Podcast
Questions and Answers
What is the measure of angle PAO given that angle AOB = 130 degrees and angle YPA = 45 degrees?
What is the measure of angle PAO given that angle AOB = 130 degrees and angle YPA = 45 degrees?
If angle AOB is 130 degrees, what is the relationship of angle YPA to angle PAO?
If angle AOB is 130 degrees, what is the relationship of angle YPA to angle PAO?
What is the total angle measure when combining angle AOB = 130 degrees and angle YPA = 45 degrees?
What is the total angle measure when combining angle AOB = 130 degrees and angle YPA = 45 degrees?
In a scenario where XY is tangent to circle O at point P, which angles must be acute?
In a scenario where XY is tangent to circle O at point P, which angles must be acute?
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If a tangent to a circle forms angles, which statement about angle AOB is accurate?
If a tangent to a circle forms angles, which statement about angle AOB is accurate?
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What is the most appropriate request to the taxi driver when you are almost late for your flight?
What is the most appropriate request to the taxi driver when you are almost late for your flight?
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Which phrase is best to use when asking your teacher about the meaning of an English word?
Which phrase is best to use when asking your teacher about the meaning of an English word?
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What is the most fitting response to congratulate a friend who has won a medal in e-sports?
What is the most fitting response to congratulate a friend who has won a medal in e-sports?
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What is the best response for Ann after Joe complimented her dress?
What is the best response for Ann after Joe complimented her dress?
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Which response would be most suitable if you want to express surprise at your friend's e-sports success?
Which response would be most suitable if you want to express surprise at your friend's e-sports success?
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When wanting to understand a word's definition, which question is least effective?
When wanting to understand a word's definition, which question is least effective?
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Given the ratio $a : b = 2 : 3$ and $b : c = 5 : 4$, and the equation $a + b - c = 390$, what is the value of $a + b + c$?
Given the ratio $a : b = 2 : 3$ and $b : c = 5 : 4$, and the equation $a + b - c = 390$, what is the value of $a + b + c$?
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If the ratios $a : 7 = b : 20$ and $b : c = 8 : 7$ hold true, what is the relationship between $a$ and $c$?
If the ratios $a : 7 = b : 20$ and $b : c = 8 : 7$ hold true, what is the relationship between $a$ and $c$?
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If $sin A + cos A = 1$ for $0 ext{ to } 90$, what is the sum of $cos 2 + cos 4 + cos 6 + ext{...} + cos 90$?
If $sin A + cos A = 1$ for $0 ext{ to } 90$, what is the sum of $cos 2 + cos 4 + cos 6 + ext{...} + cos 90$?
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Based on $a : b = 2 : 3$, if $b$ is 90, what is the inferred value of $a$?
Based on $a : b = 2 : 3$, if $b$ is 90, what is the inferred value of $a$?
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In the ratio $b : c = 5 : 4$, if $b$ is doubled, how does it affect the value of $c$?
In the ratio $b : c = 5 : 4$, if $b$ is doubled, how does it affect the value of $c$?
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Given the equation $sin A + cos A = 1$, at what angle does this relationship hold true?
Given the equation $sin A + cos A = 1$, at what angle does this relationship hold true?
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What must be done to the distance from the center of the Earth for a satellite with a 3-hour orbital period to match the Earth's rotational period?
What must be done to the distance from the center of the Earth for a satellite with a 3-hour orbital period to match the Earth's rotational period?
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What is the specific heat capacity of water used in the problem?
What is the specific heat capacity of water used in the problem?
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Which of the following correctly expresses the power in terms of energy and time?
Which of the following correctly expresses the power in terms of energy and time?
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How far does B travel when they meet, given that A takes a 4-hour break?
How far does B travel when they meet, given that A takes a 4-hour break?
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What is the value of A + B if A = log(35) - log(1) + log(5) and B = log(3)/4 + log(5)/105 + log(7)/105?
What is the value of A + B if A = log(35) - log(1) + log(5) and B = log(3)/4 + log(5)/105 + log(7)/105?
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If the sum of the squares of three consecutive odd positive numbers equals 1,091, what is the sum of those numbers?
If the sum of the squares of three consecutive odd positive numbers equals 1,091, what is the sum of those numbers?
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What combined speed do A and B have when they travel towards each other?
What combined speed do A and B have when they travel towards each other?
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What mathematical operation would you use to simplify the expression A = log(35) - log(1) + log(5)?
What mathematical operation would you use to simplify the expression A = log(35) - log(1) + log(5)?
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What is the average speed of A during their entire trip including rest time before meeting B?
What is the average speed of A during their entire trip including rest time before meeting B?
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Study Notes
Exam Instructions
- Each question has only one correct answer; multiple selections result in no points for that question.
English Language Questions
- Airport Scenario: Ask the taxi driver to "speed up, please."
- Word Meaning Inquiry: Politely request, "May I use a dictionary?"
- Congratulations Message: Celebrate a friend's e-sports medal with "Congratulations!"
Math and Logic Problems
- Distance Problem: If A and B start 200 km apart, with speeds of 4 km/h and 5 km/h, A taking a 4-hour break, calculate B’s distance when they meet.
- Logarithmic Expression: Evaluate the expression A + B, where A and B are based on logarithms with specific values.
- Sum of Squares: The sum of squares of three consecutive odd positive integers equals 1,091; determine their sum.
Ratio and Proportion
- Given ratios a : b = 2 : 3, b : c = 5 : 4, and total a + b - c = 390, find the total a + b + c.
- For given ratios involving a, b, and c, determine a : c.
Trigonometric Functions
- If sin A + cos A = 1 within the range of 0° to 90°, find the sum of cos 2, cos 4,..., cos 90.
Geometry Questions
- Determine the angle PAO using given angles and a tangent line to circle O.
Algebraic Expression
- Solve the expression involving fractions with variables.
Physics Problem
- A satellite with a 3-hour orbit needs a distance increase from Earth's center for its orbit to match Earth's rotation. Calculate the necessary factor of distance change.
Thermal Energy Transfer
- Calculate the final temperature of 2 kg of water heated for 3 minutes with a specific heat capacity, considering energy efficiency at 70%.
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Description
Test your English language skills with this quiz consisting of 50 multiple-choice questions. Each question requires selecting the best answer among the given options, aiming to enhance your comprehension and communication abilities. Prepare to challenge yourself and improve your English proficiency!
