Maths Questions (Help needed please) (1 Viewer)

[reggie7]

Hello everyone, I recently did Maths Trials test and I am really not happy. It is truly one big wake up call for me since I regard Maths probably as my best subject (equal with english). I also ran out of time and did really bad at the start with the first 20 questions with some silly mistakes.

In this test you really had the read the whole question and there were key words and a few questions i got wrong during final calculations.

Anyway I have some questions from the trials that I got wrong, a few that I can see how I got them wrong but a few that I can't. I'd really appreciate some help and some tips on how to remember things.

NON CALCULATOR:

Q.4: (Don't see how I got this wrong).

There are cows and pigs on a farm in the ratio 3:2

By what percentage does the number of cows on the farm exceed the number of pigs?

My Answer: 20%
Right Answer: 50%

What I did was add 3 and 2 together... cows is 3/5 which is 60. pigs is 2/5 which is 40. 60% - 40% = 20%


Q.20: (I kinda get this - I need it explained)

The bicycle with a front wheel and a small rear whell is called a "Penny Farthing"

The ratio of the radius of the small wheel to the large whell is 1:5.

When the small whell rotates 150 times, how many revolutions will the large wheel complete?

My Answer: 750 (lol)
Right Answer: 30

I think you just divide 150 by 5?? I don't get it though, I really hate ratio questions.


Q.23 (It's a drawing - and it's a question i really don't understand)

It says: Draw the reflection of the triangle at the line using a ruler...
Does anyone know a method in which to draw reflections of shapes??


CALCULATOR:

Q.50: (It has a drawing also)

The shaded triangle ABC with a base x cm is similar to large triangle ADE with base length 2x cm? (wtf is a question mark doing there i don't know)

*Picture of Triangle ADE , with Triangle ABC within it. ABC's base has x cm and ADE's base has 2x cm*

What is the ratio of the area of ABC to the area of BCED?

*Now BCED isn't a triangle it's a trapezium with 2x cm as it's base and x cm as the top length*

(A) 1:2 (B) 2:3 (C) 1:3 (D) 1:4

Teacher's answer: C
My Answer: A (guessed)



Q.51: (Okay, this question I can't understand how I got wrong)

When Melinda borrows $28 000 for a new car, she pays the loan off in equal monthly payments of $625 over a period of 5 years.

What was the annual rate of simple interest charged on Melinda's loan?

(A) 6.79% (B) 25.3% (C) 26.8% (D) 33.9%

My Answer: (D)
Teacher's Answer: (A)

What I did was: 625 * 12 = * 5 = 37'500 (loan payment)
Then 37'500 - 28'000 = 9500 (keep that in mind)

I then used the process of elimination, got to (D): 28'000 * 0.339 = 9492 (which is basically 9500)

9500 = 9500 = (D)


Q.65: (drawing in this)

A vertical blind consists of rectangular slats, each of width 12 cm. When the blind is closed, the slats overlap by 1cm as shown in the diagram.

-1cm- -1cm-
----------------------------------------------------------------------------
' ' ' ' '
' ' ' ' '
' ' ' ' '
' ' ' ' '
' ' ' ' '
' ' ' ' '
' ' ' ' '
' ' ' ' '
------------------------------------------------------------------------------
-1cm- -1cm-
--------12cm-----------
-----------------12cm---------------


What is the toal width (in cm) of the blind if it has n slats?

(A) 12n + 1 (B) n - 11 (C) 11n + 1 (D) 12n - 1

My Answer: (D) guessed
Teacher's Answer: (C)

Do not get this at all


Q.71: (I get this and did it by guessing some numbers but I'd like an easier and quicker way to work it out)

Three beakers contain liquid.

Beaker C has 700 mL and this is 40% more than the contents of Beaker A and 25% more than the contents of Beaker B.

By what percentage do the contents of Beaker B exceed the contents of Beaker A?

this answer is 12.

What I did was picked some numbers ... I figured out Beaker A was 500 (500 * 0.4 (40%) = 200 ...... 200 +500 = 700 (Beaker C) and then figured Beaker B was 560 (took time guessing) .. 500 * 0.12 (12%) = 60.

I just need a better way to figure that question out.


