Mathematics
Grade 10
15 min
Find start and end times
Find start and end times
What you'll learn
- Apply the Pythagorean theorem and trigonometric functions (sine, cosine, tangent) to determine the modulus (r) and argument (θ) of a complex number given in rectangular form (a + bi) with 80% accuracy.
- Solve for the argument (θ) of a complex number, expressed in rectangular form, using inverse trigonometric functions, considering the quadrant in which the complex number lies, with 75% accuracy.
- Explain the relationship between the rectangular (a + bi) and polar (r(cos θ + i sin θ)) forms of a complex number, including a discussion of how 'r' and 'θ' relate to the complex plane, in a written explanation that demonstrates comprehension of key concepts.
- Convert at least 4 out of 5 complex numbers from rectangular form to polar form, expressing the argument (θ) in radians, accurately to two decimal places.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Calculate an end time given a start time and a duration, crossing AM/PM and midnight boundaries.
Calculate a start time by working backward from a known end time and duration.
Convert fluently between 12-hour (AM/PM) and 24-hour (military) time formats to simplify calculations.
Solve multi-step word problems involving multiple durations, such as work periods and breaks.
Incorporate time zone conversions (e.g., UTC offsets) to find start or end times for international events.
Determine start or end times in problems involving rates, such as speed, distance, and time.
Planning a video call with a friend in another country? 🌍 Let's master the math to ensure no one shows up three hours early or late!
This tutorial moves beyond basic time calculations....
2
Key Concepts & Vocabulary
TermDefinitionExample
Duration (Elapsed Time)The amount of time that passes between a start time and an end time.The duration between 8:30 AM and 11:10 AM is 2 hours and 40 minutes.
24-Hour Time (Military Time)A timekeeping convention where the day runs from midnight to midnight and is divided into 24 hours, numbered from 0 to 23. It eliminates the need for AM/PM.3:45 PM is represented as 15:45 in 24-hour time.
Time ZoneA region of the globe that observes a uniform standard time for legal, commercial, and social purposes.New York is in the Eastern Time Zone (ET), which is typically UTC-5 (or UTC-4 during daylight saving).
UTC (Coordinated Universal Time)The primary time standard by which the world regulates clocks and time. It is the reference point for all other time zones, which are exp...
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Core Formulas
Finding the End Time
T_{end} = T_{start} + \Delta t
To find the end time (T_end), add the duration (delta t) to the start time (T_start). It is often easiest to convert all times to a common unit (like minutes) or use 24-hour format to avoid AM/PM errors.
Finding the Start Time
T_{start} = T_{end} - \Delta t
To find the start time (T_start), subtract the duration (delta t) from the end time (T_end). 'Borrowing' an hour (60 minutes) is often necessary during subtraction.
Time Zone Conversion
T_{local} = T_{UTC} + \text{Offset}
To find the local time in a specific time zone, add the time zone's offset to the Coordinated Universal Time (UTC). The offset can be positive (ahead of UTC) or negative (behind UTC).
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Challenging
A traveler flies from New York (UTC-4) to London (UTC+0), and then from London to Dubai (UTC+4). The first flight departs at 19:00 on Monday and lasts 7 hours. There is a 3-hour layover in London. The second flight lasts 6 hours and 30 minutes. What is the local time and day of arrival in Dubai?
A.Tuesday at 18:30
B.Tuesday at 19:30
C.Wednesday at 07:30
D.Tuesday at 15:30
Challenging
A self-driving car starts a 500 km trip at 07:00. For the first 2 hours, it travels at 100 km/h. It then encounters traffic and slows to 60 km/h for the remainder of the trip. At what time does it reach its destination?
A.14:00
B.13:30
C.14:30
D.15:00
Easy
A movie starts at 7:15 PM and has a duration of 2 hours and 10 minutes. What time does the movie end?
A.9:15 PM
B.9:20 PM
C.9:25 PM
D.9:35 PM
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Frequently asked questions
What grade level is "Find start and end times"?
Find start and end times is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Find start and end times?
You'll be able to: Apply the Pythagorean theorem and trigonometric functions (sine, cosine, tangent) to determine the modulus (r) and argument (θ) of a complex number given in rectangular form (a + bi) with 80% accuracy; Solve for the argument (θ)….
Is "Find start and end times" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Find start and end times?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.