Free Bachelor of Mathematics: Mathematical Proof and Logic Questions and Answers

Question 1

Which of the following is a way to improve your mental math skills?

Accepted Answer

Practice regularly and consistently

Answer

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?

Accepted Answer

Carry over to the next digit

Answer

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?

Accepted Answer

Convert them to decimals

Answer

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?

Accepted Answer

Subtract each digit from 9 and the last from 10

Answer

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?

Accepted Answer

Multiply the first digit by itself plus one and append "25"

Answer

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.

BMath Bachelor of Mathematics Practice Test

BMath Bachelor of Mathematics Practice Test

Free Bachelor of Mathematics: Mathematical Proof and Logic Questions and Answers