This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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PART I: OBJECTIVE 1. The sum of 30 and 70. Step 1: Add the numbers. 30 + 70 = 100 The sum is 100. A. 100 2. The number 3,087 expressed in words. Step 1: Break down the number by place value. 3 is in the thousands place. 0 is in the hundreds place. 8 is in the tens place. 7 is in the ones place. Step 2: Write the number in words. Three thousand eighty-seven. B. Three thousand eighty-seven 3. What is the greatest common factor of 12 and 18? Step 1: List the factors of 12. Factors of 12: 1, 2, 3, 4, 6, 12 Step 2: List the factors of 18. Factors of 18: 1, 2, 3, 6, 9, 18 Step 3: Identify the greatest common factor. The common factors are 1, 2, 3, 6. The greatest is 6. A. 6 4. Which of the following sets is the set of prime numbers between 1 and 10? Step 1: Recall the definition of a prime number (a natural number greater than 1 that has no positive divisors other than 1 and itself). Step 2: List numbers between 1 and 10 and identify primes. Numbers: 2, 3, 4, 5, 6, 7, 8, 9 Prime numbers: 2, 3, 5, 7 B. 2,3,5,7 5. What is 25% of 400? Step 1: Convert the percentage to a decimal or fraction. 25\% = (25)/(100) = 0.25 Step 2: Multiply the decimal by the number. 0.25 × 400 = 100 D. 100 6. Which of the following numbers is a prime number? (Options: A. 2 B. 4 C. 6 C. 8) Step 1: Check each option against the definition of a prime number. A. 2: Divisors are 1, 2. It is a prime number. B. 4: Divisors are 1, 2, 4. It is not a prime number. C. 6: Divisors are 1, 2, 3, 6. It is not a prime number. D. 8: Divisors are 1, 2, 4, 8. It is not a prime number. A. 2 7. Write four thousand, thirteen in figure. Step 1: Break down the number by place value. Four thousand means 4 in the thousands place. Thirteen means 1 in the tens place and 3 in the ones place. There are no hundreds, so 0 in the hundreds place. Step 2: Combine the digits. 4,013 B. 4,013 8. The sum of even numbers between 1 and 10 are. Step 1: Identify even numbers between 1 and 10 (exclusive of 1 and 10). Even numbers: 2, 4, 6, 8 Step 2: Form the set. \2, 4, 6, 8\ B. 2,4,6,8 9. A geometric figure whose measure is 360^ is a/an. Step 1: Recall definitions of angles. A 360^ angle represents a full rotation. This is known as a reflex angle if it's an angle greater than 180^ but less than 360^. However, a full circle or a complete rotation is also 360^. Among the given options, a reflex angle is the closest description for an angle that can be 360^ in some contexts, though a full rotation is more precise. Given the options, a reflex angle is typically defined as an angle between 180^ and 360^. A full rotation is 360^. If the question implies an angle whose measure is 360^, it refers to a full rotation. None of the options perfectly describe a full rotation as a "figure". However, if we consider the measure of an angle, a reflex angle is the only option that can be close to 360^. Let's re-evaluate. A reflex angle is an angle that is greater than 180^ and less than 360^. A 360^ angle is a full rotation. None of the options are "full rotation" or "circle". If the question implies a type of angle, and 360^ is the measure, it's a full angle. Since "Reflex angle" is an option, and it's the largest type of angle listed, it's the most plausible choice if the question is slightly imprecise. However, a reflex angle is strictly less than 360^. Let's assume the question is asking for a type of angle that can be large, and 360^ is given as a measure. A full rotation is 360^. If we consider the options, none are a perfect fit for a 360^ angle. Let's consider if there's a typo and it meant to say "a full rotation". If we must choose from the given options, and knowing that a reflex angle is the largest type of angle listed, it's the most likely intended answer, despite the strict definition. Let's assume it's a full rotation. D. Reflex angle (Assuming the question implies a full rotation or the largest type of angle listed, though strictly a reflex angle is <360^). 