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Questions and Answers
Which of the following is a correct factorization of $2x^2 + x - 6$?
Which of the following is a correct factorization of $2x^2 + x - 6$?
Which point lies on the graphs of $y = 2x + 1 - x^2$, $y = x^2 - 4x + 1$, and $y = 2x^2 - 8x + 1$?
Which point lies on the graphs of $y = 2x + 1 - x^2$, $y = x^2 - 4x + 1$, and $y = 2x^2 - 8x + 1$?
If Fatima eats 40% of 6 cupcakes in 30 minutes, how many hours will it take her to finish all cupcakes?
If Fatima eats 40% of 6 cupcakes in 30 minutes, how many hours will it take her to finish all cupcakes?
What is the 2024th digit in the sequence of the numbers written by Abdullah?
What is the 2024th digit in the sequence of the numbers written by Abdullah?
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How many hours are there in half of a third of a quarter of a day?
How many hours are there in half of a third of a quarter of a day?
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What is the largest difference possible between two 3-digit numbers using each digit only once?
What is the largest difference possible between two 3-digit numbers using each digit only once?
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What is the sum of the largest 6-digit palindromic number and the smallest 5-digit palindromic number?
What is the sum of the largest 6-digit palindromic number and the smallest 5-digit palindromic number?
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What information is essential to determine the area of a given shape?
What information is essential to determine the area of a given shape?
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If Hassan rolls a die 20 times and gets a 6 each time, which of the following values of n for tossing a coin would be possible, given that getting tails n times is less likely?
If Hassan rolls a die 20 times and gets a 6 each time, which of the following values of n for tossing a coin would be possible, given that getting tails n times is less likely?
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What is the area of triangle PQR formed by points of tangency on circles inscribed in a rectangle with sides of lengths 14 cm and 2 cm?
What is the area of triangle PQR formed by points of tangency on circles inscribed in a rectangle with sides of lengths 14 cm and 2 cm?
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What is the probability of selecting 2 kings from a group of 6 playing cards, where only 2 are kings?
What is the probability of selecting 2 kings from a group of 6 playing cards, where only 2 are kings?
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Given four distinct whole numbers a, b, c, and d, if ab + bc + cd + ad is odd, how many of these numbers can be even?
Given four distinct whole numbers a, b, c, and d, if ab + bc + cd + ad is odd, how many of these numbers can be even?
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What proportion of a circle contains points closer to point A on the boundary than to center O?
What proportion of a circle contains points closer to point A on the boundary than to center O?
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In a circle filled with five whole numbers, with no two or three consecutive numbers summing up to a multiple of 3, how many numbers can be divisible by 3?
In a circle filled with five whole numbers, with no two or three consecutive numbers summing up to a multiple of 3, how many numbers can be divisible by 3?
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If a rectangle has a length of 14 cm and a width of 2 cm, which of the following could represent the area of a triangle formed by points tangent to circles inside the rectangle?
If a rectangle has a length of 14 cm and a width of 2 cm, which of the following could represent the area of a triangle formed by points tangent to circles inside the rectangle?
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What is a possible value of n such that the probability of tossing n tails is less than the probability of rolling a 6 twenty times?
What is a possible value of n such that the probability of tossing n tails is less than the probability of rolling a 6 twenty times?
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Which of the following numbers could not have been an integer root of the polynomial x7 + 2x6 + ... + 6?
Which of the following numbers could not have been an integer root of the polynomial x7 + 2x6 + ... + 6?
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What is the highest possible number that Ahmad could have written if the mean of the ten distinct positive numbers is 10?
What is the highest possible number that Ahmad could have written if the mean of the ten distinct positive numbers is 10?
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In the scenario where each animal claims the one on their right is a fox, what can be inferred about the total number of animals on the island?
In the scenario where each animal claims the one on their right is a fox, what can be inferred about the total number of animals on the island?
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How many cats are needed to catch 100 rats in 100 minutes based on the given ratio of cats to rats?
