Download summary YR 9 questions 2003 - 2007 and answers

MATHS MIND QUESTIONS 2003 YEAR 9
9/1.
Each child in a family has at least 2 brothers and 2 sisters. What is the smallest number of children
the family might have?
9/2. There is a pole in a lake. One-half of the pole is in the ground, another one-third of it is covered by
water, and 9 metres is out of the water. What is the total length of the pole?
9/3.
A number of children are standing in a circle. They are evenly spaced and the 5th child is directly
opposite the 18th child. How many children are there altogether?
9/4.
Haretown and Tortoiseville are 33 km apart. A hare travels at 9 km per hour from Haretown to
Tortoiseville, while a tortoise travels at 2 km per hour from Tortoiseville to Haretown.
If both set out at the same time, how many km will the hare have to travel before meeting the
tortoise en route?
9/5.
Last weekend, I went to play in the nearby park. It was real fun! I rode my new bicycle that Mum gave me
for my birthday.
On reaching the park, I saw that there were a total of 15 bicycles and tricycles. If the total number
of wheels was 36, how many tricycles were there?
9/6.
Two books cost a total of $20.95. One of the books costs $3.15 more than the other. What is the cost
of the less expensive book?
9/7.
In a box of 40 cookies, 24 of the cookies were round and 20 of them were made of chocolate. If 12
cookies were neither round nor made of chocolate, how many round chocolate cookies were in the
box?
9/8.
Six years ago, Samuel was 3/5 of his current age. How old is Samuel now?
9/9.
The integers from 1 to 9 are each written once in a
3 x 3 table. The totals of the values in each row and column are given. What number is in the space
indicated by the * ?
9/10. In a computer room there are 3 times as many boys as girls. If 4 boys and 4 girls leave the
room then 5 times as many boys will be in the room as girls. How many students were there in the
room originally?
9/11.
An integer is composed of three digits. The first digit is even. The second digit is six less than the
first digit. The third digit is three less than the first. If the integer is not divisible by five, what is the
sum of the three digits?
9/12.
How many different squares are there in the figure shown?
9/13.
1
What is the value of:
3
1
1
1
2
9/14.
A large water tank has two inlet pipes (a large one and a small one) and one outlet pipe. It takes 2
hours to fill the tank with the large inlet pipe. On the other hand, it takes 5 hours to fill the tank
with the small inlet pipe. The outlet pipe allows the full tank to be emptied in 7 hours. If the tank
holds 700 litres and is empty, how many litres would the tank hold in one and a half-hours if all 3
pipes were in operation?
9/15. A man figured out that he can cover the floor of a square-shaped room with square tiles
without having have to cut any tile. First he put tiles all around the edges of the floor using 56 tiles.
How many tiles does he need in total to cover the whole floor?
9/16.
Alex draws 300 circles with a diameter of 1 unit. Brian draws 400 squares with side length 1 unit.
Colin draws 500 equilateral triangles with side length 1 unit. What is the total length of all the sides
of all the shapes all three people have drawn?
9/17.
One afternoon Lisa notices that the current time is 10% of the way from 3.00pm to 4.00pm. What
fraction of the time from 2.00pm to 5.00pm has elapsed (in it’s simplest form)?
9/18.
A special bike lock has 3 columns of digits from which the bike owner can mix and combine to
deter any potential thieves. However, the first column only contains the digits 1 and 2; the middle
column only contains the digits 0, 4 and 8; the right hand column contains the digits 3,5,6 and 7.
What are all the three digit primes that can be produced by setting the columns in various
positions?
9/19.
Calculate the following:
(1998)(1996)(1994)(1992)  16
9/20.
Find the largest prime number that divides (evenly) into the answer to this equation:
85 - 55 - 35
MATHS MIND QUESTIONS 2004 YEAR 9
9/1
Allie takes fruit, cake and cookies to a picnic. She has 3 boxes labelled FRUIT, CAKE
and COOKIES respectively. Her mother plays a trick and puts every treat in the wrong
box. The only thing that Allie knows is that the fruit is not in the CAKE box. Where
is the cake?
