Chapter 5 Algebraic Techniques and Index Laws Review

Summary of algebraic techniques including pronumerals, terms, index laws, expanding/factorising, and algebraic fractions based on CambridgeMATHS Stage 4 Year 8 curriculum.

What is a pronumeral?

A letter that represents a number.

In an algebraic expression, how is the coefficient defined?

The number multiplied by a pronumeral. For example, in $5x$, the coefficient of $x$ is $5$.

In the expression $5x^2y - 2ab^2 + 4ab^2 + 7p^2q^3 - 8$, what is the constant term?

$$-8$$

What is the meaning of 'like terms' in algebra?

Terms where the pronumerals have identical expanded forms (e.g., $6a^2m$ and $5ma^2$).

What is the rule regarding the sign of an algebraic term during addition or subtraction?

The sign in front of the term belongs to that term.

In algebra, what do the terms 'evaluate' and 'substitute' require you to do?

Replace pronumerals with numbers and calculate the final answer.

How are equivalent expressions defined?

Expressions that are equal no matter what numerical value is substituted for the pronumeral.

What is the Distributive law for expanding the bracket $a(b+c)$?

$$ab + ac$$

What is the first step in factorising an expression like $12x + 6a$?

Identify the Highest Common Factor (HCF), which is $6$, then write as $6(2x + a)$.

What is the result of multiplying the terms $-5x^2y \times 2xy$?

$$-10x^3y^2$$

State Index Law 1 for multiplication: $a^m \times a^n$.

$$a^{m+n}$$

State Index Law 2 for division: $a^m \times a^n$.

$$a^{m-n}$$

State Index Law 3 for a power of a power: $(a^m)^n$.

$$a^{mn}$$

State Index Law 4 regarding the zero power: $a^0$.

$$a^0 = 1$$

Simplify the expression $(4a^3)^2$ using index laws.

$$16a^6$$

How do you add or subtract algebraic fractions with different denominators, such as $\frac{3a}{2} + \frac{7m}{5}$?

Find a common denominator by multiplying the denominators (e.g., $2 \times 5 = 10$) and adjust the numerators accordingly.

What is the procedure for dividing algebraic fractions, such as $\frac{15x}{y} \div 20x$?

Multiply the first fraction by the reciprocal of the second: $\frac{15x}{y} \times \frac{1}{20x}$.

What is the result of the division $\frac{16k^2at}{12kt}$?

$$\frac{4ka}{3}$$