Essay about Mathematics Questions: Algebraic Methods

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For Supervisor’s use only

90147

1

Level 1 Mathematics, 2004
90147 Use straightforward algebraic methods and solve equations
Credits: Four
9.30 am Thursday 11 November 2004

Check that the National Student Number (NSN) on your admission slip is the same as the number at the top of this page.
You should answer ALL the questions in this booklet.
You should show ALL working.
If you need more space for any answer, use the page provided at the back of this booklet and clearly number the question.
Check that this booklet has pages 2–7 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.

Achievement Criteria
Achievement
Use straightforward algebraic methods.

For Assessor’s use only

Achievement with Merit
Use algebraic methods and solve equations in context.

Achievement with Excellence
Use algebraic strategies to investigate and solve problems.

Solve equations.

Overall Level of Performance (all criteria within a column are met)
© New Zealand Qualifications Authority, 2004
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 25 minutes answering the questions in this booklet.

At the Pool
You should show ALL working.
QUESTION ONE
Solve these equations:
(a)

(3x – 1)(x + 2) = 0
1)(

(b)

6x – 2 = 2x + 9

(c)

5x
−1= 3
2

QUESTION TWO
Expand and simplify:
(3x – 1)(2x + 5)

Assessor’s use only

3

QUESTION THREE

Assessor’s use only

Factorise completely: x2 – 7x + 6

QUESTION FOUR
Simplify:
12 x 6
4x2

QUESTION FIVE
In a diving competition, the score (R) for a dive is calculated using the formula
(
R = 0.6 DT where D is the degree of difficulty for the dive and T is the total of the judges’ marks.
Jill does a dive with degree of difficulty D = 2.5.
The judges’ marks had a total T = 34.5.
Calculate the score, R, for Jill’s dive.

R=

4

QUESTION SIX
Simplify:
3a 2 − 15ab
15
6a2

QUESTION SEVEN
John saved $4000 for a trip to the Olympic Games.
He wanted to buy as many tickets to the swimming as possible.
Each ticket to the swimming costs $85.
Travel, food and accommodation cost $3100.
Use this information to write an equation or inequation.
Solve your equation or inequation.
What is the greatest number of tickets to the swimming that John could buy?

Assessor’s use only

5

QUESTION EIGHT
Janet bought tickets to the diving and the swimming at the Olympic Games.
She paid $1095 for 15 tickets.
The tickets for the diving cost $65 and the tickets for the swimming cost $85.
Solve the pair of simultaneous equations to find the number of tickets Janet bought for the swimming. 65d + 85w = 1095 d d + w = 15

Assessor’s use only

6

QUESTION NINE
At the Olympic Games 40 years ago, the average number of competitors per sport was 5 times the number of sports played.
In 2004 there were 10 more sports than there were 40 years ago.
In 2004 the average number of competitors per sport was 3.5 times greater than 40 years ago.
At the 2004 Olympic Games there were 10 500 competitors.
Write at least ONE equation to model this situation.
Use the model to find the number of sports played at the Olympic Games 40 years ago.
Show all your working.

Assessor’s use only

7

Extra paper for continuation of answers if required.
Clearly number the question.
Question _________________________________________________________________________
Number

_________________________________________________________________________
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