The Canadian School Math Page
Grade Nine Problems
1)
Elizabeth visits her friend Andrew and then returns home by the same
route. She always walks 2km/h when going uphill, 6km/h when going downhill
and 3km/h when on level ground. If her total walking time is 6 hours, then
what is the total distance she walks in km?
Need A Hint?
Answer
2)
Joyce was decorating her store window for a going out of business sale.
She wanted to make a figure that looks like the following. The shaded piece
is made of a different material. How much material does she need in
metres squared?
Need A Hint?
Answer
3)
In # 2 Joyce needed to find the material she would need for the shaded
region. How much material would she need for the unshaded region in m^{2}?
Need A Hint?
Answer
4)
George and Phil were playing with their fish tank again. They had a
difficult time keeping their fish alive. The fish tank is 100cm long, 60 cm
wide and 40 cm high. They tilted the tank, as shown, resting on a 60 cm edge,
with the water level reaching the midpoint of the base. When they rest the
tank down to a horizontal position, what is the depth of the water in cm?
Need A Hint?
Answer
5)
Alex, Fred and Thomas run at constant rates. In a race of 1,000m, Alex
finished 200m ahead of Fred and 400m ahead of Thomas. When Fred finished,
how far was he ahead of Thomas? (in m)
Need A Hint?
Answer
6)
If ABCD is a square and ABE is an equilateral triangle, then what is the
measure of < BFC?
Need A Hint?
Answer
7)
An unusual die has six faces labelled 1,2,3,5,7 9. If two of these
dice are rolled, and the numbers showing on the upper faces are added, what
is the number of possible different sums?
Need A Hint?
Answer
8)
The Quinpool family decided to build a pool of the following shape. The
sides of their 12 * 9 yard are trisected. What is the perimeter of the
shaded pool?
Need A Hint?
Answer
9)
A classroom contained an equal number of boys and girls. Eight girls left
to play hockey, leaving twice as many boys as girls in the classsroom.
What was the original number of students present?
Need A Hint?
Answer
10)
Flora had an average of 56% on her first 7 exams. What would she
have to make on her eighth exam to obtain an average of 60% on 8 exams?
Need A Hint?
Answer
11)
I have a broken fan belt on my car. The belt goes around 2 pulleys,
whose centers are 15cm apart and each pulley is 4 cm in diameter. How long
should the belt be?
Need A Hint?
Answer
12)
Coming out of the grocery store, Ebree has eight coins, of which none
is a half-dollar, that add up to $1.45. Unfortunately, on the way home
she loses one of them. If the chances of losing a quarter, dime or nickel are
equal, which coin is most probably lost?
Need A Hint?
Answer
13)
Joe gives Nick and Tom as many peanuts as each already has. Then Nick
gives Joe and Tom as many peanuts as each of them then has. Finally, Tom
gives Nick and Joe as many peanuts as each has. If at the end each has
sixteen peanuts, how many peanuts did each have at the beginning?
Need A Hint?
Answer
14)
After a Math test, each of the twenty-five students in the class got a
peek at the teacher's grade sheet. Each student noticed five A's. No student
saw all the grades and no student saw his or her own grade. What is the
minimum number of students who scored A on the test?
Need A Hint?
Answer
15)
Bart Simpson goes to the corner store and buys an equal number of 35
cent and 30 cent candies for $22.75 (that's a lot of candy!!) How many candies did
he buy?
Need A Hint?
Answer
16)
The Band Committee of 100 people wishes to set up a telephone call system.
The initial contact person calls three other people, each of whom call three
others and so on, until all the people in the Band Committee have been
contacted. What is the maximum number of people they need to make the calls.
Need A Hint?
Answer
17)
Students in an elementary class decided to spend D dollars for a
present for their favourite teacher, Mrs. Ballentine, each contributing an
equal amount. Because fifteen students refused to contribute, each of those
remaining agreed to contribute an additional, equal amount. What was the
additional amount each had to contribute, in dollars?
Need A Hint?
Answer
18)
Ian was entering a Math contest for Grade 9. He was working on this
particular problem. He was having difficulty with the answer. This was the
problem: The integers greater than 1 are arranged, four in each row, in 5
columns, as follows:
a b c d e
2 3 4 5
9 8 7 6
10 11 12 13
17 16 15 14
If he followed the pattern what column would the number 1002 fall in?
Need A Hint?
Answer
19)
Three grade nine Math students were given the following problem:
A three digit number 2A4 is added to 329 and gives 5B3.
If 5B3 is divisible by 3, then what is the largest possible
value of A? One student thought A could be 1. Another
student thought A was 5. The last student thought A was 4.
Who was correct?
Need A Hint?
Answer
20)
Joy, Noella and Holly were playing jump rope. Joy and Noella at points B
and C were twirling the skipping rope waiting for Holly at point A to jump
into
the middle of the rope (at point D). The three girls formed a 90 degree
angle. Holly was 1m away from Noella and 1m away from Joy. How far does
she
have to jump into the middle of the skipping rope? AD is perpendicular
to BC.
Need A Hint?
Answer
21)
You are given this graph of a triangle DEF and you are asked its area.
What do you think it is?
Need A Hint?
Answer
22)
Constable Bob is driving along the Trans-Canada Highway at 100 km/h. He
is passed by Melissa who is driving in the same direction at a constant speed.
Ten seconds after Melissa passed Bob, their cars are 100m apart. What is the
speed of Melissa's car in km/h?
Need A Hint?
Answer
23)
Triangle ABC is an isosceles right angled triangle with BC = AB = 2.
A circular arc of radius 2 with centre C meets the hypotenuse at D. A
circular arc of radius 2 with center a meets the hypotenuse E. What is
the area of the shaded region?
Need A Hint?
