FAQ Math 12

1. How Was Math Used in Building the Great Pyramid?

The construction of the Great Pyramid of Giza involved advanced mathematical concepts, including:

• Geometry: The pyramid’s precise triangular faces required knowledge of geometry to ensure they were symmetrical.
• Proportions: The ratio of the pyramid’s height to its base is close to the Golden Ratio ($\phi$ ), which is thought to have aesthetic and structural significance.
• Measurements: The use of standardized units and measuring tools ensured accuracy in dimensions.
• Pythagorean Theorem: To create right angles and proper alignment, early builders likely used basic geometric principles like the Pythagorean Theorem.

2. Is AS Maths Hard?

AS Maths can be challenging, especially for students who haven’t developed strong problem-solving and algebra skills. It requires:

• A good understanding of algebra, trigonometry, and calculus.
• Regular practice to master different types of questions. The difficulty level varies depending on your math foundation and interest.

3. Is Discrete Math Easier Than Calculus?

Discrete Math and Calculus are different branches of mathematics, so the difficulty depends on the student’s strengths:

• Discrete Math involves logic, set theory, combinatorics, and algorithms. It is more abstract and requires logical thinking.
• Calculus involves continuous functions, derivatives, and integrals and is more computational. Some students find Discrete Math easier because it’s less about complex calculations and more about logical reasoning.

4. Is Further Maths Needed for Engineering?

Further Maths isn’t always mandatory for engineering, but it is highly beneficial:

• Engineering courses rely heavily on advanced mathematics, including calculus, differential equations, and linear algebra, which are covered in Further Maths.
• Benefits: Students who take Further Maths often have a stronger foundation in math concepts and perform better in their engineering studies.

5. Was Math Invented or Discovered?

This is a philosophical question debated by mathematicians:

• Discovered View: Some argue that math exists independently of human thought, and humans simply discover mathematical truths (like the properties of numbers and geometry).
• Invented View: Others believe that math is a human creation, a language invented to describe patterns and relationships in the natural world.

6. What Can You Do with a Math Major?

A math major opens doors to various careers, including:

• Data Scientist/Analyst: Analyzing data to drive business or research decisions.
• Actuary: Assessing risk and uncertainty in insurance or finance.
• Engineer: Using mathematical principles to design and innovate.
• Software Developer: Applying logic and algorithms in programming.
• Financial Analyst: Working in investment banking, trading, or finance.
• Math Educator: Teaching mathematics at different levels.
• Research Mathematician: Conducting theoretical or applied research in math.

7. What Do Two Straight Lines Mean in Math?

Two straight lines, written as $|x|$, represent the absolute value of a number $x$. Absolute value refers to the distance of a number from zero on the number line, regardless of direction.

• Example: $|-3| = 3$ .

8. What Do You Learn in 7th Grade Math?

7th-grade math typically includes:

• Algebra: Basic operations with variables, solving simple equations.
• Ratios and Proportions: Understanding and solving ratio problems.
• Geometry: Properties of shapes, area, perimeter, volume.
• Statistics: Mean, median, mode, and introduction to probability.
• Fractions and Decimals: Operations with fractions, decimals, and percentages.

9. What Does Certain Mean in Math?

In probability, certain means an event will definitely happen, with a probability of 1 or 100%.

• Example: If you roll a six-sided die, the probability of rolling a number between 1 and 6 is certain (probability = 1).

10. What Does Complementary Mean in Math?

Two angles are complementary if their measures add up to 90 degrees.

• Example: If one angle is 30 degrees, its complementary angle is 60 degrees because $30 + 60 = 90$ .

11. What Does Congruent Mean in Math?

Congruent means two shapes or figures have the same size and shape.

• Example: Two triangles are congruent if all their corresponding sides and angles are equal.

12. What Does Consistent Mean in Math?

A system of equations is consistent if there is at least one solution to the system.

• Example: The system $x + y = 2$  and $x – y = 0$  is consistent because it has a solution $(x = 1, y = 1)$.

13. What Does Expression Mean in Math?

A mathematical expression is a combination of numbers, variables, and operations (like +, -, ×, ÷) that represents a value.

• Example: $3x + 2$  is an algebraic expression.

14. What Does Factor Mean in Math?

A factor of a number is a number that divides into it exactly without leaving a remainder.

• Example: The factors of 12 are 1, 2, 3, 4, 6, and 12.

15. What Does Factorising Mean in Maths?

Factorising means writing an expression as a product of its factors.

• Example: Factorising $x^2 – 5x + 6$  gives $(x – 2)(x – 3)$ .

16. What Does LCM Mean in Math (Example)?

LCM stands for Least Common Multiple, which is the smallest number that is a multiple of two or more numbers.

• Example: The LCM of 4 and 6 is 12, as 12 is the smallest number divisible by both 4 and 6.

17. What Does Output Mean in Math?

Output refers to the result of applying a function or operation to an input.

• Example: In the function $f(x) = 2x + 3$ , if $x = 2$ , the output is $f(2) = 2(2) + 3 = 7$ .

18. What Does SF Stand for in Maths?

SF stands for Significant Figures, which are the digits in a number that carry meaningful information about its precision.

• Example: In the number 123.45, there are 5 significant figures.

19. What Does Sigma Mean in Math?

Sigma ($\Sigma$ ) represents summation in mathematics, indicating the sum of a sequence of terms.

• Example:

$$\Sigma_{i=1}^{4} i = 1 + 2 + 3 + 4 = 10$$ 

This means summing the values from 1 to 4.