9/2
A tramper’s hut contains enough emergency food to sustain 8 trampers for 3 days. How
long could this be expected to last for 6 trampers?
9/3
How many even 4-digit numbers can you make using each of these digits only once 2,
5, 3, 8?
9/4
At a children’s cycle day some children brought bicycles and some brought tricycles.
There were 18 cycles altogether with a total of 43 wheels. How many bicycles and
how many tricycles were there?
9/5
Lauren’s average mark after 2 tests is 82%. After a third test mark is included her
average becomes 86%. What did she score in that third test?
9/6
Which 2 digit number is one more than a square and one less than a cube?
9/7
A snail begins to crawl up a garden wall which is 48cm high on the morning of March
7. If it crawls 8cm a day but slips back 3cm each night, on what day will it first reach
the top of the wall?
9/8
Malcolm has 2 fuel-saving inventions which are able to work without affecting each
other; one saves 30% and the other 20%. What percentage do they save when used
together?
9/9
A hiker walks up a hill at 3km/hr and down it by the same path at 6km/hr. What is her
average speed?
9/10
A container when half full holds 3.6litres. How much more fluid is required to make it
two thirds full?
9/11
* is an operation defined in such a way that 1*2=7, 2*1=8, 1*1=5 and 2*2=10. What
does 2*3 equal?
9/12
A painter stands on a rung of a ladder. She notices that there are twice as many rungs
below her as above her. After descending three rungs she notices that the number of
rungs above and below her are equal. How many rungs are there on the ladder?
9/13
To encourage Lisa to do her homework more carefully, her father decided to pay her 5
cents for each correct problem and to fine her 10 cents for each one she got wrong.
One night Lisa had 30 problems to do and she earned 90 cents from her father. How
many did she get right?
9/14
There are 12 people in a room. If each person shakes hands exactly once with each of
the others, how many handshakes will there be altogether?
9/15
In a certain triangle one angle is equal to twice the average of the other two. If the
smallest angle is 40, what is the size of the largest angle?
9/16
How long is the side of a square whose area is numerically equal to twice its perimeter?
9/17
How many students are there in a class if two students remain after four rows of seats
are filled and nine students remain after three rows are filled?
9/18
At the “Tui Meeting” 7 tuis arrive at the tree to join those already there, then half the
whole group flies away. This process happens 7 times over after which there are just 8
tuis left on the tree. How many tuis were on the tree originally?
9/19
In extending my square courtyard which contained an even number of square tiles I
added a further 80 tiles. The result is still a square courtyard. How many tiles does it
now contain?
9/20
A block of wood in the form of a cuboid 3cm x 6cm x 10cm is painted black. If the
block is then cut into 180 cubes each 1cm x 1cm x 1cm , how many of these would
have no paint on them?
MATHS MIND QUESTIONS 2005 YEAR 9
9/1
If a ball bounces 0.8 the distance it falls, how many bounces will a ball make before it
rises to less than 1 metre if it is originally dropped from 6 metres?
9/2
An open box is constructed by starting with a rectangular sheet of metal 10cm by
14cm. Pieces are cut out of each corner so that when the sides are folded up the box
will be 1.5cm deep.
What is the volume of the box in cm3?
9/3
Twenty people at a gathering all shake hands with each other.
How many handshakes will occur for everyone to meet each other?
9/4
A farmer has a herd of n cows and divides them up between his four sons as follows.
The oldest son receives
third son receives
1
1
of the herd, the second eldest receives of the herd, the
2
4
1
of the herd and the youngest son receives seven cows.
5
How many cows are there in the herd?
9/5
Two boys each have a different number of Smurfs. One boy says ”If you give me 5 of
yours, I’ll have as many as you”. The other boy says “If you give me 5, I’ll have twice
as many as you”.
How many Smurfs does each boy have?
9/6
Two consecutive prime numbers have a product of 899.
What are the two prime numbers?
9/7
Six consecutive multiples of 5 add to make a sum between 340 and 350.
What is the lowest of the six numbers?
9/8
A man makes a trip by car and travels at an average speed of 50kph. He returns over
the same route at an average speed of 45kph.