Q.84:


The Sum of three consecutive even numbers is 78.

The median of the numbers is 2x - 4.

(a) Write down expressions in terms of x, for the other two numbers.

(b) By writing an equation, calculate the value of x.

(c) Using the value of x, determine the numerical value of the product of the three numbers.

Answers according to teacher:

(a) (2x - 6) & (2x - 2)

(b) 6x - 12 = 78
x = 15

(c) (30 - 6) (30 - 4) (30 - 2) 17472




I know there's a few maths question threads created but I'd rather create a new thread than not get my question answered.

Thanx in advanced, help would be greatly appreciated. Just spent about 45 mins typing this up.

Real Test is on Tuesday btw ..

 

[backrowcentre]

Q.51: (Okay, this question I can't understand how I got wrong)

When Melinda borrows $28 000 for a new car, she pays the loan off in equal monthly payments of $625 over a period of 5 years.

What was the annual rate of simple interest charged on Melinda's loan?

(A) 6.79% (B) 25.3% (C) 26.8% (D) 33.9%

My Answer: (D)
Teacher's Answer: (A)





I also got D for this, and I'm trying to figure this out now...


625 * 60 (number of months) = 37500
prt = 28000 * 6.79%(0.0679) * 5 = 9506.
28000 + 9506 = 37506, which means 6.79% gets you closest to the final amount...

Sorry I can't explain it better. Maths is what I would consider my best subject, but after trials...

 

[mohamed100]

Q.51: (Okay, this question I can't understand how I got wrong)

When Melinda borrows $28 000 for a new car, she pays the loan off in equal monthly payments of $625 over a period of 5 years.

What was the annual rate of simple interest charged on Melinda's loan?

(A) 6.79% (B) 25.3% (C) 26.8% (D) 33.9%

My Answer: (D)
Teacher's Answer: (A)





I also got D for this, and I'm trying to figure this out now...


625 * 60 (number of months) = 37500
prt = 28000 * 6.79%(0.0679) * 5 = 9506.
28000 + 9506 = 37506, which means 6.79% gets you closest to the final amount...

Sorry I can't explain it better. Maths is what I would consider my best subject, but after trials...

an initial judgement, without calculating, im guessing you've calculated the simple interest rate over 5 years. the question asks for simple interest p.a. So you would have to divide the answer you arrived at by 5, and that would yield option A.

STEPS:
-total amount repaid = 60*625 = 37500.
-amount borrowed = 28000.
-therefore, amount of interest paid over 5 years = 37500-28000 = 9500.
-every year, 9500/5 = 1900 every year.
-so 1900/28000 *100 should be the answer

 

[kwokie]

Q.4: (Don't see how I got this wrong).

There are cows and pigs on a farm in the ratio 3:2

By what percentage does the number of cows on the farm exceed the number of pigs?

My Answer: 20%
Right Answer: 50%

What I did was add 3 and 2 together... cows is 3/5 which is 60. pigs is 2/5 which is 40. 60% - 40% = 20%

That is easy there is 1 cow more than pigs.

1/2=50%

Q.51: (Okay, this question I can't understand how I got wrong)

When Melinda borrows $28 000 for a new car, she pays the loan off in equal monthly payments of $625 over a period of 5 years.

What was the annual rate of simple interest charged on Melinda's loan?

(A) 6.79% (B) 25.3% (C) 26.8% (D) 33.9%

My Answer: (D)
Teacher's Answer: (A)

What I did was: 625 * 12 = * 5 = 37'500 (loan payment)
Then 37'500 - 28'000 = 9500 (keep that in mind)

I then used the process of elimination, got to (D): 28'000 * 0.339 = 9492 (which is basically 9500)

9500 = 9500 = (D)

The question said ANNUAL INTEREST.....
It is over 5 years and u got the total interest.
Basically divide the total interest by 5 years.
33.9% divide by 5= 6.79%

 

[reggie7]

Thanx for everyone's help

I forgot to add part of question 84 as exphate said, here is the full question:

Q.84:


The Sum of three consecutive even numbers is 78.

The median of the numbers is 2x - 4.

(a) Write down expressions in terms of x, for the other two numbers.

(b) By writing an equation, calculate the value of x.

