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 x2 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)
x3 x7 2 5 2
3
5 2m 15
2
iii)
27 b3 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...