Help Needed: High School Math Test Decides My Future

[Dagenais]

My school is making the students take a test that compares us with all the other schools in our area. It includes mental mathematics, number sense, reasoning etc.

Unfortunately, I forgot a lot of the way to solve these things and a few are 'trick' questions.

I need help on the ones I am unsure of or have no clue how to do. I'm hoping some of you may choose to do 1 or 2 and tell me if I'm right or wrong?

This test decides whether I graduate High School or not. I've got the English part down pretty well...but not the math. I assure you I did ask the teacher for help, but I was not finished with the assignment, so I need help on the ones I have just finished.

Here are the questions I need help on from my prep worksheet:

Square ABCD has all four of its vertices on a circle with diameter 10 units in length. Segments AC and BD are diameters. How many square units of area does ABCD have?

My answer: 14.14 units squared. I came to this conclusion because the 2 diameters cross each other making 4 triangles. I'm not sure if I'm allowed too since nothing is said about the diameters bisecting creating 4 congruent lines, but I labeled each of the 4 lines in the square with the value "5". I then had enough information to find the missing side of the triangle with the Pythogorean Theorom, resulting in 7.07, and I multiplied it by 2. 7.07 represents the side of the square.

My problem here is that I am not sure if the 2 10 unit diameters bisect each other to create 4 congruent lines of 5.

Next Problem

Rectangular cards, 2 inches by 3 inches, are cut from a rectangular sheet 2 feet by 3 feet. What's the greatest number of cards that can be cut from the sheet?

My answer: I don't know. 144. The area of the large sheet divded by the area of the cards.

Next Problem

A train travels 1 mile in 1 minute 30 seconds. At this rate, how many miles will the train travel in 1 hour?

My answer: 78 miles because 1 mile is 1 minute 30 seconds, and 1 hour equals 60 minutes. I multiplied 1.30 with 60.

Next Problem

A motorist madea 60 mile trip averaging 20 miles per hour. On the return trip, he averages 30 miles per hour. What was the motorist's average speed for the entire trip?

My answer: 25MPH.

Next Problem

Suppose 5 days after the day before yesterday is Friday. What day of the week will tomorrow then be?

My answer: What!? Huh!?...Friday?



Next Problem

A dog takes 3 steps to walk the same distance for which a cat takes 4 steps. Suppose 1 step of the dog covers 1 foot. How many feet would the cat cover in taking 12 steps.

My answer: 16. I can't even tell what I did, so I know I did this wrong. I need to know how to solve it though.


Thanks in Advance. And yes...I know I better study...

 

[chroot]

...resulting in 7.07, and I multiplied it by 2. 7.07 represents the side of the square.

The sides of the square certainly are $5 \sqrt 2$, but since when has the area of a square been twice the length of its sides? I always thought a square with sides s units has s² area.

The area of the large sheet divded by the area of the cards.

That's not true in general, but happens to be true here, since you can evenly divide both sides of the large sheet by 12.

My answer: 78 miles because 1 mile is 1 minute 30 seconds, and 1 hour equals 60 minutes. I multiplied 1.30 with 60.

Quick sanity check: if it takes more than a minute to go a mile, you're not going more than 60 mph. 78 mph is obviously wrong. Watch your unit conversion:

(1 mile / 90 seconds) * (3600 seconds / 1 hour) = ?

My answer: 25MPH.

No. He road a total of 120 miles, and it took him 5 hours to do it. That's 24 mph.

My answer: What!? Huh!?...Friday?

Draw it on a piece of paper. If today is Tuesday, the day before yesterday is Sunday. Five days after Sunday is Friday.

My answer: 16. I can't even tell what I did, so I know I did this wrong. I need to know how to solve it though.

If the dog's footstep is 1 foot, then the cat's footstep is 3/4 of one foot. If the cat takes 12 steps, each of which is 3/4 of a foot, he's gone 9 feet.

Looks like your school's not going to fare well against its competitors.

- Warren

 

[Dagenais]

If the dog's footstep is 1 foot, then the cat's footstep is 3/4 of one foot. If the cat takes 12 steps, each of which is 3/4 of a foot, he's gone 9 feet.

Damn, I can't believe I missed that. I knew it was 3/4th of something, but I just got confused thinking that mixing up the # of steps with the feet.

Looks like your school's not going to fare well against its competitors.

It never has.

My goal is just to pass the math part.

 

[chroot]

Damn, I can't believe I missed that. I knew it was 3/4th of something, but I just got confused thinking that mixing up the # of steps with the feet.

Mind your units. When it doubt, write 'em out:

12 cat steps * (3 dogs steps / 4 cat steps) * (1 foot / 1 dog step) = 9 feet.

- Warren

 

[Dagenais]

Thanks. I'm looking at a real version of the test right now straight from the site. Turns out the questions are easier.

Maybe I'll pass afterall.