Free Bachelor of Mathematics: Mathematical Proof and Logic Questions and Answers — Questions and Answers
Question 1: Which of the following is a way to improve your mental math skills?
- Always use a calculator for complex problems
- Ignore patterns and shortcuts
- Practice regularly and consistently (Correct answer)
- Studying math only when preparing for a test
Correct answer: Practice regularly and consistently
Like any skill, mental math improves significantly with consistent practice. Regularly engaging in mental calculations helps to strengthen numerical fluency, recall of basic facts, and the ability to apply various mental strategies quickly and accurately. Avoiding calculators and actively looking for shortcuts during practice are key components to developing strong mental math abilities.
Question 2: In multiplication by 11, what rule is applied when the sum of two adjacent digits is more than 9?
- Carry over to the next digit (Correct answer)
- The sum becomes a single digit number
- The sum is ignored
- The product becomes zero
Correct answer: Carry over to the next digit
When multiplying by 11 using the 'sum of adjacent digits' trick, if the sum of two adjacent digits exceeds 9, the tens digit of that sum is carried over to the next leftward sum. This is analogous to carrying over in standard addition, ensuring the correct product is formed. For example, 38 x 11: 3_(3+8)_8 -> 3_11_8 -> (3+1)_1_8 -> 418.
Question 3: How does the document suggest dealing with percentages?
- Convert them to decimals (Correct answer)
- Convert them to fractions
- Write them out as words
- Leave them as they are
Correct answer: Convert them to decimals
The document suggests converting percentages to decimals for easier mental calculation. For example, to find 20% of a number, it's often simpler to think of it as multiplying by 0.20. This transformation simplifies the arithmetic, especially when dealing with multiplication or division, making mental calculations more straightforward.
Question 4: what is the trick to subtracting any number from 1000 quickly?
- Add instead of subtracting
- Subtract each digit from 9 and the last from 10 (Correct answer)
- Multiply by -1
- None of these
Correct answer: Subtract each digit from 9 and the last from 10
This is a common mental math trick for subtracting from powers of 10. To subtract a number like 456 from 1000, you subtract each digit from 9 (9-4=5, 9-5=4) and the last digit (units place) from 10 (10-6=4). Combining these results in 544, which is the correct answer.
Question 5: What method does this document suggest for squaring numbers ending in 5?
- Multiply by 5 and add 25
- Multiply the first digit by itself plus one and append "25" (Correct answer)
- Square each digit separately then add them together
- None of these
Correct answer: Multiply the first digit by itself plus one and append "25"
This is a well-known mental math trick for squaring numbers ending in 5. For a number like `N5` (e.g., 35), you take the first digit `N` (3), multiply it by `N+1` (3 * 4 = 12), and then append '25' to the result. So, 35 squared is 1225.
Question 6: According to this document, multiplying by 4 can be done faster by doing what instead?
- Multiplying by 2 twice (Correct answer)
- Dividing by 0.25
- Adding four times
- Subtracting from a multiple of four
Correct answer: Multiplying by 2 twice
Multiplying by 4 is mathematically equivalent to multiplying by 2, and then multiplying that result by 2 again. This strategy can be faster mentally because doubling a number is often easier than multiplying by 4 directly, especially for larger numbers. For example, 37 x 4 = (37 x 2) x 2 = 74 x 2 = 148.
Question 7: What method does this document recommend for multiplying two-digit numbers less than twenty but more than ten together?
- Simply multiply as normal
- Subtract both numbers from twenty then multiply
- Add ten to both numbers then multiply
- Apply cross multiplication (Correct answer)
Correct answer: Apply cross multiplication
The 'cross multiplication' trick for numbers between 10 and 20 involves a specific method: add one number to the units digit of the other, then multiply this sum by 10, and finally add the product of the two units digits. For example, 12 x 13: (12 + 3) x 10 + (2 x 3) = 150 + 6 = 156.
Free Bachelor of Mathematics: Mathematical Proof and Logic Questions and Answers
Which of the following is a way to improve your mental math skills?