National 4XDOLÛFDWLRQV 2018
FOR OFFICIAL USE
N5 National Qualications 2018 X847/75/01
FRIDAY, 4 MAY 9:00AM ? 10:15AM
Mark
Mathematics Paper 1 (Non-Calculator)
*X8477501*
Fill in these boxes and read what is printed below. Full name of centre
Town
Forename(s)
Surname
Number of seat
Date of birth
Day
Month
Year
Scottish candidate number
Total marks -- 50
Attempt ALL questions. You may NOT use a calculator. To earn full marks you must show your working in your answers. State the units for your answer where appropriate. Write your answers clearly in the spaces provided in this booklet. Additional space for answers is provided at the end of this booklet. If you use this space you must clearly identify the question number you are attempting. Use blue or black ink. Before leaving the examination room you must give this booklet to the Invigilator; if you do not, you may lose all the marks for this paper.
?
*X847750101*
A/HTP
FORMULAE LIST The roots of Sine rule: Cosine rule: Area of a triangle:
ax2 + bx + c = 0 are x = -b ?
(b2 - 4ac) 2 a
a sin
A
=
b sin
B
=
c sinC
a2
=
b2
+
c2
-
2bc cos
A
or
cos
A
=
b2
+ c2 - 2bc
a2
A
=
1 2
absin C
Volume of a sphere:
V
=
4 3
r3
Volume of a cone:
V
=
1 3
r
2h
Volume of a pyramid:
V
=
1 3
Ah
Standard deviation:
s=
(x - x)2 n -1
or s =
x2
-
(
x)2 n
n -1
,
where
n
is
the
sample
size.
*X847750102* page 02
Total marks -- 50 Attempt ALL questions
1.
Evaluate
2
1 3
+
4 5
.
MARKS DO NOT WRITE IN THIS MARGIN
2
2. Expand and simplify (3x + 1)( x - 1) + 2( x2 - 5).
3
*X847750103* page 03
[Turn over
3. Solve, algebraically, the system of equations
4x + 5 y = -3 6x - 2 y = 5.
MARKS DO NOT WRITE IN THIS MARGIN
3
1
6
4.
Two
vectors
are
given
by
u
=
51
and
u+
v
=
-4 3
.
Find vector v.
Express your answer in component form.
2
*X847750104* page 04
5. Solve
x2 - 11x + 24 = 0 .
MARKS DO NOT WRITE IN THIS MARGIN
2
6. Part of the graph of y = a cos bx? is shown in the diagram.
y 5
0
90
180 x
-5
State the values of a and b.
2
*X847750105* page 05
[Turn over
7. The cost of a journey with Tom's Taxis depends on the distance travelled.
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The graph below shows the cost, P pounds, of a journey with Tom's Taxis against the distance travelled, d miles.
P B
A
O
d
Point A represents a journey of 8 miles which costs ?14. Point B represents a journey of 12 miles which costs ?20.
(a) Find the equation of the line in terms of P and d.
Give the equation in its simplest form.
3
*X847750106* page 06
7. (continued) (b) Calculate the cost of a journey of 5 miles.
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1
8. Determine the nature of the roots of the function f ( x) = 2x2 + 4 x + 5.
2
*X847750107* page 07
[Turn over
9. In the diagram shown below, ABCDEFGHJK is a regular decagon. ? Angle KLJ is 17?. ? AKL is a straight line.
E
F
D
G
C
H
J B
17?
A
K
Calculate the size of shaded angle KJL.
MARKS DO NOT WRITE IN THIS MARGIN
L 2
*X847750108* page 08
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