# Maths Ext1

## Maths Ext1

2007 Preliminary Half Yearly

MATHEMATICS
General Instructions          Reading time – 5 minutes Working time – 1 hour and 30 minutes Write using black or blue pen Board-approved calculators may be used Write your name and your teacher’s name at the top of every page Start each question on a new page. Write on only one side of the paper Marks may be deducted for careless or illegible work. Show all necessary working -15 x 12 mark questions Attempt all questions

Question 1 (12 marks)
Start each new question on a new page. Write your name and your teacher’s name at the top of the page Marks a) b) c) Evaluate Express
3.142 2  0.858 2 correct to 3 significant figures.

2 1

5 as a recurring decimal. 110

Factorise completely: i) ii) x2 – 4x + 4 ab – 3bc + 4a – 12c 1

2

d)

Express

2 7 1

in simplest form with a rational denominator.

2

e)

Simplify:

a 3  a  9a

2

f)

Simplify:
x 144 x  12  x2 x3  8
2

2

-2-

Question 2 (12 marks)
Start each new question on a new page. Write your name and your teacher’s name at the top of the page Marks a) Solve the following i) ii)

x3 x7 2 5 2

3

5  2m  15

2

iii)

27 b3  9

2

b)

Solve and graph the following

3

2m  3  17

c)

Solve simultaneously

2

2 x  4 y  28 2 x  3 y  11

-3-

Question 3 (12 marks)
Start each new question on a new page. Write your name and your teacher’s name at the top of the page Question 3 a) Find the area of the following figure, given AB = AD = DC A B Not to scale Marks 2

D b) c)

6m

5m

C 1 1

Find the size of the exterior angle of a regular pentagon. In the diagram BC = AC, and ACD is a straight line. Find the size of  BCD B
24

Not to scale

A C

D

Question 3 is continued on the next page

-4-

Question 3 continued d) B A 5m E D

15m C Not to scale

In the diagram above, AB is parallel to CD. BE = 5m and CE = 15m. i) ii) iii) Briefly explain...