TCE Year 11 Maths Methods Foundation practice exams with worked answers

Algebra is the language every other area of this course is written in, so fluency here pays off in functions, calculus and probability. An expression such as 3x² − 5xy has no equals sign; an equation states that two expressions are equal; a formula links several variables; and a system of simultaneous equations is a set of equations that must all be true at once.

When you build an expression from words, define every variable first, for example “let n be the number of tickets sold”.

Function notation. Writing y = f(x) names the rule f. To evaluate f(a), replace every x with a, using brackets around negative values. If f(x) = 2x² − 3x then f(−2) = 2(−2)² − 3(−2) = 8 + 6 = 14.

Rearranging formulae. To make a variable the subject, undo operations in reverse order, doing the same thing to both sides. Keep the subject positive and on the left at the end.

Index laws. For a non-zero base: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ, (ab)ⁿ = aⁿbⁿ, a⁰ = 1 and a⁻ⁿ = 1/aⁿ. A rational index links to surds: a^(1/n) = ⁿ√a and a^(m/n) = (ⁿ√a)ᵐ. So √(x³) = x^(3/2). To solve an index equation, write both sides with the same base and equate the indices.

Algebraic fractions follow the same rules as numerical fractions: factorise first, find a common denominator, combine numerators, then cancel common factors (never individual terms). State any values that make a denominator zero.

Scientific notation writes a number as m × 10ᵏ with 1 ≤ m less than 10. Multiply by combining the m values and adding the powers of ten, then re-adjust m.