Algebra and Functions
What Algebra and Functions covers
This domain tests pattern rules, missing numbers, simple expressions, one-step and two-step equations, and input–output relationships. You need to translate a written rule into symbols, substitute values, and use inverse operations to solve for an unknown. Function tables often ask you to find the rule linking input to output and then extend it.
Core rules
- A variable is a letter standing for a number; 3n means 3 × n, not 3 + n.
- An expression has no equals sign; an equation states two expressions are equal.
- To solve, keep the equation balanced: do the same operation to both sides. Undo addition/subtraction first, then multiplication/division.
- Substitute by replacing the variable with brackets: if x = 4, then 2x + 3 = 2(4) + 3 = 11.
- In a function table, test whether the rule is additive (output = input + constant), multiplicative (output = input × constant), or a combination.
- A pattern can be described by its starting value and its step; the nth term of a simple additive pattern is start + (n − 1) × step.
Worked example
Solve 3x + 7 = 25. Subtract 7 from both sides: 3x = 18. Divide both sides by 3: x = 6. Check by substitution: 3(6) + 7 = 18 + 7 = 25. In a table where input 1 gives 5, input 2 gives 8, and input 3 gives 11, the output increases by 3 each time, so the rule is output = 3 × input + 2; input 10 gives 32.
Traps that cost marks
Applying operations in the wrong order when solving is a frequent error: undo the +7 before dividing by 3. Reading 3x as 3 + x changes the value. Confusing an expression with an equation leads to “solving” something that has no equals sign. When extending a pattern, check whether the step is added or multiplied; a table that goes 2, 6, 18 is multiplying by 3, not adding 4. Finally, substitute the found value back into the original equation-not into a rewritten line-to confirm the check.