(c) Using the value of x, determine the numerical value of the product of the three numbers.

Answers according to teacher:

(a) (2x - 6) & (2x - 2)

(b) 6x - 12 = 78
x = 15

(c) (30 - 6) (30 - 4) (30 - 2) 17472


I need those answers explained cause i got no idea how to work out the questions.

 

[Zorbini]

Question (b):

Providing you get question (a) right you can solve it.

"The sum of three consecutive even numbers is 78"
2x-2 + 2x-4 + 2x-6 = 78

6x-12=78
6x=90
x=15

Question (c):

With x=15...
[(2x15)-2] x [(2x15)-4] x [(2x15)-6] = 17,472

 

[Continuum]

Question 4

There are cows and pigs on a farm in the ratio 3:2

By what percentage does the number of cows on the farm exceed the number of pigs?

Just make up any number in the ratio of 3:2. I chose 150:100 because we're dealing with percentages. Therefore, we have 150 cows and 100 pigs.

There are 50 more cows than the number of pigs, and the question wants this to be over the number of pigs there are. In other words, 50 over 100 - making it 50%.

Question 20

The bicycle with a front wheel and a small rear whell is called a "Penny Farthing"

The ratio of the radius of the small wheel to the large whell is 1:5.

When the small whell rotates 150 times, how many revolutions will the large wheel complete?

For this question, you really need the picture to be able to do it.

You can see that when the front wheel (the larger one) goes around in a circle, the smaller wheel will move. Since this front wheel is 5 times larger than the smaller wheel, if you think about it, it would take 1 revolution of the larger wheel to complete 5 revolutions of the smaller wheel. Thus, simply put it into a ratio:

1 revolution of larger wheel = 5 revolutions of smaller wheel
x revolution(s) of larger wheel = 150 revolutions of smaller wheel

To get 150 from 5, you times it by 30. So you simply do that to 1 to get x, getting you the correct answer 30.

Question 23

Kind of hard to explain, but I just use my visualisation to get the question. You could always just fold the reflection line, remember where the corners of the reflected shape should be after holding the pages up to the light and then draw it using those. Yeah, sorry for the crummy explanation.

Question 50

The shaded triangle ABC with a base x cm is similar to large triangle ADE with base length 2x cm? (wtf is a question mark doing there i don't know)

*Picture of Triangle ADE , with Triangle ABC within it. ABC's base has x cm and ADE's base has 2x cm*

What is the ratio of the area of ABC to the area of BCED?

*Now BCED isn't a triangle it's a trapezium with 2x cm as it's base and x cm as the top length*

(A) 1:2 (B) 2:3 (C) 1:3 (D) 1:4

This is the full question:

In this triangle you know that the triangle ABC has a base of x and the triangle AED has a base of 2x. Since the answer you need to find is in ratio form, it's much easier to let x equal something. I use x=1 because it's good for ratios (notice how 3 of the answers have the number 1 in the ratio?).

Hopefully, you have learnt how you can convert the ratio of sides to the ratio of areas - all you do to find the ratio of the area is square the ratio of the sides. In other words, if the ratio of sides is x:2x (in this case), then the ratio of the areas would be x^2: (2x)^2.

Remember how we let x=1? The ratio of the sides is 1:2. Thus, the ratio of the areas are 1^2:2^2. In other words, 1:4. Now we know that the triangle ABC is 1cm^2, whereas the triangle AED is 4cm^2. However, we don't want AED, we want BCDE. To do this, you just go area of AED - area of ABC. This is 4-1=3. So the area of BCDE is 3cm^2.

Thus, now that you have found what could be the area of AVC and BCDE, you can just put it into a ratio. For example, 1cm^2:3cm^2 would make the ratio of 1:3 - giving you the answer C.

I'll type up the rest after dinner.

 

[Continuum]

Question 51

When Melinda borrows $28 000 for a new car, she pays the loan off in equal monthly payments of $625 over a period of 5 years.

What was the annual rate of simple interest charged on Melinda's loan?

