Please, beg you help me with these Grade 9 math questions. Just explain the solutions to me so I can learnhow?

Question

to solve these equations on my own. I really need help and am so stuck!

Here is the link to see the equations, some deal with triangles, my greatest weakness!! Please help me from questions 6-25, and do as many as you can. If you want to email me the solutions & explanations email me at [e-mail]

http://cemc.math.uwaterloo.ca/contests/past_contests/2008/2008PascalContest.pdf

Answer 1

6) angle in a straight line =180 degrees

therefore angle RQS = 180 - 136 = 44

sum of angle in a triangle = 180 degrees...

hence x = 180 - ( 64 + 44)

x = 72

Ans: A

7) Probability = no of possible ways of getting the item / total no of possible outcomes

here,no of blue jelly = 8

total outcome = 5+6+7+8 = 26

hence, probability blue jelly = 8/26 = 4/13

Ans: D

8)

1 hour 30 mins can be written as 3/2 hours

hence,  6 hours ---> 108 apples

3/2 hours ----> 108 /6 * 3/2 = 27 apples

Ans: A

9) since the grids are of equal length, 5 grids make up a length of 10

implying that 1 grid makes up a length of 10/5 = 2

therefore, 1 whole grid being of 4 sides will take up 4*2= 8 length

hence, 15 grids will take 8*15 =120

Ans: C

10)S= 3/4 * ( 46- -14)

= 45

T = 1/3 *  ( 46- -14)

= 20

TS = 45 -20

= 25

Ans: D

11) no of boys receiving certificates = 30% * 30 = 9

no of girls receiving certificates =40% * 20 = 8

% of students receiving certificates = (9+8) / 50 * 100 = 34%

Ans: A

12)  Perimeter = ( x + 4 + x -2) *2

=(  2x -2) * 2 = 56

2x -2 =28

2x = 30

x = 15

length = x + 4 = 15 + 4 = 19

width = x -2 = 15- 2 = 13

area= length * width = 19 * 13 = 247

Ans: A

13) when the base is equal while doing multiplication, u can add the powers, therefore,

2^3 * 2^2 = 2^5= 32

3^3 * 3^2 = 3^5=243

hence, 32 * 243 = 7776 = 6^5

Ans: A

14) can't really explain this one but answer is 21

Ans:C

15) consider triangle QSR

length of QS = sqrt of 25^2 - 20^2 = 15

consider triangle QSP

length of QP = sqrt of 15^2 + 8^2 = 17

therefore perimeter = 17 + 8 + 20+ 25 = 70

Ans:E

16) Area of circle = M = pie * r^2

perimeter of circle = N =2 pie r

M/ N = 20

pie *r^2 / 2pie r = 20

r/2 = 20

r = 40

Ans: C

Well.. i'm tired now... try to continue on ur own... best of luck...  

Answer 2

The point of tests is seeing how good you are at a subject, not cheating to get a good grade.

Answer 3

I usually agree with what Darklighta said, but this seems different: it's a competition test that has already happened.  I don't think you're cheating, so I'll give you some hints.

6) Angles PQS and RQS are supplements.  Can you use this to find the measure of angle RQS?

7) Each marble is as likely to get pulled as any other.  The probability will be a fraction: number of blue marbles over number of (all) marbles.

8) How many apples does Olave sell per hour?

9) Total up the horizontal wire lengths, and then the vertical wire lengths, and then add them together.

10) If you add 14 to both numbers (so P is at 0 and Q is at 60), you'll slide the entire problem to the right.  This won't change the distance from T to S, but it will make the numbers a lot easier to work with.

11) How many students won awards?  How many student participated?  Find the ratio between these two numbers, and convert to a percent.

12) Add up the four sides of the rectangle (x-2, x+4, x-2, and x+4) to get the perimeter.  We know this is 56, so set 4x+4=56.  Solve for x.  Now you can write the side lengths as plain old numbers.

13) When you multiply different powers of the same base, add the exponents.  For example, 5^2 * 5^7 = 5^9.  Also, when you multiply the same powers of different bases, leave the exponent alone and multiply the bases.  For example, 3^4 * 7^4 = 21^4.

14) What must c+f be, in order to get a 0 in the units place?  What gets carried?  What must (b+e+carry) be, in order to get 0 in the tens place?  What does that make b+e?  Continue.

15) Use the Pythagorean Theorem on SQR, and then use it again on PQS.  (You might recognize SQR as a blown-up 3-4-5 right triangle, too.)

16) Do you know the formulas for area and circumference of a circle, in terms of the radius r?

17) What is the area of one face of the large cube? How long is each side?  How long is each side of the small cube?

18) Try to get as close to $2.65 as you can, using only quarters.  Can you go the rest of the distance using dimes?  If not, throw away one quarter and try again.  Repeat if necessary.

19) How many upright integers end in 1?  How many end in 2?  Extend the pattern.

20) Don't get bogged down trying to figure out which four of the six have and average of 2008.  Instead, realize that whichever four they are, their sum is 4*2008.  Likewise, the sum of the other two numbers is 2*(the missing average).  We can find the sum of all six numbers in two ways: (1) just add up all six of them; (2) add 4*2008 to 2*x.  Set these equal to each other and solve for x.

21) By setting p and q to their extreme values, find the largest and smallest possible values of p/q.  (Largest happens for big p and small q; smallest happens the other way around.)

22) First, convert 3 3/4 min into hours.  If t is how many hours it takes Ginger to run to school, then t+(that converted number) is how long it will take her to walk.  Since d=rt, we have 6t = 4(t+number).  Solve for t, then for d.

23) If x is where the cut happens, then the left side of the cut has a total length of x+(x-3)+(x-2)+(x-1.5), where those subtracted bits are the distances from logs to M.  The total lengths of the logs is 5+3+5+4=17, which must be double the left side length.  Set (x stuff) = 8.5 (which is half of 17), and solve for x.

24) There's one circle connected to three others.  Call it A.  Pick any color for A that you like, and then count the number of ways you could finish coloring the square.  Double your answer, because there are two ways to color the oddball circle hanging off the bottom; then, triple this number because you could have started with any of three colors at A.

25) I felt pretty uncreative when I solved this by analytic geometry.  Put P at (0,0), Q at (2,0), and R at (0, 2sqrt3).  Line PL has a slope of 1/sqrt(3).  Find equations for line PL and line RM, the find coordinates for their point of intersection, F.  I think there's a much better solution, though.