FEUCAT Mathematics — Word Problems — Number, Age, Work, Motion, Mixture, InvestmentRevision Notes

Formulas

Exam Tips

• Always define what your variable represents clearly
• Circle or highlight key information and question being asked
• Check your answer by substituting back into the original problem
• Practice translating common phrases until they become automatic

Key Points

• READ the problem thoroughly to understand what is being asked
• REPRESENT the unknown quantities using variables (usually x, y, z)
• RELATE the variables to each other and the given values
• EQUATE by setting up equations based on the problem's facts
• SOLVE the equation systematically
• PROVE by checking if your answer satisfies all conditions

Definitions

Section Title

The 3 R's and ESP Problem-Solving Method

Common Mistakes

• Not reading the problem completely before starting
• Mixing up 'less than' and 'subtracted from' - these require switching the order
• Forgetting to check if the answer makes sense in the original context
• Using the same variable for different unknown quantities

Formulas

Exam Tips

• Always verify that consecutive integers are actually consecutive
• In digit problems, check that all digits are between 0 and 9
• For 'less than' problems, remember the order switches
• Draw a number line for consecutive integer problems if needed

Key Points

• Consecutive integers differ by 1: x, x+1, x+2, ...
• Consecutive odd/even integers differ by 2: x, x+2, x+4, ...
• Two-digit numbers can be represented as 10x + y where x is tens digit, y is ones digit
• Reversed numbers swap the digits: if original is 10x + y, reversed is 10y + x

Definitions

Section Title

Number Problems

Common Mistakes

• For consecutive odd/even integers, using +1 instead of +2
• In digit problems, forgetting that digits must be single-digit numbers (0-9)
• Confusing the original number with its reverse
• Not checking if the solution gives valid digits

Formulas

Exam Tips

• Always make a table with columns for different time periods
• Assign variables to present ages first
• Double-check the time direction (past vs future)
• Verify your answer by checking all age relationships

Key Points

• Ages change at the same rate for everyone
• Use a table to organize present, past, and future ages
• If someone is x years old now, they were (x-n) years old n years ago
• If someone is x years old now, they will be (x+n) years old in n years

Definitions

Section Title

Age Problems

Common Mistakes

• Adding years when going to the past (should subtract)
• Subtracting years when going to the future (should add)
• Forgetting that everyone ages at the same rate
• Not organizing the information in a clear table format

Formulas

Exam Tips

• Always set up a work table with Rate × Time = Work columns
• Remember: faster worker = higher rate = smaller time to complete alone
• Check answer: combined time should be less than either individual time
• Practice converting between different rate formats

Key Points

• Work = Rate × Time is the fundamental equation
• If someone completes a job in n hours, their rate is 1/n jobs per hour
• When working together, add the individual work rates
• Total work done by all people equals 1 complete job

Definitions

Section Title

Work Problems

Common Mistakes

• Adding times instead of rates when people work together
• Forgetting to convert rates to the same time units
• Not setting up the work table correctly
• Confusing individual rates with combined rates

Formulas

Exam Tips

• Always draw a diagram showing the motion situation
• Set up a table with Distance, Speed, and Time columns
• Check units throughout the problem
• Verify answer makes physical sense (reasonable speeds and distances)

Key Points

• Distance = Velocity × Time is the fundamental equation
• Use tables to organize distance, speed, and time for each object
• Objects moving toward each other: add distances to get total
• Objects moving in same direction: use equal distances for overtaking problems
• Pay attention to units (km/h, m/s) and convert when necessary

Definitions

Section Title

Motion Problems

Common Mistakes

• Mixing up units (km/h with m/s)
• Using wrong formula for meeting vs overtaking problems
• Forgetting to consider direction of motion
• Not setting up the motion table properly

Formulas

Exam Tips

• Always set up a table with % solution, Volume, and Pure substance columns
• Convert percentages to decimals before calculating
• Check: final concentration should be between the original concentrations
• Practice with different types: dilution, strengthening, and mixing problems

Key Points

• Focus on the amount of pure substance (solute) in each mixture
• Percentage × Total Volume = Amount of pure substance
• When mixing solutions, pure substance amounts add up
• Total volumes also add up in the final mixture
• Use tables to organize percentage, volume, and pure substance amount

Definitions

Section Title

Mixture Problems

Common Mistakes

• Adding percentages instead of amounts of pure substance
• Forgetting to convert percentages to decimals
• Mixing up solute amounts with total volume amounts
• Not checking if final percentage makes sense

Formulas

Exam Tips

• Set up a table with Principal, Rate, Time, and Interest columns
• Always convert percentage rates to decimal form
• Pay attention to time units and convert if necessary
• For compound interest, apply interest multiple times

Key Points

• Interest = Principal × Rate × Time
• Simple interest: calculated only on original principal
• Compound interest: calculated on principal plus accumulated interest
• Annual rate means per year; adjust for different time periods
• Total return = Principal + Interest earned

Definitions

Section Title

Investment Problems

Common Mistakes

• Using percentage form instead of decimal form for rate
• Mixing up simple and compound interest formulas
• Wrong time units (using months when rate is annual)
• Forgetting to add principal and interest for total value