Download 1. Harris N5 Prelim 2014 - Paper 1

N5
Harris Academy
Prelim Examination 2014
MATHEMATICS
National Qualifications - National 5
Paper 1 (non-calculator)
Time allowed
-
1 hour
Fill in these boxes and read carefully what is printed below
Full name of centre
Town
Forename(s)
Date of birth
Day Month Year
Surname
Candidate number
Seat number
Total marks - 40
1.
2.
3.
4.
5.
6.
7.
You may NOT use a calculator.
Use blue or black ink. Pencil may be used for graphs and diagrams only.
Write your working and answers in the spaces provided. Additional space for answers
is provided at the end of the booklet. If you use this space, write clearly the number of
the question you are attempting.
Square ruled paper is provided.
Full credit will be given only where the solution contains appropriate working.
State the units for your answer where appropriate.
Before leaving the examination room you must give up this booklet to the invigilator. If
you do not, you may lose all the marks for this paper.
FORMULAE LIST
 b  (b 2  4ac)
2a
The roots of ax2 + bx + c = 0 are x =
Sine rule:
a
b
c


sin A sin B sin C
Cosine rule:
a2
Area of a triangle:
Area = ½ ab sin C
Volume of a sphere:
Volume =
4 3
r
3
Volume of a cone:
Volume =
1 2
r h
3
Volume of a Pyramid:
Volume =
1
Ah
3
Standard deviation:
=
s=
b2
+
c2
b2  c2  a2
 2bc cos A or cos A =
2bc
 (x  x)2
n 1

 x 2  ( x) 2 / n , where n is the sample size.
n 1
All questions should be attempted
1
6
2
5
1.
Calculate 2 
2.
Find the gradient of the line which has equation
2
5x + 7y + 35 = 0
3.
Marks
Change the subject of this formula to ‘r’
V   r 2h
2
2
Do not
write in
this
margin.
Marks
4.
5.
(a)
Factorise
2x2  x  3
2
(b)
Factorise fully
4x2  9
1
(c)
Simplify
2x2  x  3
1
4x2  9
The probability that a bus arrives on time is
Do not
write in
this
margin.
4
.
7
Out of a sample of 210 buses how many would you expect to be late?
2
2
Marks
6.
7.
Multiply the brackets and simplify
(3 x  1) 2  (2 x  1)( x  2)
3
A function is given as f ( x )  3 x 2  5 .
(a)
Find f (2)
1
(b)
Given that f (a )  43 , find the two values of a
3
Do not
write in
this
margin.
3
Marks
8.
The following number pattern can be used to find the sum of
consecutive square whole numbers.
12  2 2 
4  3 5
12
12  2 2  3 2 
6 47
12
12  2 2  3 2  4 2 
859
12
12  2 2  3 2  .......  8 2 
16  9  17
12
Write out 12  2 2  32  .......  12 2 in the same way and calculate the sum of the
first twelve square whole numbers.
9.
3
Write as a single fraction in its simplest terms
2
5

x  2 x 1
x  2; x  1
3
Do not
write in
this
margin.
Marks
10.
A
4
B
6
3
C
Show clearly that the exact value of Cos ABC = 
11
24
3
11.
PQ is a diameter and O is the centre
of the circle shown opposite. QS is a tangent
to the circle with Q the point of contact.
Q
If  QPR = 54o, find the size of  RQS.
O
P
54o
S
R
3
Do not
write in
this
margin.
Marks
12.
A group of smokers were asked how many cigarettes they smoked in a day and
how many chest infections they had suffered in the last ten years. The results
are shown in the scattergraph .
.
The line of best fit has also been drawn on the graph.
Number of chest infections in last 10 years( I )
I
8
7
6
5
4
3
2
1
0
5
10
15
20
25
30
35
40
45
C
Number of cigarettes smoked in a day ( C )
Determine the equation of this line of best fit.
4
Do not
write in
this
margin.
Marks
13.
The parabola in the diagram below has equation of the form y = (x + a)² + b with
turning point (3, – 2).
The broken line in the diagram is horizontal and passes through the points A and B.
y
7
A
B
x
0
(3, – 2)
(a)
Write down the equation of the parabola.
1
(b)
Given that the x – coordinate of the point A is 1, find the equation of
the line AB.
3
Establish the coordinates of the point B.
1
(c)
End of Question Paper
Do not
write in
this
margin.