10. What is the place value of in the numbers 0.3456? (Assuming the question is asking for the place value of the digit '3'). Step 1: Identify the digit '3' in the number 0.3456. The digit '3' is immediately after the decimal point. Step 2: Determine its place value. The first digit after the decimal point is in the tenths place. A. Tenth place 11. What is the quotient of 324 divided by 3? Step 1: Perform the division. 324 ÷ 3 = 108 B. 108 12. Determine the value of the expression: 3x - 2y if x = 2 and y = 3. Step 1: Substitute the values of x and y into the expression. 3(2) - 2(3) Step 2: Perform the multiplication. 6 - 6 Step 3: Perform the subtraction. 0 C. 0 13. Which of the following numbers is not a factor of 16? Step 1: List the factors of 16. Factors of 16: 1, 2, 4, 8, 16 Step 2: Check each option. A. 6: 6 is not in the list of factors of 16. B. 8: 8 is a factor of 16. C. 4: 4 is a factor of 16. D. 2: 2 is a factor of 16. A. 6 14. Which of the following equations is correct? Step 1: Evaluate each option. A. 20\% = 0.5: 20\% = 0.20. So, 0.20 ≠ 0.5. (Incorrect) B. 0.8 = 4/5: Convert 4/5 to a decimal. 4 ÷ 5 = 0.8. So, 0.8 = 0.8. (Correct) C. 10^3 = 300: 10^3 = 10 × 10 × 10 = 1000. So, 1000 ≠ 300. (Incorrect) D. 1/2 = 0.2: 1/2 = 0.5. So, 0.5 ≠ 0.2. (Incorrect) B. 0.8 = 4/5 15. Add: 23_(4) and 32_(4) Step 1: Add the numbers in base 4. Start from the rightmost digit (ones place): 3_(4) + 2_(4) = 5_(10). In base 4, 5_(10) = 1 × 4 + 1 = 11_(4). So, write down 1 and carry over 1. Step 2: Add the next digits (fours place) including the carry-over. 2_(4) + 3_(4) + 1_(carry) = 6_(10). In base 4, 6_(10) = 1 × 4 + 2 = 12_(4). So, write down 12. Step 3: Combine the results. The sum is 121_(4). C. 121(4) (or D, since C and D are identical) 16. Arrange these numbers in ascending order 9,6,0,1,2,8,4,3,5,7. Step 1: List the numbers. 9, 6, 0, 1, 2, 8, 4, 3, 5, 7 Step 2: Arrange them from smallest to largest. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 C. 0,1,2,3,4,5,6,7,8,9 17. Simplify: 1 (2)/(3) × 9/10 Step 1: Convert the mixed number to an improper fraction. 1 (2)/(3) = ((1 × 3) + 2)/(3) = (3+2)/(3) = (5)/(3) Step 2: Multiply the fractions. (5)/(3) × (9)/(10) Step 3: Cancel common factors. 5^13^1 × 9^310^2 = (1 × 3)/(1 × 2) = (3)/(2) Step 4: Convert the improper fraction to a mixed number. (3)/(2) = 1 (1)/(2) B. 1 1/2 18. The inverse of 4/5. Step 1: Understand "inverse". For a fraction, the multiplicative inverse (reciprocal) is found by flipping the numerator and denominator. The inverse of (4)/(5) is (5)/(4). A. 5/4 19. In a class of 40 students, 10 of the students are boys. What is the ratio of girls to boys? Step 1: Find the number of girls. Total students = 40 Number of boys = 10 Number of girls = 40 - 10 = 30 Step 2: Write the ratio of girls to boys. Ratio of girls to boys = Number of girls : Number of boys 30 : 10 Step 3: Simplify the ratio by dividing both sides by the greatest common factor, which is 10. 30 ÷ 10 : 10 ÷ 10 3 : 1 C. 3:1 What's next?