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

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3. Solve, algebraically, the system of equations

4x + 5 y = -3 6x - 2 y = 5.

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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 .

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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

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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

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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.

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L 2

*X847750108* page 08

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