Download Level X Subject (90 ) 2011

1
To be completed by Candidate and School:
Name:
NSN No:
School Code:
DAY 3
THURSDAY
SUPERVISOR’S USE ONLY
Level 1 Mathematics and Statistics CAT, 2011
91027 Apply algebraic procedures in solving problems
Thursday �����������������
22���������������
September 2011
Credits: Four
You should attempt ALL the questions in this booklet.
Calculators may NOT be used.
Show ALL working.
If you need more space for any answer, use the page(s) provided at the back of this booklet and clearly
number the question.
Check that this booklet has pages 2 – 8 in the correct order and that none of these pages is blank.
YOU MUST HAND THIS BOOKLET TO THE SUPERVISOR AT THE END OF THE EXAMINATION.
ASSESSOR’S USE ONLY
Achievement
Apply algebraic procedures in solving
problems.
Achievement Criteria
Achievement with Merit
Apply algebraic procedures, using
relational thinking, in solving problems.
Achievement with Excellence
Apply algebraic procedures, using
extended abstract thinking, in solving
problems.
Overall level of performance
© New Zealand Qualifications Authority, 2011. All rights reserved.
No part of this publication may be reproduced by any means without the prior permission of the New Zealand Qualifications Authority.
2
You are advised to spend 60 minutes answering the questions in this booklet.
QUESTION ONE: EQUATIONS
Solve these equations:
(a)2(x – 2) = 24
(b)6x – 2 = 8x + 6
(c)(i)
3− 4x
=7
5
3− 4x
(ii)
>7
5
Mathematics and Statistics CAT 91027 (Day 3), 2011
ASSESSOR’S
USE ONLY
3
(d)(a 2) 3 = 64
ASSESSOR’S
USE ONLY
(e)
A drink costs $2.50 more than a packet of chips.
2 drinks and 4 packets of chips cost a total of $17.
You must show at least one equation that can be used in solving this problem.
What is the cost of 1 drink?
Mathematics and Statistics CAT 91027 (Day 3), 2011
4
QUESTION TWO: RELATIONSHIPS
(a)
Simplify fully:
(i)4ab2 + 3a2b – a2b
10 a 2
(ii)
2a
(b) Expand and simplify (2x + 5)(x – 2)
(c) The formula for the volume of a cone is
π 2
r h
3
where r is the radius and h is the height of the cone.
V=
(i)
Write the formula for the radius, r, of the cone in terms of V, h and π.
Mathematics and Statistics CAT 91027 (Day 3), 2011
ASSESSOR’S
USE ONLY
5
(ii) Aria has two cones that have the same volume.
One cone is 3 times the height of the other.
Give an expression for the radius, r, of the shorter cone
in terms of R, the radius of the taller cone.
Give your answer in the simplest form.
ASSESSOR’S
USE ONLY
R
r
Diagram is
NOT to scale
(d) Mele is exploring the sequence of numbers given by the rule
2n2 – n + 3
Give the rule for finding the difference between any two consecutive terms from the sequence
2n2 – n + 3 in its simplest form.
(Hint: consecutive terms follow each other, eg the 5th and 6th terms or the 17th and 18th
terms or the nth and the (n + 1)th terms.)
You must show your working.
Mathematics and Statistics CAT 91027 (Day 3), 2011
6
QUESTION THREE: QUADRATIC EXPRESSIONS AND EQUATIONS
(a)Factorise:
(i)
ab2 + a2b
(ii)
x2 – 4x – 5
(b)Solve x2 – 4x – 5 = 0
(c)
(i)
x2 − 4 x − 5
Simplify fully the fraction 2
x + 6x + 5
x2 − 4 x − 5
=2
(ii)Solve 2
x + 6x + 5
Mathematics and Statistics CAT 91027 (Day 3), 2011
ASSESSOR’S
USE ONLY
7
(d) Aroha and her son Zac are throwing a ball to each other
on the deck of their house.
Zac misses the ball, and it falls to the ground.
The path of the ball can be modelled by the equation
h = – t2 + 6t + 7,
where t is the time in seconds since the ball is thrown,
and h is the height in metres above the ground at any
time t.
http://topophilia.net/images/Deck.jpg
(i) How long after it is thrown, will the ball hit the ground?
Explain what you are calculating at each step of your answer.
(ii) How much higher does the ball rise above the height of the point from which it is
thrown?
Explain what you are calculating at each step of your answer.
Mathematics and Statistics CAT 91027 (Day 3), 2011
ASSESSOR’S
USE ONLY
8
91027
QUESTION
NUMBER
Extra paper if required.
Write the question number(s) if applicable.
Mathematics and Statistics CAT 91027 (Day 3), 2011
ASSESSOR’S
USE ONLY