Year 8 Maths • AC9M8A01 • Authored homework
Linear expressions
Practise Linear expressions through calculations, explanation, modelling and checking. Show reasoning in full sentences where useful, and check calculations or conclusions before finishing.
Part A
Short-answer questions
Expand 3(2x + 5).
Factorise 8x + 12.
Simplify 4a + 7 - 2a + 5.
A student writes 2(x + 3) = 2x + 3. Correct the expansion.
Write the rule or formula most useful for Linear expressions.
Show how to check one answer using estimation, substitution or inverse operations.
Write one common mistake students make in Linear expressions and correct it.
Create a small table, diagram or equation that represents this topic.
State where units, exact form or rounding matter in this topic.
Write one exam-style short question on Linear expressions and solve it.
Part B
Long-answer questions
Simplify 5(2x - 1) - 3(x + 4) and explain each algebraic property used.
Create two different expressions that simplify to 6x + 9, then explain how you know.
Solve a multi-step problem involving Linear expressions and explain every step clearly.
Create a realistic word problem for Linear expressions, solve it and interpret the answer.
Compare two methods for a problem in Linear expressions and explain which is more efficient.
Write a worked solution that includes a check for reasonableness.
Create a problem with a deliberate trap, then solve it correctly and explain the trap.
Use a diagram, table, graph or equation to model a situation involving Linear expressions.
Explain how this topic connects to a previous Year 7 or Year 8 maths skill.
Write a full-mark response to a challenging Linear expressions question, including reasoning and final answer.
Part C
Research and understanding task
Research one situation that can be represented by a linear expression, such as taxi fares or membership fees. Create and simplify an expression.