Grade Eight Hints

Question #1

Hints:

1) Try and calculate the amount of money that they would have to pay for the installment plan.

2) Calculate the difference between the installment plan and the initial amount if they paid today.

Hints:

1) What information is important in this question?

2) How long did it take her to run 200m in seconds?

Hints:

1) Make a chart of the percentages scored on each test for each student. As the following:

           PERCENTAGE FOR FIRST TEST	 PERCENTAGE FOR SECOND TEST	DIFFERENCE
MARK			
JAKE			
MARILYN			

2) If you forget how to do percent, heres a hint: divide the denominator into the numerator and multiply by 100%

Part B

Hint:

1) Try making another chart with percentages of each test. Like the following:

	     30% of first test	  70% of second test	 SumFinal Mark
MARK			
JAKE			
MARILYN			

Question #4

Hints:

1) Make a chart to help you use logical reasoning

Question #5

Hints:

1) Try to draw a sketch of how many sheets are piled as the pile is cut each time.

2) Now try to find a pattern in the numbers.

3) How many sheets will you have after the sheets are cut and piled 10 times.

4) How many cm high is this pile. Don't forget to change your mm to cm.

Question #6

Hints:

1) When all else fails, make a chart or a table. Start by writing the numbers in columns and rows.

ex. 0   1   2   3   4   5   6   7   8   9
   10  11  12  13  14  15  16  17  18  19
   20  21  22  23  24  25  26  27  28  29
    |   |   |   |   |   |   |   |   |   |
    |   |   |   |   |   |   |   |   |   |

2) Now examine the digits in the rows (horizontal). What do you notice about digits? Try and find a pattern in the ones place.

3) Carry on to find a pattern in the ten's place.

4) Don't forget about the number 100!!

Question #7

Hints:

1) To find the percentage increase in the dry cleaning of a sports coat, set up an algebraic equation.

4 * x = 5.00

2) Now what is the price of the new cost of dry cleaning a jacket?

Question #8

Hints:

1) How many faces / sides are on a cube. How long is the piece of ribbon on each side? Find the total length of the ribbon on the sides.

2) Now the top and the bottom look like:

What is the total length of the ribbon for the top and bottom?

3) Find the total length of all the ribbon in meters.

Question #9

Hints:

1) Draw and label the diagram with the dimensions given.

2) Now find the inner dimensions of the paneling and find the area.

Question #10

Hints:

1) Do you remember how many degrees there are in a triangle or a straight line?

2) There are 180 degrees in a triangle. That is the sum of the angles in a triangle is 180 degrees. A straight line is 180 degrees.

3) Say your diagram was as the following:

? = 180 degrees - 150 degrees

? = 30 degrees

4) Solve the problem!!!

Question #11

Hints:

1) What does Mr. MacDonald have to do to find the average mark of his class?

2) Average means the sum of the test marks divided by the number of students. So, what was the sum of all the tests?

3) After you have the sum of all the tests you can find the correct average by correcting Mr. MacDonald's sum and finding the correct average.

Question #12

Hints:

1) Try different numbers that will satisfy the conditions given in the number.

2) The sum of the numbers of acorns is twice six. Find out the how many Chip had and Dale had.

Question #13

Hints:

1) One way to overcome this problem is to think of percentages. What is the percent of $15 out of the total $120 earnings?

2) Now we know what percent of his total earnings is. How many degrees are in a circle?

3) The percent of money he spends on music is how many degrees in the circle?

Question #14

Hints:

1) Show diagram.

2) Do you remember how to find the missing side of a right triangle?

3) The Pythagorean theorem says, the hypotenuse, which is the longest side opposite the right angle, is equal to the square root of the sums of the squares of the other two sides.

Z² = X² + Y²

4) How many additional meters would she have to walk?

Question #15

Hints:

1) You must find the total area of the pool.

2) The pool can be divided into 3 different shapes.

3) The area of a circle is A = Pi * r²

4) Find the total amount of money given that it costs $5.00 per meter squared.

Question #16

Hints:

1) You must use the Pythagorean theorem to help Lisa!

2) Divide the line LM into two parts. Solve the distance of each part.

3) Don't forget to convert to mm.

Question #17

Hints:

1) Divide the square into 4 equal parts. Can you see the answer?

Question #18

Hints:

1) If the snake is one meter long in real life and 2cm long in the picture, how high is the building if it is 4.5cm long in the picture.

2) The easiest way to do this is to set up a ratio like:

    100      x
    ----  = ---
    2cm     4.5cm
    Solve for x, which is the height of the building.

Question #19

Hints:

1) Make a chart

 -> 1st birthday  $1
    2nd birthday  $2
    3rd birthday  $4
     |
     |

2) How much did he get in total?

Question #20

Hints:

1) Try to limit the amount of possibilities for each teacher.

Example: Ms. Garcia can't teach art because she has taught more years than the mathematics teacher, and the art teacher has taught the least number of years.

Question #21

Hints:

1) The best way to approach this problem is to work backwards. Try starting with statements: If Bob has 27 comic books and Charles has 2/3 as many, how many does Charles have?

