a=16. there is no maximum since 
(10,10,)
Question 8:
(a)(i)
(10)
b (i)
(ii) 4-2
(10,10,)
C
The area
required is the area under the curve between 0 and p less the area of the
Triangle
(20)
Conclusion
this was the easiest shortest higher Maths paper ever who said the Department
of Education did not have heart!