E: Chapter 2: Mathematical Revision

Question 1

Absolute Value:

Answer 1

Absolute value refers to the magnitude or distance of a number from zero on the number line. It is denoted by two vertical bars (| |). For a real number ‘x’, the absolute value of x (|x|)

Absolute Value Function:
* is |x| if x is positive or zero,
* Is |x| if -x.

Examples:
* |-1| = 1
* |-14| = 14
* |1| = 1
* |0| = 0
* |7| = 7
* |7-2| = |5| = 5
* |2+3| = |5| = 5
* |-3×5| = |-15| = 15

Question 2

BODMAS:

Answer 2

It’s a set of rules to determine the sequence in which calculations should be performed in a mathematical expression to ensure consistency and accuracy.

BODMAS is an acronym used to remember the order of operations in arithmetic:
1) Brackets,
2) Orders (exponents and roots),
3) Division and Multiplication (from left to right),
4) Addition and Subtraction (from left to right).

Question 3

3. Fractions:

Answer 3

Fractions represent parts of a whole or ratios between quantities.

They consist of a numerator (top number) and a

denominator (bottom number), separated by a horizontal line.

The numerator represents how many parts are being considered, while the denominator indicates how many parts make up a whole.

Question 4

4. Inequalities:

Answer 4

Inequalities express relationships between two values that are not equal.

Common inequality symbols include
‘<’ (less than),
‘>’ (greater than),
‘<=’ (less than or equal to), a
nd ‘>=’ (greater than or equal to).

An inequality indicates that one value is smaller or larger than another.

Question 5

5. Linear Function:

Answer 5

A linear function is a mathematical relationship between two variables, typically represented graphically as a straight line. It has the form:

y = mx + b,

where ‘y’ is the dependent variable,
‘x’ is the independent variable,
‘m’ is the slope (rate of change),
and ‘b’ is the y-intercept (where the line crosses the y-axis).

Question 6

6. Percentages:

Answer 6

Percentages express a proportion as a fraction of 100. It’s often used to represent ratios in a more easily understandable form.

To calculate a percentage, divide the part by the whole and multiply by 100.

Question 7

7. Power:

Answer 7

A power, also known as an exponent, indicates how many times a base number is multiplied by itself.

For example, in the expression 2^3,
2 is the base and 3 is the exponent.

It signifies 2 multiplied by itself three times (2 × 2 × 2 = 8).

Question 8

8. Square Root:

Answer 8

The square root of a number ‘x’ is a value ‘y’ that, when multiplied by itself, equals ‘x’. It is denoted by the symbol (√).

For instance, the square root of 9 (√9) is 3 because 3 × 3 = 9.

Question 9

9. Summation Operator:

Answer 9

The summation operator (Σ) represents the sum of a sequence of numbers. It is often used to add up a set of terms, usually with a specified pattern.

The variable below the Σ symbol indicates the starting point of the sequence, while the variable above it indicates the ending point. The expression after Σ defines the terms to be summed.