2) Jim has 3 times as many as Charles. So how many comic books does Jim have?

3) If you need help in setting up equations, here's a start:

    2/3 * # of Bob's comics = # of Charles comics
    =>Now do the same thing for Jim:
    3 * # of Charles comics = # of Jim's comics

Question #22

Hints:

1) First try and calculate how much Friendly's paid for each handkerchief when they bought them and how much a customer paid for each handkerchief. You can set up algebraic expressions to help you.

6p = $10 and 4s = $10

p = price of hamdkerchiefs and s = selling price of handkerchief

-> Find p and s

2) Now how can we tackle how many handkerchiefs they sold if the store made $60.00? One way to start is to set up an algebraic expressions that will solve for the number of handkerchiefs. If the store pays $10/6 for a handkerchief and sells it for $2.50 then how many should it sell make $60.00?

(s-p)*x = $60.00

-> Solve this algebraic equation for x, where x is the number of handkerchiefs.

Question #23

Hints:

1) In order to find the average speed, you must find the tthe total time it took you to travel to and from Carolina beach.

2) Remember: Rate = distance/time

3) The average speed is the total distance divided by the total time.

Question #24

Hints:

1) Set a variable x equal to the number of 2kg disks. If x is the number of 2kg disks, what is the number of 5kg disks?

2) The number of 5kg disks is:

14 - x = (total number of disks - the number of 2kg disks)

3) We know that the weight of the 2kg disks equals the weight of the 5kg disks.

So 2kg * x = 5kg(14 -x)

Solve for x.

4) What is the total weight?

5)Total weight=2 kg *( # of 2 kg discs) + 5 kg * ( # of 5 kg discs)

Question #25

Hint:

1) Try to think of a good solution!!

Question #26

Hints:

1) This is a reasoning problem. Use the clues to figure out the problem.

Question #27

Hints:

1) What is the distance from D to E?

2) What is the distance from B to D?

3) What is the distance from D to C?

Question #28

Hints:

1) How many pages are in the book?

2) How many pages has Bob read?

3) How fast does he read?

4) How many page does Bob have left to read?

5) If Bob had 48 pages left to read, how many days would it take?

6) How should you determine the number of days it will take to read 288 pages?

b)

Hints:

1) Try using what you learned in part a to solve b.

Question #29

Hints:

1) This is a trial and error problem. You must first try one set and then add up the rows, columns, and diagonals. If it works you've found an answer.

Question #30

Hints:

1) Make a guess then check your guess!

2) If Homer ate one pie the first day how many would he eat the second day?

3) If he ate 10 pies on the first day, how many would he have eaten all together at the end of the 6 days?

4) Would guessing that Homer ate 20 pies on the first day be a good guess?

5) Try another number!

Question #31

Hints:

1) Set up a proportional equation

2) $1.70/ 1/2 kilogram = x/2.5 kilograms

Solve for x

Question #32

Hints:

1) Find the dimensions of the cube: the length, width and height.

2) Now you can find the volume! Remember, the volume of a cube is l*w*h

Question #33

Hints:

1) There will be a fence post in each corner of the field.

2) How many posts are on each side of the field?

3) If there is 5m between each pair of posts, what is the length of a side of the square?

4) What is the area? Remember A = l*w

5) What are the units?

Question #34

Hints:

1) This is a trial and error problem. You must practice your square numbers. Try different combinations.

2) After you've found one combination see if you can find any others.

Question #35

Hints:

1) How many sit-ups would you have to do to tie the record?

2) If you can do 40 sit-ups per minute, how many minutes does it take to do 17,000?

3) To answer the secnd part, what is the rate of sit-ups/minute of the Canadian record?

Whose rate is better?

Question #36

Hints:

1) One way to approach this problem is with algebraic expressions. Let x = # of incorrect answers. What does the number of correct answers equal in terms of x?

2) The number of items on the test equals the number of incorrect answers + the number of incorrect answers.

Question #37

Hints:

1) Is there a pattern in piling the grapefruit?

2) Make a chart and find the sum.

			1st	 1
			2nd	 4
			3rd	 9
			  |	 |
			  |	 |

Question #38

Hints:

1) Try to decide how you could break up the figure and find the area.

2) How would you find the perimeter? You must know the length of the sides.

3) HINT!!! Divide the figure by connecting the midpoints of each side by a line. Now do you see?

Question #39

Hints:

1) You could start by guessing the length and width, but that may take a long time. Try and solve this problem by setting one dimension equal to x. What is the other variable equal to?

2) If the width is equal to x, then what is the length equal to in terms of x?

3) x = width

4*x = length

Now try and find the variable x by solving for the area = 100 meters squared.

Question #40

Hints:

1) Do you remember what the rate is equal to in terms of distance and time?

2) Rate = distance/time

3) You are asked to find the times of the two trips. What does time equal in terms of distance and rate?

4) Use the times you calculated to find how much longer the trip is going West.

Question #41

Hints:

1) This is a trial and error problem. Answering these questions will help you: