MATHS MIND QUESTIONS 2003 YEAR 10
10/1.
There is a number, greater than zero, that is 3 times the sum of its digits. What is this number?
10/2.
What is the next number in this sequence?
1 , 2 , 5 , 12 , 29 , 70 , …
10/3.
If A is 10% of C, and B is 25% of C, what percent of B is A?
10/4.
Suppose that What is the value of (1*2)*(2*1)?
10/5.
A snake slides horizontally through a long cylindrical tunnel at 6 centimetres per second. The tunnel is 7.74 metres in length. The snake takes 14 seconds to enter the hole.
(a) What is the length in centimetres of the snake?
(b) How many seconds does the snake take to exit the hole after entering it?
10/6.
When I add 6 times my age 6 years from now to 7 times my age 7 years from now, I get 14 times my current age. How old will I be 4 years from now?
10/7.
Two prime numbers whose difference is 2 are called twin prime numbers, e.g., 3 and 5. How many twin prime numbers are there between 50 and 100?
10/8.
I divide $289 (in whole $ increments) into a number of bags so that I can ask for any amount between $1 and $289, and you can give me the proper amount by giving me a certain number of these bags without opening them. What is the minimum number of bags you will need to give me?
10/9.
A block of wood in the form of a cuboid 5cm x 8cm x 13cm has all its six faces painted pink. If the wooden block is cut into 520 cubes of
1cm x 1cm x 1cm, how many of these would have some pink paint on them?
10/10.
The product (multiplication) of two numbers is 84. The first number is divided by 3 and the second number is multiplied by 4. The product of the two new numbers is then divided by 2. What is the final result of this calculation?
10/11.
The sum of the first 100 terms of the sequence 1, -2, 3, 4, -5, 6, 7, -8, 9, 10… is 1750. The sum of the first 100 terms of the sequence 1, 2, -3, 4, 5, -6, 7, 8, -9, 10… is equal to what?
10/12.
A cylinder 90 cm high has a circumference of 24 cm. A string makes exactly 5 complete turns round the cylinder while its two ends touch the cylinder's top and bottom. How long is the string in cm?
10/13.
A student walks from home to school and returns riding on a bus along the same route. The entire trip takes 40 minutes. If the bus travels 7 times as fast as the student can walk, how long would it take the student to walk in both directions?
10/14.
Rui has 27 coloured pearls in her hair. She has twice as many yellow as red pearls. She has the same number of green and blue, but less then the number of red pearls. How many of each colour does she have?
10/15.
The squares of two consecutive integers differ by 1987. What is the sum of these two integers?
10/16.
In US currency, a quarter has the value of 25 cents and a penny has a value of 1 cent. A quarter has the same weight as two pennies. If a kilogram of quarters is worth $25, then how much is a kilogram of pennies worth?
10/17.
How many different even four-digit numbers can you make, using each of these digits once only?
1, 9, 7, 6
10/18.
The perimeter of a rectangle is 54cm. If the length is twice the width, what is the area of the rectangle?
10/19.
During the first four days of Arthur’s new job, he had to wake up at 5.30, 5.30, 7.10 and 7.30. What is the mean time Arthur had to wake up each morning?
10/20.
A square is constructed on the hypotenuse of a right angled triangle whose two shorter sides have lengths 2 and . This forms a pentagon if the shape is looked at end on. What is the area of this pentagon?
MATHS MIND QUESTIONS 2004 YEAR 10
10/1
Two robots strutting through cyberspace. Abot says to Bbot “I get a headache trying to listen to all these radio signals at the same time. Do you know that if you gave me 2 of your antennae we’d have the same number?”. Bbot retorts “That’s nothing! If I had 2 of your antennae I’d have 5 times as many as you!”. How many does each have?
10/2
Tourists to New Zealand are not required to pay the 12.5% Goods and Service Tax. If an object is priced at $72, what is the ‘duty free’ price for the tourist?
10/3
How many litres of water must be added to a 100 litre container of ‘orange juice’ that is 20% water to produce a mixture that is water?
10/4
In a group of people at a party each person shakes hands with every other person. If there are 45 handshakes altogether, how many people are present?
10/5
If each side of a square is increased by 10% what is the percentage increase in area?
10/6
Box P contains 4 yellow and 8 red marbles while box Q contains 15 yellow and 9 red marbles. How many redmarbles should be transferred from box Q to box P so that the fraction of yellow marbles in box P equals the fraction of red marbles in box Q?
10/7
What is the result when the sum of the first 43 odd numbers is subtracted from the sum of the first 43 even numbers?
10/8
In a set of five prime numbers, only one number is bigger than the mean. 5 is not the only mode. The mean and median are both 7. List the five numbers.
10/9
When a traffic survey is carried out in a street where trucks are banned a total of 52 vehicles pass in the first hour. The total number of wheels (not counting spares) on these cars and motorbikes is 160. How many cars were surveyed?
10/10
If 18 boys sat a test and averaged 55% and 32 girls sat the same test and averaged 62%, what was the average mark for all 50 candidates?
10/11
In a year level of 50 pupils of the students who play two sports ;12 play golf and cricket, 7 play cricket and rugby and 6 play golf and rugby. 24 in total play golf while 10 play only rugby and 5 play only cricket. 4 pupils play all 3 sports. How many play none of the sports?
10/12
If and find the value of each letter.
10/13
In the Pacific Zone hockey tournament Australia won both its games scoring a total of 3 goals while conceding 1. New Zealand won one and lost one with 4 goals for and 4 against, while the other team Fiji scored 2 goals and conceded 4. What was the score for the New Zealand Fiji game?
10/14
If one quarter is three quarters of a number, what is the number?
10/15
If it takes 4 men 3 hours to lay 600 paving stones, how long would it take 5 men working at the same rate to lay 500 paving stones?
10/16
How can you write 100 using just four 9s and no calculations?
10/17
A parent leaves $36 000 to be shared among her three children in the ratio of their ages. The middle child receives exactly one third while the eldest receives $9 000 more than the youngest. What are their ages if none of them are over 15 years old?
10/18
A student is driven to school by a parent but walks home travelling along the same route. The entire trip takes 36 minutes. If the car travels 8 time as fast as the student walks how long would it take the student to walk in both directions?
10/19
A rhombus has 2 diagonals. One is 18cm long while the other is 12cm long. What is the area of the rhombus?
10/20
The sum of the first 100 terms of the sequence 1, -2, 3, 4, -5, 6, 7, -8, 9, 10… is 1750. The sum of the first 100 terms of the sequence 1, 2, -3, 4, 5, -6, 7, 8, -9, 10… is equal to what?
MATHS MIND QUESTIONS 2005 YEAR 10
10/1
If is of ‘it’, what is ‘it’ ? (Answer as a fraction)
10/2
In a group of cows and chickens the number of legs was 84 more than twice the number of heads.
How many cows were there ?
10/3
The sum of the 4 consecutive integers squared is equal to the sum of three consecutive integers squared.
What are the 3 consecutive integers ?
10/4
A function machine produces results according to the following table
INPUT / OUTPUT3 and 5 / 21
4 and 7 / 29
0 and 3 / 9
5 and 0 / 10
1 and 4 / 14
What is the result if the INPUT numbers were 8 and 12 ?
10/5
If a # b = ab + 1 and a * b = a + b, what is the value of
4 # ((6 * 8) * (3 # 5)) ?
10/6
A set of dominoes with 6 as the highest number of spots in any one square is formed as follows:
There are double dominoes: 6-6, 5-5,…, 0-0.
There are then dominoes with all possible pairs 0 to 6 such as 3-4, 2-6, etc. In all there are 28 dominoes.
How many would there be in a set if the highest number of spots in any one square is 12 ?
10/7
A horse is tethered to a rope which is tied to a corner on the outside of a square stockyard that has a side length of 10 metres. The length of rope is 18 metres.
What is the total grazing area available to the horse ? (Answer in m2 to 2d.p.)
10/8
A boat can travel at a rate of 15 kmph in still water. A river has a current of 5 kmph. If a boat goes downstream then returns to its starting point what is the average rate of speed for the whole trip in kmph ? (Answer to 2 d.p.)
10/9
Joe Doubtful says he has a 55% chance of going to the school gala if it does not rain and a 30% chance of going if it does. The weatherman says there is a 40% chance of it raining on the day of the gala.
What is the chance that Joe Doubtful will go ? (Give the answer as a percentage)
10/10
A student has 4 Science books, 3 English books and 2 Mathematics books to place on a bookshelf. He wishes to keep all books of the same subject together on the shelf. How many ways can the books be arranged?
10/11
A rectangle has dimensions 4cm by 5cm. The sides are divided into lengths of one cm and lines drawn parallel to the sides creating a grid of 20 unit squares each of area 1 cm2.
How many squares may be found in this figure by using the lines of the grid ?
10/12
A coin 1cm in diameter is thrown onto a square grid consisting of a set of squares of side 4 cm. What is the probability that if it falls within the within the grid it will not touch the grid lines? (Give the answer as a fraction)
10/13
How many triangles in this figure?
10/14
A set of books consists of 10 volumes each having 250 pages with a total thickness of 1.2 cm, two covers each 0.1cm thick and front and back pages each 0.003cm thick. The 10 volumes are arranged in order (left to right) on a shelf in order vol.3,vol.1,vol.4,vol.2,vol.6,vol.10,vol.7,vol.8,vol.5,vol.9.
If a bookworm starts on page 1 of vol.1 (after the front page) and takes the shortest path to page 250 of vol 10 what distance does it travel? (in cm)
10/15
In a group of people there are 10 more men than boys, 5 more women than girls, twice as many boys as girls and 105 people in all.
How many boys are there?
10/16
A cylindrical can ( ) has its height increased by 25%. By what percent (to the nearest tenth of a percent) must the radius be decreased in order to maintain the some volume ?
10/17
A sequence is formed as follows: 32 + 42 = 52
52 + 122 = 132 132 + n2 = (n+1)2
(n+1)2 + y2 = (y+1)2
Find y.
10/18
The sum of two consecutive, positive odd integers is of (their product increased by one).
What are the numbers ?
10/19
The two commonly used temperature scales are set up as follows:
On the Fahrenheit scale the freezing point of water is 32 degrees and the boiling point is 212 degrees.
On the Centigrade scale these two values are respectively 0 degrees and 100 degrees.
For what temperature is the reading of the two scales the same?
10/20
If x cats eat y tins of cat food in z days, how many tins of cat food would p cats eat in q days?
MATHS MIND QUESTIONS 2006 YEAR 10
10/1 In order to make a Muesli Mix, Mrs Moppet mixes 4kg of Apricots @ $10.50 per kg,3 kg of Branflakes @ $2.40 per kg, 1 kg of Currants @ 55 cents per 100g and 2kg of
Pineapple Chunks @ 70 cents per 100g. She mixes it together as a 10kg mix.
She sells it @ 95 cents per 100g. How much profit will she make if she sells all 10kg?
10/2 Every number can be reduced to a single digit if we add the individual digits until we get
a number less than 10.
Eg. 13→ 4 thus D(13)=4
6453→18→9 thus D(6453) = 9
231675 → 24 → 6 thus D(231675) = 6
a)What is D ( 45321) ?
b)What is D ( 9x8x7x6x5x4x3x2x1) ?
10/3 Population, in billions
This graph depicts the world population in billions from 1800 to 2000. On average, from 1950 to 2000 approximately how many million people were added each year to the world’s population?
10/4 According to the novel, “The Da Vinci Code”, the number of members of the Priory of Sion is
one more than the sum of the first six positive powers of three. If true, how many members does
the Priory of Sion have?
10/6 How many guests were present at a party if every two used a dish for rice between them,
every three used a dish for soup between them, every four used a dish for meat between them,
and there were 65 dishes altogether?
10/7 A rectangular picture measures 16cm by Acm.
If 2cm were cut off from all four sides, the new area of the picture would be 228cm2.
What was the value of A?
10/8 How many different pairs of prime numbers sum to 50?
10/9 A swimming pool measures 100m by 20m and is 2m deep. A bottle of soft drink contains 500ml.
( A litre has a volume of 1000 cm3 ). How many soft drink bottles would we need to fill the pool?
10/10
How many triangles are there? (There are over 20)
10/11 B is a digit in the seven-digit whole number 8,642,B35.
8,642,B35 is divisible by 3. What is the sum of all possible
values of the digit B?
10/12 “Good morning George, how are your three children?”
“They are good Condalisa. It was their birthday yesterday. Did you know they were all born on Feb 10th?”
“ That’s amazing George.”
“ Did you know that their ages multiply to 60, and that I’m 40 next week.”
“What did the twins get as a present, George?”
“ I bought them a couple of oil wells each, Condalisa.”
How much do the children’s ages add to?
10/13 A triangle has one angle 30 degrees greater than the smallestand 18 degrees less than the largest.