(A) 6.79% (B) 25.3% (C) 26.8% (D) 33.9%

This question is really crummy. Took me a few minutes to get it correct. :mad1:

The first step is to find the amount of interest that she paid. In other words, total amount of money she repaid minus the total amount of money she borrowed. To find the amount of money she repaid, simply go: $625 monthly payments x 12 months x 5 years = $37500. $37500 minus $28000 means that Melinda paid a total of $9500 of interest.

It says to find the annual simple interest rate, so you want to find the amount of interest she paid in 1 year. The one that we got ($9500) was paid over 5 years, so that means that in one year she paid $1900 of interest in 1 year. Next, all you need to do is put $1900 over $28000. This gives you a fraction of 19 over 280 and after you convert it into a percentage, you get 6.79%.

Question 65

For this one, the easiest way (by far) is to simply figure out the distance of 4 slats. I was able to figure out that 4 slats would have a length of 45cm. Looking at all of the equations, only 11n+1 (C) would fit.

Question 71

Three beakers contain liquid.

Beaker C has 700 mL and this is 40% more than the contents of Beaker A and 25% more than the contents of Beaker B.

By what percentage do the contents of Beaker B exceed the contents of Beaker A?

Beaker C has 700ml, in other words, 140% of Beaker A. 700 divided by 140% gives you 1% and the value 5. So to find 100% of Beaker A when you have the value 1%=5, just multiply 5 by 100. Therefore, Beaker A would have 500ml.

You do the same with Beaker C and Beaker B. Beaker C has 700ml, in other words, 125% of Beaker B. 700 divided by 125% gives you 1% and the value 5.6. So to find 100% of Beaker B when you have the value 1%=5.6, just multiply 5.6 by 100. Therefore, Beaker B would have 560ml.

Now, you know that Beaker B has 60ml more than Beaker A. Put this amount (60ml) over the amount in Beaker A (500ml), then convert this to a percentage. This gives you 12%.

Question 84

The Sum of three consecutive even numbers is 78.

The median of the numbers is 2x - 4.

(a) Write down expressions in terms of x, for the other two numbers.

(b) By writing an equation, calculate the value of x.

(c) Using the value of x, determine the numerical value of the product of the three numbers.

1. The median number is 2x-4 and the information that it is consecutive even numbers. Therefore, as the median number is the middle and it goes up/down by 2, you simply add 2 to the equation of the median number as well as minus 2 from the equation of the median number.
   
   Thus, the equations of the 3 numbers are: 2x-2, 2x-4 and 2x-6.
   [*]2x-2+2x-4+2x-6=78 (the sum of the 3 numbers [see above] equals 78 [says so in the question]). After simplifying, you get 6x-12=78. Thus, x=15.
   [*]Find out all the numbers, using the equations from the first aprt of this question and the fact that x=15. You get the numbers 24 x 26 x 28. The product of these 3 numbers are therefore 17472.

 

[Kujah]

Whens the Maths exam? Tuesday?

 

[reggie7]

Whens the Maths exam? Tuesday?

yup.

 

[reggie7]

thanks continuum.

 

[Continuum]

No problem.

Sure allowed me to get away from civics crap - hate that crummy subject. Now I'm procrastinating, as usual.

 

[acevipa]

A tip for when drawing a reflection, is to fold the page. If you have any other questions or any questions unanswered questions, just remember to post them. I'm surprised your teacher didn't go through them with you. Our teacher pretty much spent a whole lesson explaining each answer and answering any of our questions. Anyways, good luck with your SC

 

[Aplus]

NON CALCULATOR:

Q.4: (Don't see how I got this wrong).

There are cows and pigs on a farm in the ratio 3:2

By what percentage does the number of cows on the farm exceed the number of pigs?

My Answer: 20%
Right Answer: 50%

What I did was add 3 and 2 together... cows is 3/5 which is 60. pigs is 2/5

There are 3 cows and 2 pigs. 3 - 2 = 1. 1/2 = 50%

 

[rainnwind]

A tip for when drawing a reflection, is to fold the page. If you have any other questions or any questions unanswered questions, just remember to post them. I'm surprised your teacher didn't go through them with you. Our teacher pretty much spent a whole lesson explaining each answer and answering any of our questions. Anyways, good luck with your SC

our teacher spent all the lessons we had this week teaching 'new' stuffs that're completely not related to sc...