To two decimal places, what is the man’s average speed in kph?
9/9
At a Dog training exercise there are both people and dogs. Counting heads I get 22.
Counting legs I get 68.
How many people are there at the Dog training exercise?
9/10
Balls are stacked in compact equilateral triangles such that the bottom layer has 15
balls on one side of the equilateral triangle. The second layer has 14 on one side and the
top layer has 1 ball.
How many balls are there in the stack?
9/11
There are 10 points evenly spaced about the circumference of a circle. These points are
to be connected by lines. Within the circle, no two lines may intersect each other.
What is the maximum number of lines that can be drawn in the circle.
9/12
Think of a number. Add 12.Multiply this answer by 4. Subtract 38 from this answer.
Divide this answer by 2.
Write two additional steps so that you get back to the original number.
9/13
A father has three sons whose ages are equally spread. At the present time the fathers
age is the sum of his sons ages. Five years ago the sum of the three boys ages was half
their fathers present age, and the eldest son was four times older than his youngest
brother.
How old are the three sons now?
9/14
A shopkeeper marks his goods for sale at a price which is 40% more than the price he
paid for them. On SALE DAY customers are given a discount of 25% on the marked
price. What percentage profit does the shopkeeper make on the goods which are sold
on SALE DAY?.
9/15
The favourite game of students in Maths World is based on Rugby. In their version of
the game, a try is worth 8 points, with the possibility of scoring another 2 points each
time a try is scored. A drop goal worth 5 points can be kicked at any time.
What is the largest score that cannot be made?
9/16
A palindrome number is one that reads the same in both directions (e.g.23432). Find
the number of palindromes less than 1000. Include only 2 or 3 digit palindromes.
9/17
If a and b are positive integers less than or equal to 100, and a  b , find the value of a
which will make the following expression as large as possible.
1 1

a b
1 1

a b
9/18
I think of a number. Sixty percent of the number is the same as 4/5 of the number
minus 12.
What is the number?
9/19
Find a four digit number abcd such that if a decimal place is put between the b and the
c, the resulting number is the average of ab and cd. The digits a, b, c and d must all be
different.
9/20
A class of 28 students are arranged in a circle. The students are then numbered off from
1 through to 28. The teacher starts at a random point around the circle, and then
eliminates every third student, continuing around and around until only two students
remain. They are students 8 and 18.
Which student was the first to be eliminated?
There are two different solutions depending on the direction counted off. Only one
correct solution is required.
MATHS MIND QUESTIONS 2006 YEAR 9
9/1 Bill lives with his wife and three young sons on a blueberry farm. The ages of Bill’s sons are three
consecutive odd numbers that are also prime numbers. What is the smallest possible product of the
ages of Bill’s sons?
9/2
An automobile dealer sells 2 models of cars, A and B.
Model A can be purchased in 7 different colours and 4 different engine sizes.
Model B comes in 8 colours and 3 engine sizes.
How many cars must the dealer order to have one car of each model in each colour and engine size?
9/3 How many segments, each
1
8
unit long, fit in the interval between 5
1
1
and 9 ?
2
4
9/4 Albert, Benny, Charlie and Dave were working on a money making scheme together. Benny always
got
twice as much as Albert. Charlie always got $50 more than Benny while Dave got $220 more than
Charlie. They made a total profit of $2 700. How much did Charlie receive?
9/5 Complete the contents of this table:
2
16
9
5
167
9/6
3
21
17
2
B
A=?
B=?
8
58
43
A
3469
In a group of 12 students, the heights of the seven boys are:
160 cm, 172 cm, 158 cm, 172 cm,
180 cm, 152 cm, and 161 cm. The heights of the five girls are: 158 cm, 170 cm, 150 cm,
165 cm, and 142 cm. If a sixth girl were to join the group, what would her height need to be
in order for the mean (average) heights of the boys and the girls to be equal?
9/7
Websites often record a date such as March 19, 2005 as the 6-digit number: 050319 to
represent the year, month, and day in that order.
If you subtract the 6-digit representation of July 4, 2001 from the 6-digit representation for Dec.
25, 2004,
what is the result?
