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Questions and Answers
Who is considered the founder of trigonometry, but is most famous for his incidental discovery of the precession of the equinoxes?
What do you call symbols that represent numbers?
What were the earliest form of numbers found on prehistoric bones?
tally marks
Which language refers to 'Mathematics' as 'Sipnayan'?
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What is 'setenta y nueve' in numerical form?
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What is the sum of 3 consecutive integers?
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In the ratio 4:3:1, how many hours does each student spend for Chemistry in a 24-hour review package?
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If m < 0 and n > 0, which of the following inequalities is true? m/n < 1
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If 2x + 4y - 5z = 19 and z = 3, what is the value of x + 2y + z?
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The product of 2 two-digit numbers is 351. What is their sum?
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In a party with 9 people where each person shakes hands with each other exactly once, how many handshakes are there in total?
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If 25% of a number is 50, what is 75% of the number?
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A certain amount of money was invested at 4% simple interest and gained Php500 in 2 years. How much was invested?
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After investing Php20,000 at 3% simple interest for x years, it became Php24,200. What is x?
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If a divider costs Php50,000 with a downpayment of Php15,000 and the rest at 5% interest for 18 months, what will be the monthly payment?
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After investing a certain amount of money at 8% simple interest rate for 5 years, it became Php35,000. How much was invested?
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If Php100,000 is invested at 3% interest compounded annually for 5 years, how much will it be?
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If Php18,000 is invested at 2% compounded quarterly for 15 years, how much will it be?
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A product was given successive discounts of 30% and 40%. By what percent was the original price decreased?
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Study Notes
Math Review
Diagnostic Test
- The test consists of 40 items, covering various math topics.
Mathematicians and Contributions
- Hipparchus: founder of trigonometry, discovered precession of the equinoxes.
- Pythagoras: famous for the Pythagorean Theorem.
- Euclid: associated with "The Elements".
- Archimedes: contributed to the principle of buoyancy related to fluids.
Numbers and Operations
- Tally marks on prehistoric bones and artifacts are the earliest form of numbers.
- Numerals are symbols that represent numbers.
- If x is an integer, x² and x³ are always odd, while x(x+1) is always even.
Problem Solving
- To prove p→q, a mathematician may assume ¬q and arrive at ¬p, which is called proof by contrapositive.
- Mathematical investigation involves exploring an open-ended situation, developing skills applicable to other problems.
Algebra
- Factorization: ab - 1 - b + a = (a-1)(b+1).
- Prime factorization: 2520 = 2³ × 3² × 5 × 7.
Geometry
- The sum of 3 consecutive integers is divisible by 3.
Statistics and Data Analysis
- If 2x + 4y - 5z = 19 and z = 3, then x + 2y + z = 20.
Finance
- Simple interest: I = Prt, where I is the interest, P is the principal, r is the rate, and t is the time.
- Compound interest: F = P(1 + rt)^n, where F is the future value, P is the principal, r is the rate, t is the time, and n is the number of times interest is compounded per time period.
Word Problems
- If 25% of a number is 50, then 75% of the number is 150.
- If a product is given successive discounts of 30% and 40%, the overall decrease in original price is 58%.
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Description
A diagnostic test for math majors preparing for the Licensure Examination for Teachers (LET) review, covering various math concepts and topics.
