Fundamental Mathemethics

• Direct Variation - a relationship between two or more quantities. They are often described as directly proportional.
• Indirect Variation - describes given quantities as "inversely proportional" to each other.
• Joint Variation - combination of direct and indirect variation with at least 3 quantities.
• Ratio - comparison of two quantities.
• Rate - ratio of two measurements having different units.
• Proportion -statement of equivalence between two ratio.
• What is the rate of an object that fell from the top of a 60-storey building in 5 minutes?

  60 storeys/5 minutes = 12 storeys/1 minute
• What is the extremes of this proportion?

  39:21 = 13:7
• Direct proportion - the product of the means is equal to the product of the extremes.
• It takes 300 bricks to build 6 meters of wall. How many bricks does it take to build 28 meters of a wall?

  300/6 = 1400/28
• Indirect proportion - the product of the quantities in the first ratio is equal to the product of the quantities in the second ratio
• Suppose people can take an orchard in 12 hours. How long will it take 8 people to rake the same orchard?

  (4)(12) = 8n

  n=6
• The PRB Triangle

  A) a part of a hundred

  B) % is the usual symbol of it

  C) ths is where you get the percenage

  
• An apprentice electrician is paid 40% of the hourly wage of a regular electrician. If the salary of a regular electrician is P200 per hour, what is the wage of an apprentice per hour?

  P = 80
• Students attending secretarial training pend 8 hours of their 40-hour workshop typing. What percent of their workshop is spent on typing?

  R = 20%
• The price of a cellular phone increased by 5%, which is equal to P500. What is the original price?

  B = 10,000
• Of means multiply.
• Words that corresponds to equal in word problem

  • is
  • are
  • as
  • were
• Discount - the reduction from the original price of a product
• A dress originally priced at P2,400 is on sale at 25%off. What is the discount price? What is the selling price?

  Discount price = P600

  Selling price = P1,800
• Mark-up - the profit in any selling transaction.
• There exist a 6% mark up to a small house which originally old at P240,000. What is the selling price?

  Selling price = P254,400
• Plinker, who is into the buy and sell business, bought Looney's Toyota Altis 2005 for Php 750,000. He plans to sell it to Tristan with a 25% profit. Tristan wants to buy his car and asks or a 10%discount discount on the selling price. How much is Plinker's profit?

  Plinker's profit = Php 93,750
• Simple interest - calculated just once throughout the loan.
• Formula of Simple Interest

  I=Prt
• Harold put P 4,500 into a savings account where money earns 3 1/2% per year. How much interest will the money earn in one year?

  I = P 4,657.50
• Compound Interest- calculated at fixed intervals over the duration of the loan.
• Formula of Compound Interest

  A = P(1+ r/m)^mt
• Find the accumulated amount of P 500 compounded quarterly at 6% interest for 1 year.

  A=P530.68
• Mean - the average of numbers.
• Mode - the number that occurs the most.
• Median - the number that is in the middle.
• What is the median in the sequence?

  10 7 5 8 9 13 1 2 3 5

  Median = 7 and 5
• Quartiles - three summary measures that divide ranked data set into four equal parts.
• Percentiles - A summary measures that divided a ranked data set into 100 equal parts.
• Deciles - summary measures that divide the ranked data set into 10 equal parts.
• D5 = P 50
• Range - the difference between the greatest and least value in a data set, or the difference between the largest and smallest value in a data set.
• Variance - the average of the square of the deviation from the mean.
• Standard deviation - square root of the variance.