How many cats are needed to catch 100 rats in 100 minutes based on the given ratio of cats to rats?
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What total distance does the fly cover while flying between Rehan and Malaik until they meet?
What total distance does the fly cover while flying between Rehan and Malaik until they meet?
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Which of the following shapes cannot be split into two trapeziums by drawing one straight line?
Which of the following shapes cannot be split into two trapeziums by drawing one straight line?
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If 3 cats catch 3 rats in 3 minutes, what will be the rate at which 5 cats can catch 5 rats in 5 minutes?
If 3 cats catch 3 rats in 3 minutes, what will be the rate at which 5 cats can catch 5 rats in 5 minutes?
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What is the smallest possible integer solution for the equation a(a + b) = 0?
What is the smallest possible integer solution for the equation a(a + b) = 0?
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Study Notes
Pakistan Mathematics Olympiad 2024 - Sample Paper
-
Exam Structure:
- Total Marks: 100
- Time Allowed: 3 hours
- Twenty questions
- Section A, B, and C
- Different point values for correct answers based on section.
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Instructions:
- Mark answers on the Student Answer Sheet.
- Dark, neat writing is required.
- Completely fill in the circles on the answer sheet for each question.
Instructions for the Exam
- Answer Sheet: Only the Student Answer Sheet will be marked.
-
Answering:
- Students can write in the booklet, but no marks are given for it.
- Pencil marks must be dark. Writing should be neat.
- Completely circle the answer choice on the answer sheet.
- Time Limit: The exam has a 3-hour time limit.
-
Scoring:
- Correct answers in section A are worth 3.5 points. Section B is worth 5 points and Section C is worth 7 points each.
- Incorrect answers score zero points.
- Unanswered questions get one point.
Sample Questions (Section A)
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Q1: Factorization of 2x² + x − 6
- Correct answer: (2x - 3)(x + 2)
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Q2: Point on the graphs of three equations:
- y = 2x + 1 - x²
- y = x² - 4x + 1
- y = 2x² - 8x + 1
- Correct answer: (1, 0)
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Q3: Time to finish cupcakes:
- Fatima ate 40% of 6 cupcakes in 30 minutes.
- Time to finish all cupcakes eating at a constant rate.
- Correct answer: 1.5 hours.
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Q4: Digit pattern of a repeated string
Sample Questions (Section B)
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Q9: Integer roots of a polynomial.
- Polynomial: x⁷ + 2x⁶ + ... + 6
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Q10: Impossibility of creating two trapezoids. Find the shape.
Sample Questions (Section C)
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Q15: Probability of rolling a die and flipping a coin.
- Roll a die 20 times, get 6 each time.
- Flip a coin 'n' times, get tails each time.
- Second event is less likely than the first.
- Find a valid value for 'n'.
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Q16: Area of a rectangle with inscribed circles.
- Rectangle's dimensions are 14 cm by 2 cm.
- Circles are identical and tangent.
- Find area of triangle PQR
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Q17: Probability of drawing two kings from a deck of cards.
- Set-up: 6 cards placed upside down, 2 kings.
- Choose two cards randomly.
- Find probability of getting two kings.
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Q18: Even and odd numbers in a set.
- Four distinct whole numbers (a, b, c, and d)
- Expression (ab + bc + cd + ad) is odd.
- How many of the original numbers could be even??
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Q19: Proportion of circle closer to a point than the center.
- Point A on circle, Center O
- Proportion of circle points closer to A than O.
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Q20: Divisible by 3 consecutive numbers.
- 5 whole numbers written in a circle
- No sum of 3 consecutive numbers divisible by 3.
- Find the number of numbers divisible by 3.
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Description
Prepare for the Pakistan Mathematics Olympiad 2024 with this sample paper. The exam consists of twenty questions over three sections, each with varying point values. Familiarize yourself with the exam structure and scoring to enhance your performance.