9/8
A 100-digit number consisting of all 8’s is multiplied by a 100-digit number consisting of all 9’s.
What is the sum of the digits in the product?
9/9
What is the next row ?
1
1
1
1
1
1
1
4
10
1
10
1
22
40
22
1
46 124 124 46
1
9/10 If two cats take three days to catch five mice, how long would it take one thousand cats to catch
five million mice?
9/11 List the following numbers from smallest to largest:
A: 22÷7
9/12
B:355÷113
C: π D: 1.46463
James wants to save for a new bicycle. He puts 5c into a jar every day for the first week, then 10c
in every day on the second week, then 15c every day for the third week and so on. How much will he
have in the jar after 50 weeks of saving?
9/13 A googol is the number represented by the digit 1 followed by a hundred zeros. If today is a
Thursday, what day of the week will it be in a googol of days? Assume that the world will still be here.
You have only TWO attempts at this question.
9/14 Suzie starts running clockwise around a large 120m by 120m square. She started at one corner.
At the same time Wendy started running clockwise from the opposite corner. Suzie runs at 8km per
hour and Wendy at 5km per hour. How far will Wendy have run before Susie passes her?
9/15 The cost of visiting a zoo is $5 for an adult and $3 for a child.
By the end of the day, 630 persons had visited the zoo and the revenue for the day was $2368.
How many children visited the zoo on that day?
9/16
I have a pair of numbers. The cube root of their difference is the smallest odd prime that is not 1.
The square root of their sum is the smallest odd perfect square greater than 1.
What are the numbers?
9/17 A number of children are standing in a circle. They are evenly spaced and the 8th child is
directly
9/18
opposite the 18th child. How many children are there altogether?
If I travel at 45km/hr I arrive an hour late. If I travel at double that speed I arrive an hour early.
How far is the return journey?
9/19 A block of wood in the form of a cuboid 5cm x 7cm x 14cm has all its six faces painted pink. If
the wooden block is cut into 490 cubes of 1cm x 1cm x 1, how many of these smaller cubes
would have pink paint on them?
9/20 "My grandson is about as many days as my son is weeks, and my grandson is as many months
as I am in years. My grandson, my son and I together are 160 years.
Can you tell me my age in years?"
MATHS MIND QUESTIONS 2007 YEAR 9
9/1
A rectangle is cut into four pieces as shown. The areas of three of them are given. What is the total area
of the rectangle?
9/2
A sheet of card measuring 30cm by 21cm is to be cut up to make as many tickets as possible, each one
measuring 6cm by 8cm. How many tickets can be made?
9/3
While watching their flocks by night the shepherds managed to lose two-thirds of their sheep. They
found four-fifths of these again in the morning. What fraction of their original flock did they then have
left?
9/4 What is
equal to?
9/5
Find a number less than 100 which is increased by 20% when its digits are reversed.
9/6
One millionth of a second is a microsecond. Roughly how long is a microcentury?
9/7
When a barrel is 30% empty it contains 30 gallons more than when it is 30% full.
How many gallons does the barrel hold when full?
9/8
Razia broke her necklace. She found one-third of the beads on the floor, one-quarter in her pocket, onefifth down the side of the sofa, while one-sixth remained on the string; six beads were never found. How
many beads were there to start with?
9/9
In how many ways can 105 be written as the sum of two or more consecutive positive integers?
9/10
What is the angle between the hands of a clock at 9:30?
9/11
A child’s box of bricks contains cubes, cones and spheres. Two cones and a sphere on one side of a pair
of scales will just balance a cube on the other side; and a sphere and a cube together will just balance
three cones. How many spheres will just balance a single cone?
9/12
Malcolm covers any distance in one-third of the time it takes
Nikki to run the same distance. They set off in opposite
directions round the track as shown. Where will they meet for
the first time?
9/13
What fraction of the area of the regular hexagon is the shaded triangle?
9/14
I am standing behind five pupils who are signalling a five-digit number to someone on the opposite side
of the playground. From where I am standing the number lookslike 23456. What number is actually
being signalled?