Answer
24)
Fred picked four numbers out of a hat. The average of the four numbers
is 9. If three of the numbers are 5, 9 and 12, then what is the fourth
number?
Need A Hint?
Answer
25)
26)
Chris asked Loretta her age and she said:
"My age?" she asked, "you'll have to guess!"
"Just let me think, AH!, that's it: yes!!"
"Reverse my age, divide by three, add thirty-four, my age you'll see!"
How old was Loretta?
Need A Hint?
Answer
27)
George Jefferson plans to drive from his home to Edmonton, a trip of
2200km. His car has a 24 gallon tank and gets 27km to the gallon. If he
starts out with a full tank of gasoline, what is the fewest number of stops he
will have to make for gasoline to complete his trip to Edmonton?
Need A Hint?
Answer
28)
Can you guess this number?
- The number is not an odd number.
- It has exactly four factors.
- If you reverse the digits, a prime number is formed.
- The sum of the digits is a two digit prime number.
- The number is less than the square root of 10^{4}.
- One of the digits is a square number.
What number are we thinking of?
Need A Hint?
Answer
29)
"Was that your bike Mom?" asked Charlene in awe. Her mother looked at
the faded old photo and replied, "My first, and I earned it. I got a job
that summer with a cycle dealer and he was to pay me thirty dollars and this
new bike for seven weeks of work. But I didn't enjoy the job so I quit after
four weeks. He gave me three dollars and I kept the bike." How much was the
bike worth?
Need A Hint?
Answer
30)
A cubic metre of water weighs 1000kg. What is the weight of a
waterbed mattress that is 2 metres by 3 metres by 20cm if the casing of
the mattress weighs 1kg?
Need A Hint?
Answer
31)
Melissa and Craig were doing their math homework. They had a
disagreement on one of the problems. The problem read, "What
is the value of (4)(2^{1996})? Melissa found it to be
(8^{1996}), but Craig disagreed and felt it was (2^{1998}).
Were either of them right? If so, who was right?
Need A Hint?
Answer
32)
33)
In a recent survey, 40% of houses contained two or more people. Of
those homes containing only one person, 25% contained a male. What is the
percentage of all houses which contain exactly one female and no males?
Need A Hint?
Answer
34)
In a recent election at the Dr. John Hugh Gillis High School, Susie
Cook received 542 votes, Greg MacDonald received 430 votes and Travis Austen
received 130 votes. If 90% of those eligible to vote did so, what was the
number of eligible voters?
Need A Hint?
Answer
35)
If the figure shown is folded to make a cube, then what is the letter
opposite the S?
Need A Hint?
Answer
36)
Jill loves math but she hates this problem. Can you help her? The sum
of four numbers is 64. If you add 3 to the first number, 3 is subtracted
from the second number, the third is multiplied by 3 and the fourth is
divided by three, then all the results will be equal. What is the difference
between the largest and the smallest of the original numbers?
Need A Hint?
Answer
37)
If the five expressions 2x + 1, 2x - 3, x + 2, x + 5, and x - 3 can
be arranged in a different order so that the first three have a sum 4x + 3,
and the last three have a sum 4x + 4, what would the middle expression be?
Need A Hint?
Answer
38)
In our volleyball league, the numbers on the jerseys may be formed
using one or two digits chosen from 1, 2, 3, 4, 5. Numbers with repeated
digits are allowed but the single digit numbers are not allowed. What is the
total number of possible jersey numbers for each team?
Need A Hint?
Answer
39)
Mark has $4.50 and Jean-Martin has $3.00. Mark spends twice as much as
Jean-Martin and now sees that he has half as much money left as
Jean-Martin has left.
How much money did Mark spend?
How much money did Jean-Martin spend?
How much do each of them have left?
Need A Hint?
Answer
40)
A motorcycle and a truck left a roadside diner at the same time. After
travelling in the same direction for one and a quarter hours, the motorcycle
had travelled 25km farther than the truck. If the average speed of the
motorcycle was 60km/hour, find the average speed of the truck.
Need A Hint?
Answer
41)
Similar rectangles are constructed on the sides of a right triangle as shown. Find their areas and a relationship among those areas. Have you seen a similar relationship?
Need A Hint?
Answer
42)
Triangle PQR is equilateral. QR = 30 units, B is the midpoint of QA. QA
is perpendicular to PR. What is the length of PB?
Need A Hint?
Answer
43)
I have sold 2/3 of my pencils for $0.15 each. If I have 8 pencils
left, how much money did I collect for the pencils I sold?
Need A Hint?
Answer
44)
The minute hand of a clock is 6cm long. To the nearest centimeter,
how far does the tip of the minute hand move in 35 minutes?
Need A Hint?
Answer
45)
The numerator of a certain fraction is 3 less than the denominator.
If the numerator is tripled and the denominator is increased by 7, the value of the resulting fraction is 3/2. What was the original fraction?
x = denominator
x-3 = numerator
Need A Hint?
Answer
46)
Darryl ate 100 peanut butter cups in five days. Each day he ate six
more than he ate the previous day. How many peanut butter cups did
Darryl eat on the first day?
Need A Hint?
Answer
47)
48)
A Roman boy was given this puzzle:
Take one hundred one, and to it affix the half of a dozen, or if you please
six; Put fifty to this, and then you will see what every good boy to others
should be.
Need A Hint?
Answer
49)
42 | | 40
----+----+----
| |
----+----+----
38 | 43 | 36
Need A Hint?
Answer
50)
Lilly had a math project to do for her geometry class. Her teacher
wrote, "A cuboctohedren is a polyhedron that can be formed by
slicing a cube at the midpoints of its edges." Lilly had to find the
surface area of the cuboctobedren formed by a cube having a side of length
4cm?
Need A Hint?
Answer