What are the three angles?
.
.
10/14 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 11m is out of the water.
What is the total length of the pole in m?
10/15 In the fraction: , place a decimal point between any two digits of “2005” AND place a decimal point between any two digits of “125”. (For example, you are allowed to use 200.5; but NOT .2005 or 2005.)
What is the sum of the least fraction and the greatest fraction that you could create?
10/16 The squares in the diagram have side length 12cm.
What is the area of the slanted rectangle? /
10/17 Glenn and Jason each have a collection of cricket balls. Glenn said that if Jason would give him 8 of his balls they would have an equal number; but, if Glenn would give Jason 8 of his balls, Jason would have 3 times as many balls as Glenn. How many balls does Jason have?
10/18 P(n) is shorthand for the product of all the numbers from 1 to n
and S (n) is shorthand for the sum of all the numbers from 1 to n.
For example P(5) = 5 X 4 X 3 X 2 X 1 = 60
S( 4 ) = 4+3+2+1 = 10
Calculate S(P(2) + P(3)) + P(S(2) + S(3))
10/19 Charlene’s birthday, March 19, is one week before her dad’s birthday and one month
before her mum’s birthday. On her dad’s birthday in 2005, Charlene noticed that her
age (in years) was exactly 1/3 of her dad’s age (in years). On her mum’s birthday in
2006, Charlene’s age (in years) will be exactly 1/3 of her mom’s age (in years).
Charlene’s mom was born in 1955. In what year was Charlene’s dad born?
10/20 There are 200 goldfish in a tank and 99% of them are red fish. How many of these do I take out of the tank to make it 98% red fish?
MATHS MIND QUESTIONS 2007 YEAR 10
10/1
In this subtraction problem, the different letters represent different digits.
What digit does C represent?
ABA
-CA
AB
10/2
What is the largest number whose digits add to 50?
10/3
If father is now 3 times as old as his daughter, how many years ago was the daughter 2 years old, and the father 28?
10/4
Two standard dice are rolled. What is the probability that the product of the two numbers obtained is 6 or less?
10/5
By placing a 2 at both ends of a number its value is increased by 23377. What is the sum of the digits in the original number?
10/6
How many ways are there of walking up a flight of 9 steps if you take either one or two stairs with each step?
10/7
A small circle just fits inside a semicircle.
What is the ratio of the area of the small
circle to the area of the shaded region?
10/8
In how many different orders can four children be arranged in a line if John and Julie refuse to stand next to one another?
10/9
If I write all the whole numbers from 1 to 500 in a row, how many digits will there be?
10/10
Which gives the biggest answer?(A) divide 2 by ½
(B) multiply ½ by 2 and add 3(C) divide ½ by ¼ and double the answer
(D) multiply 3 by ½ and divide the answer by ⅓
(E) divide ⅔ by ½ and double the answer
10/11
In my class of no more than 40 pupils there are exactly 10% more girls than boys. How many girls are there?
10/12
A man has 720 sheep. He shears half of them on Thursday and two-thirds of the remainder on Friday. How many are left to be sheared on Saturday?
10/13
The largest prime factor of 2310 is:
10/14
A farmer had 200 sheep. Eighty died, and all but 25% of those remaining ran away. How many were left?
10/15
The circle centre O has radius 5 cm. A point P
is chosen at random inside this circle. What is the
probability that P is inside the shaded circle?
10/16
What is the difference between the sum of all the odd numbers up to 1992 and the sum of all the even numbers up to 1992?
10/17
Andrea, Brian and Claire spent an afternoon picking strawberries. Andrea picked
3 kg more than Brian but 2 kg less than Claire. If Brian picked three-quarters of the amount that Claire picked, how much did the three friends pick in total?
10/18
A rectangular piece of metal has squares cut from
its four corners, and then the sides bent up to form
an open box with dimensions as shown. What was
the area of the piece of metal before it was cut?
10/19
A1573B is a six-digit number in which A and B are digits. If this number has 72 as a factor, what digit is A?
10/20
Jeremy has three times as many $1 coins as $2 coins. His sister Louise has three times as many $2 coins as $1 coins. Together they have $43. How many coins do Jeremy and Louise have altogether?
10/21
There are 150 children at Feelgood School and 40% are boys. At this school 25% of the boys and 30% of the girls have brown eyes. How many children at FeelgoodSchool have brown eyes?