Algebra 1

Section 1Symbols and expressions

Algebra uses letters, called variables, to stand for numbers. An expression is a mathematical phrase without an equals sign, such as 3x + 5. In plain words, algebra lets you describe a pattern before you know the exact value.

Section 2Directed numbers

Directed numbers are positive and negative numbers. Adding a negative moves left on the number line, while subtracting a negative moves right. Watch out: 7 - (-3) becomes 7 + 3, not 7 - 3.

Section 3Substitution

Substitution means replacing a variable with a given value. Use brackets when substituting negative values, especially with powers. For example, if x = -2, then x^2 = (-2)^2 = 4.

Section 4Collecting like terms

Like terms have the same variable part, such as 4x and -7x. You can add or subtract like terms, but you cannot combine unlike terms like 3x and 3y. Easy to mix up - x^2 and x are not like terms.

Section 5Expansion

Expansion means multiplying out brackets. Use the outside factor on every term inside the bracket. Here's the trick: 3(x + 4) means 3 times x and 3 times 4, so it becomes 3x + 12.

Section 6Factorisation

Factorisation is the reverse of expansion. Look for the highest common factor in all terms, then place it outside the bracket. For example, 6x + 9 = 3(2x + 3).

Section 7Using algebra in context

Algebra can model real-life costs and quantities. If one lunch costs x dollars, then four lunches cost 4x dollars, and four lunches plus a J$300 drink total 4x + 300. The expression changes only when the situation changes.