SC maths test 2006 help! (1 Viewer)

[GAELL]

hi,
could you please explain how to do:
SC Maths test 2006
Questions: 72, 75, 77, 78, 79,80
I have the answers - but still can't see how they got them!
Thanks for your help.

 

[kurt.physics]

I dont really have enough time to do all of them right now, but because 80 is quick i will do that one.

80 - When reading a page of his book, Jarrod declared, ‘There are twice as many
pages after this page than before this page’.
How many pages could this book contain?
Indicate whether each of the following is Correct or Incorrect.
a. 202 b. 303 c. 404 d. 505

Okay, so what we have to do first is make a formula for how many pages there are. If we let the pages before him be x, then the pages ahead of him is 2x, there is also the 1 pages he is on, so the formula is

x + 2x + 1

= 3x + 1

Now, what do we know about x, x is a number of pages, therefore it must be an interger (whole number) as you dont have half-pages.

So the trick now is to make 3x + 1 = the number, say 202, for example, then solve and see if x is a whole number, if it is, then that could be the number of pages.

 

[clintmyster]

72) Im guessing your thinking 4. Firstly, you need to know what an isosceles triangle is being a triangle with two equal length sides. Now since they want a right angled triangle, its quite obvious that you should place C so that it is perpendicular to AB at A and B from above and below (hope that makes sense or ask me otherwise). Now the other two points lie on the basis that you can find another place for C where AC = AB. That would be in the middle of AB and above/below it so that a right angle is made.


77) for a) take rise over run, therefore m = 2 / 4 =1/2, therefore this is true
b) well you know that m cannot = -4 because we just found in a that is 1/2 therefore this not true either
c) well the x intercept is at -4,0 so this is wrong
d) use one point gradient formula to work out eqn of line so y - y1 = m(x -x1) replace x1 and y1 with a point so (-4,0) and you get y = 1/2x + 2
now sub in 2,3 and see if it satisfied, therefore 3 = (1/2)2 + 2 = 3 therefore this works

therefore a) and d) are correct

 

[GAELL]

72) Im guessing your thinking 4. Firstly, you need to know what an isosceles triangle is being a triangle with two equal length sides. Now since they want a right angled triangle, its quite obvious that you should place C so that it is perpendicular to AB at A and B from above and below (hope that makes sense or ask me otherwise). Now the other two points lie on the basis that you can find another place for C where AC = AB. That would be in the middle of AB and above/below it so that a right angle is made.


77) for a) take rise over run, therefore m = 2 / 4 =1/2, therefore this is true
b) well you know that m cannot = -4 because we just found in a that is 1/2 therefore this not true either
c) well the x intercept is at -4,0 so this is wrong
d) use one point gradient formula to work out eqn of line so y - y1 = m(x -x1) replace x1 and y1 with a point so (-4,0) and you get y = 1/2x + 2
now sub in 2,3 and see if it satisfied, therefore 3 = (1/2)2 + 2 = 3 therefore this works

therefore a) and d) are correct

thanks for your help
i still dont quite get question 72
do i put the perpondicular line inbetween a and b?
i can see 6 triangles - but are they isosceles triangles?

could you also explain question 49 please

 

[GAELL]

I dont really have enough time to do all of them right now, but because 80 is quick i will do that one.

80 - When reading a page of his book, Jarrod declared, ‘There are twice as many
pages after this page than before this page’.
How many pages could this book contain?
Indicate whether each of the following is Correct or Incorrect.
a. 202 b. 303 c. 404 d. 505

Okay, so what we have to do first is make a formula for how many pages there are. If we let the pages before him be x, then the pages ahead of him is 2x, there is also the 1 pages he is on, so the formula is

x + 2x + 1

= 3x + 1

Now, what do we know about x, x is a number of pages, therefore it must be an interger (whole number) as you dont have half-pages.

So the trick now is to make 3x + 1 = the number, say 202, for example, then solve and see if x is a whole number, if it is, then that could be the number of pages.

thanks
knowing how to do it makes it seem simple

 

[Lyly]

The 2006 maths SC was notoriosuly difficult... :mad1:
Thank god it was easier last year!

And yeah, the way kurt.physics showed you to work out Question 80 was correct, my maths teacher showed me the exact same thing

 

[kurt.physics]

For question 75, that is

a▲b=1 – a/b.

For example, 5 ▲6=1 – 5/6.
What is the value of (1 ▲2) ▲(3 ▲4)?
(A) –1 (B)1/2 (C)4/7 (D) 7/8

All you have to do is substitute the values, but what we will do is get the value for the 1▲2 and then 3▲4

1▲2 = 1 - 1/2 = 1/2
3▲4 = 1 - 3/4 = 1/4

So we have the numbers 1/2 and 1/4 and the question becomes

1/2▲1/4 = 1 - (1/2)/(1/4) = 1 - 1/2 divided by 1/4

which is = 1 - 1/2 x 4
= 1 - 2
= -1

So the answer is (a) -1

 

[kurt.physics]

Question 78

Raelene earns $600 per week. Naomi earns $1100 per fortnight. Danny earns
more than Naomi but less than Raelene.
How much could Danny earn each month?

Indicate whether each of the following is Correct or Incorrect.
a. $2250 b. $2330 c. $2500 d. $2580

Okay, there is not much work involved with this at all, all we have to do is get Raelene's and Naomi's money in to months so we can compare them.

So Raelene earns $600/week, so thats $600 x 4 per month, ie $2400

Naomi earns $1100/2 weeks, so thats $1100 x 2 per month, ie $2200

Now Danny earns more than Naomi, ie more than $2200, and less than Raelene, ie less than $2400

So in other words, he earns between $2200 and $2400 a month.

So if we look at all the possible answers, it is easy to conclude that it is

(a) Correct
(b) Correct
(c) False
(d) False

 

[rolror88]

Question 78

Raelene earns $600 per week. Naomi earns $1100 per fortnight. Danny earns
more than Naomi but less than Raelene.
How much could Danny earn each month?

Indicate whether each of the following is Correct or Incorrect.
a. $2250 b. $2330 c. $2500 d. $2580

Okay, there is not much work involved with this at all, all we have to do is get Raelene's and Naomi's money in to months so we can compare them.

So Raelene earns $600/week, so thats $600 x 4 per month, ie $2400

Naomi earns $1100/2 weeks, so thats $1100 x 2 per month, ie $2200

Now Danny earns more than Naomi, ie more than $2200, and less than Raelene, ie less than $2400

So in other words, he earns between $2200 and $2400 a month.

So if we look at all the possible answers, it is easy to conclude that it is

(a) Correct
(b) Correct
(c) False
(d) False

It's actually C and D

52 weeks in a year, 26 fortnights, 12 months

Raelene: =$600 x 52/12=$2600
Naomi - $1100 x 26/12 =$2382.33

Danny can earn c) and d)

 

[kurt.physics]

It's actually C and D

52 weeks in a year, 26 fortnights, 12 months

Raelene: =$600 x 52/12=$2600
Naomi - $1100 x 26/12 =$2382.33

Danny can earn c) and d)

Okay, thanks for that.