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Questions and Answers
How many diagonals does a regular hexagon have?
Which of the following polygons has 5 sides?
What is the sum of the exterior angles of any polygon?
What type of triangle has no congruent sides?
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Which term describes a polygon with at least one interior angle greater than 180 degrees?
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How many triangles can be formed inside a regular nonagon?
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What type of angles are formed by two adjacent angles that share a common side?
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Which of the following polygons has two pairs of equal sides?
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What is the measure of the interior angles of a polygon with n sides?
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Which formula correctly represents the calculation of percentage increase?
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What does the letter 'D' represent in the discount formula?
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In calculating commission, the formula C = TS x R denotes which variables?
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What is the appropriate formula for calculating sales tax?
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What does 'SP' represent in the sales pricing formulas?
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How many triangles can be formed in a polygon with n sides?
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The interest rate is defined as which of the following?
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What is the formula used to calculate the principal amount when interest, rate, and time are known?
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Which of the following describes a terminating decimal?
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If 10 is 5% of a number, what mathematical operation is used to find the number?
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What percent of 180 is 90?
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How is the unit rate defined?
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Which of the following represents an improper fraction?
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In the decimal representation, which of the following is classified as a repeating decimal?
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What will be the profit if Loisa sells all the ballpens she bought for Php 1,300 at Php 11 each, assuming each ballpen costs Php 9?
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Study Notes
Polygon Properties
- A regular polygon has congruent sides and angles.
- An irregular polygon does not have congruent sides or angles.
- Congruent means having the same measure of sides or angles.
- A convex polygon has all interior angles less than 180 degrees.
- A non-convex polygon or concave polygon has at least one interior angle greater than 180 degrees.
- The number of triangles that can be formed in a polygon is calculated by (n-2), where n is the number of sides.
- The sum of the interior angles of a polygon is calculated by (n-2)180, where n is the number of sides.
- The sum of the exterior angles of a polygon is 360 degrees.
- Adjacent interior and exterior angles form a linear pair, meaning they add up to 180 degrees.
- Vertical angles are always congruent.
- An equilateral triangle has all sides equal.
- An isosceles triangle has at least two sides equal.
- A scalene triangle has no congruent sides.
Angle Relationships
- Supplementary angles add up to 180 degrees.
- Complementary angles add up to 90 degrees.
- Adjacent angles share a common side.
- Linear pairs are two adjacent angles that form a straight line.
- Vertical angles are opposite angles formed by two intersecting lines.
Percentage Calculations
- Percentage increase is the amount of increase compared to the original value, expressed as a percentage.
- Percentage decrease is the amount of decrease compared to the original value, expressed as a percentage.
Formula Table
| Formula | Description |
|---|---|
| PI = (NV -- OV) / OV x 100% | Percentage Increase |
| PD = (OV -- NV) / OV x 100% | Percentage Decrease |
| D = OP x R | Discount |
| SP = OP -- D | Sale Price |
| OP = SP -- D or OP = SP/1 -- R | Original Price |
| C=TS x R | Commission |
| R = C/TS x 100% | Commission rate |
| ST = TAP x R | Sales tax |
| I = Prt | Simple Interest |
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Notes:*
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OV = Original Value
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NV = New Value
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I = Increase
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D = Decrease
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PI = Percentage Increase
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PD = Percentage Decrease
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OP = Original Price
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R = Rate of Discount
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SP = Sales Price
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C = Commission
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TS = Total Sales
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ST = Sales Tax
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TAP = Total Amount of Product
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P = Principal Amount
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r = Rate of Interest
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t = Time
Additional Information
- Discount is a reduction in the original price of a product or service.
- Sale price is the final price after discounts are applied.
- Selling price is the original price without discounts.
- Commission is a percentage earned by a person for selling a product.
- Commission rate is the percentage taken from the selling price.
- Sales tax is an amount added to the total price of a product, often referred to as Value Added Tax (VAT).
- Interest is the amount earned from investing or borrowing money.
- Interest rate is the percentage of interest.
- Principal is the amount of money invested or borrowed.
- Time is the duration of the investment or loan (in years).
- Ratio compares two quantities of the same unit.
- Rate compares two quantities of different units.
- Unit Rate is a rate with a denominator of 1 unit.
Number Types
- Whole numbers are positive integers (e.g., 25, 52, 90).
- Proper fractions have a numerator smaller than the denominator (e.g., ¼, 3/5, 2/13).
- Improper fractions have a numerator greater than or equal to the denominator (e.g., 4/3, 11/2).
- Mixed fractions combine a whole number and a proper fraction (e.g., 63 ¼ , 2 ½).
- Terminating decimals have a finite number of digits after the decimal point (e.g., 1.25, 3.14, 142.24).
- Non-terminating decimals have an infinite number of digits after the decimal point (e.g., 2.718.... and 4.156254.......).
- Repeating decimals have a repeating pattern of digits after the decimal point (e.g., 0.333..., 12.757575..., 1.23232).
- Percentage is a fraction out of 100 (e.g., 10%, 54%, 100%).
- Rational numbers can be written as a ratio of two integers, where the denominator is not zero (e.g., integers, fractions, mixed numbers, and percentages).
Problem-solving Examples
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Example 1: If Php10 is 5% of a number, what is the number?
- Solution: Php10 / 0.05 = Php 200
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Example 2: What is 18% of 150?
- Solution: 150 x 0.18 = 27
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Example 3: What percent of 180 is 90?
- Solution: 90/180 = 0.5 = 50%
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Example 4: The book is worth Php 199 and on 30% sale. How much is the discount price?
- Solution: 199 x 0.3 = 59.7
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Example 5: How much will you invest (principal amount) in 10 years to earn Php 75,000 (interest) with an interest rate of 6% a year?
- Solution: P = I/rt = 75,000 / (0.06 x 10) = 75,000/0.6 = Php 125,000
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Example 6: Loisa bought ballpens on Shoppee worth Php 1,300. She plans to sell it to her classmates worth Php 11 each. How many ballpens does she buy in Php1,300 if the ballpen is worth Php 9 pesos each on Shoppee? How much is her profit if she will be able to sell it all?
- Solution: Number of ball pens bought: 1300/9 = 144.44 (approximately 144 ballpens) - Profit: (11 x 144)- 1300 = Php 154
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Example 7: 7 boys can finish the work for 5 hours, how many workers would it be if the work should finish within 8 hours?
- Solution: This problem involves the concept of inverse proportion. As the time decreases, the number of workers needed increases:
- Workers x Time = Constant
- 7 x 5 = Workers x 8
- 35 = Workers x 8
- Workers = 35/8 = 4.375 (approximately 5 workers)
- Solution: This problem involves the concept of inverse proportion. As the time decreases, the number of workers needed increases:
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Description
Test your knowledge on the properties of polygons with this quiz. Explore the differences between regular and irregular polygons, understand the concepts of convex and concave shapes, and learn about triangle classifications. Challenge yourself and see how well you grasp these fundamental geometric concepts!
