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1.How much interest is charged when ₱15,000 is borrowed for 8 months at an annual interest rate of 12%?1,200 2. Mark borrowed 15,000 from his sister Maricar. If Mark agreed to pay 3% annual rate of interest. How can you find the simple interest if the loan is for 2 year. 900 3. Calculate the maturity value of ₱8,000 loan with the simple interest of 20% per year. The duration of loan is 5 years 4. Find the compound amount on deposit at the end of 2 year if P30, 000 is deposited at 5% compounded annually. 33,075 5. What amount must be invested in order to have P128, 376.52 after 8 years if money is worth 6% compounded semi-annually? 80,000 6. Maria borrowed 19,000 from her sister Miramar. If Maria agreed to pay 9% annual rate of interest. How can you find the simple interest if the loan is for 3 year. 7. Jerry borrowed ₱100,000 from her auntie. If Jerry agreed to pay 20% annual interest rate, what will be the amount of interest she must pay if the loan period is 6 months? 10,000 8. Harry buys a new car using an interest only loan where he pays only the interest on the value of the car each month. The car is valued at ₱200,000 and Harry pays 15% interest per year on the car. How much is his monthly interest payment? 30,000 9. If an entrepreneur applies for a loan amounting to ₱55,000 in a bank, the simple interest of which is ₱157,500 for 3 years, what interest rate is being charged? 10. When invested at an annual interest rate of 30%, an amount earned ₱50,000 of simple interest in three years. How much money was originally invested?55,555.56 11. A bank offers 0.15% annual simple interest rate for a particular deposit. How much interest will be earned if 1 million pesos is deposited in this savings account for 2 year?3,000 12. Sheryl decided to save ₱10,000 at the end of each month. If the bank pays 4% compounded monthly, how much will his money be at the end of 9 years? 13. What is the present value of ₱66,000 in 2 years if money is worth 50% compounded annually? 14. How much interest is charged when ₱50,000 is borrowed for 4 months at annual interest rate of 20% A relation is a set of ordered 2 parts of relation The domain is the set of all x values in the relation. The range is the set of all y values in the relation. A function f from set A to set B is a rule of correspondence that assigns to each element x in the set A exactly one element y in the set B. (9,5), (3,6), (1,0), (5,9) 1. {(0,0), (3, −3), (2, −1), (−2, −2)(−3, −3)} 2. {(6,4), (5,1), (1, −2), (−1,1), (−2,4)} The second condition says each x can have only one y, but it CAN be the same y as another x gets assigned to. All x’s are assigned No x has more than one y assigned Polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction and non-negative integer and non-fraction exponents of variables Identify if it is polynomial or not polynomial. 1. 6𝑎3 3 2. 5𝑦 2 −2 3. 5𝑥 +1 Solve the equation 2 3 1. 2𝑥+4 = 𝑥+2 𝑥 3𝑥 1 2. 2𝑥 + 9 = 2 𝑥−5 𝑥−4 3. – =1 3 5 (𝑓𝜊 𝑞)(𝑥) What is the domain of the function 𝑥+5 1. 𝑓(𝑥) = 3𝑥−4 . 𝑓(𝑥) = 2𝑥 + 1 𝑞(𝑥) = 𝑥 2 − 2𝑥 + 2 Find and simplify 2. is defined by (𝑓𝜊 𝑔)(𝑥) = 𝑓(𝑔(𝑥)) The process of obtaining a composite function is called function composition. The composite function. Power law of logarithmic function 𝑙𝑜𝑔𝑎 𝑋 𝑛 = 𝑛𝑙𝑜𝑔𝑎 (𝑋) 𝑥 Quotient law of logarithmic function 𝑙𝑜𝑔𝑎 (𝑦) = 𝑙𝑜𝑔𝑎 (𝑋) − 𝑙𝑜𝑔𝑎 (𝑌) Product law of logarithmic function 𝑙𝑜𝑔𝑎 (𝑋𝑌) = 𝑙𝑜𝑔𝑎 (𝑋) + 𝑙𝑜𝑔𝑎 (𝑌) Expand the following 𝑥 3 1. 92𝑥−𝑦 = 3 and 81𝑥+2𝑦 = 243. 𝑙𝑜𝑔6 23 COMPOSITION OF FUNCTIONS Let 𝑓 and𝑔 be functions. 125𝑥−1 = 25𝑥+3 2. 2 3b / 2 –b = 4 2 3. 𝑙𝑜𝑔4 (𝑚) 1 4 2. denoted by (𝑓𝜊 𝑔).EXPONENTIAL FUNCTION 𝑓(𝑥) = 𝑟 𝑥 What is ¼ of 42 Solve the following 1. 𝑓(𝑥) = 𝑥−2 𝑥+5 2. Write the following functions on the board. 𝑙𝑜𝑔4 (24 ∙ 54 ∙ ( ) ) 2 3. then. a conditional statement is compound sentence that is usually expressed with the key words 'If.. . The symbol for this is ν.. Simple Sentences Compound Sentence : disjunction p: The clock is slow. p Λ q : Joe eats fries.Negation Indicates the opposite. q: Maria drinks soda. p ν q : The clock is slow. That was fun. conjunction is a compound sentence formed by using the word and to join two simple sentences. usually employing the word not. A disjunction is a compound sentence formed by using the word or to join two simple sentences. q: The time is correct. and maria drinks soda. The Conditional In logic.. Simple Sentences Compound Sentence : Conditional p: You are absent q: You have a make up assignment to p q : If you are absent.'. The symbol for this is Λ. Simple Sentences Compound Sentence : conjunction p: Joe eats fries.. The symbol to indicate negation is : ~ Original Statement Negation of statement Today is Monday. That was not fun. Using the variables p and q to represent two simple sentences. then you have a make up complete. or the time is correct.. assignment to complete. the conditional "If p then q" is expressed symbolically as p q. Today is not Monday.