9/15
If the shading of squares is continued so that m and m’ become lines of symmetry of the completed
diagram, what is the largest possible number of squares left unshaded?
9/16
Ali (A) and Baba (B) are shown surrounded by six thieves. The thieves’ ages are given. Ali’s age is the
average of his four nearest neighbours,and so is Baba’s. How old is Ali?
9/17
The symbol 50! represents the product of all the whole numbers from 1 to 50 inclusive; that is, 50! = 1 x
2 x 3 x …..x 49 x 50. If I were to calculate the actual value, how many zeros would the answer have at
the end?
9/18
A new sculpture in Aotea Square consists of three cubes sitting one on top of the other without any
overhang (as shown). The cubes have sides of lengths 2, 3, and 4 metres respectively. The bottom cube
is sitting on the ground and each of the other two are glued to the cube below. All the outside surfaces of
the sculpture are to be painted red. If one tin of paint is needed to cover one square metre, how many tins
are needed altogether?
9/19
Seven cubes are glued together face to face as shown.What is the surface area, in square centimetres, of
thesolid if its volume is 189 cubic centimetres?
9/20
I picked a bunch of flowers from a bucket containing 3 colours. All except 6 were white. All except 6
were blue. All except 6 were yellow. How many flowers were in the bunch?
9/21
At the farmers’ market, a horse costs the same as a pig and a cow, a cow costs the same as a pig and a
pony, and two horses cost the same as three ponies.
How many pigs cost the same as a horse?
9/21
At the farmers’ market, a horse costs the same as a pig and a cow, a cow costs the same as a pig and a
pony, and two horses cost the same as three ponies.
How many pigs cost the same as a horse?
9/22
How many positive integers less than 500 have the sum of their digits equal to 4?
9/23
The figure on the right is made from small squares all of the same size. If the area of the figure is 275
square centimetres, what is its perimeter in centimetres?
9/24
Maryanne thinks of a three digit number. She counts backwards, starting with this number and at the
same time and the same speed, her friend Mark starts to count 2, 4, 6…
At the same moment that Mark says 106, Maryanne says 75. What was Maryanne’s starting number?
2003 Mathsmind Year 9 Answers
Question
Number
Answer
1
6
2
54
3
26
4
27km
5
6
6
$8.90
7
16
8
15
9
6
10
32
11
9
12
14
13
1
14
585 litres
15
18
225
4042.48 (2 d.p,)
accept any correctly
rounded version
11
30
103, 107, 203, 207, 247,
283, 287 (all required)
19
3 980 020
20
7
16
17
2004 Mathsmind Year 9 Answers
Question
Number
1
Answer
2
4 days
3
12 numbers
4
5
11 bikes & 7
trikes (need
both)
94%
6
26
7
March 16
8
44%
9
4km/hr
10
1.2 litres
11
12
12
19 rungs
13
26
14
66 handshakes
15
90
16
8
17
30 students
18
135 tuis
19
144
20
32 cubes
Fruit box
2005 Mathsmind Year 9 Answers
Question
Number
1
Answer
2
115.5
3
190
4
140 (Cows)
5
25 and 35
6
29 and 31
7
45
8
47.37
9
10 (people)
10
680
11
17
12
-5 and  2
13
7, 10 &13
14
5%
15
27
16
99
17
a = 99
18
60
19
49.50
20
28 or 26
9 (times)
2006 Mathsmind Year 9 Answers
Question
Number
1
2
Answer
105
3
52 or
28 of A and 24
of B
30
4
5
$730
A=9 B=1651
6
205cm
7
030521 or
3 yrs 5 months
21 days
900
8
9
10
1, 94, 340,
496,340,94,1
6000
11
CBDA
12
$446.25
13
14
Monday
(only two
attempts)
400m
15
391
16
27 and 54
17
20
18
360km
19
310
20
96
2007 Mathsmind Year 9 Answers
Question
Number
1
40sq units
2
9
3
13/15
4
5
4/5
45
6
1hour
7
75 gallons
8
120
9
7
10
105°
11
2
12
E
13
1/3
14
42635
15
9
16
38
17
6 pigs
18
15
19
270cm2
20
12
Answer