Year 10 Maths • AC9M10A01 • Authored homework
Expand, factorise, simplify and solve algebraically
Expand, factorise and simplify algebraic expressions, apply index laws to variables, and solve algebraic equations using clear inverse operations. Show working, use correct notation and check reasonableness.
Part A
Short-answer questions
Expand 5(2x - 3).
Simplify 4a - 3b + 2a + 7b.
Factorise 12x + 18 fully.
Expand (x + 4)(x - 7).
Factorise x^2 + 8x + 15.
Simplify x^3 × x^5 using index laws.
Simplify y^7 ÷ y^2 using index laws.
Solve 3x - 7 = 11.
Correct this error: (x + 5)^2 = x^2 + 25.
Explain how expanding can be used to check factorising.
Part B
Long-answer questions
Expand and simplify 4(3x - 2) - 2(x + 5).
Factorise 6x^2 - 15x fully and check by expanding.
Expand (2x - 3)(x + 6), then substitute x = 2 to check the expression.
Factorise x^2 - 9 and explain why it is a difference of squares.
Solve 2(x - 3) + 5 = 3x - 4 and check your solution.
Simplify (3x^2y)(4xy^3) using index laws and explain each exponent change.
Factorise and solve x^2 + 5x + 6 = 0.
A rectangle has side lengths x + 2 and x + 9. Write an expression for its area, expand it, then explain what each term represents.
A student factorises 10x + 25 as 5(2x + 25). Explain the error and correct it.
Write a full algebra solution that includes expansion, simplification, factorising and checking by substitution.
Part C
Research and understanding task
Create an algebraic area model using a rectangle or composite shape. Write expressions for side lengths, expand to find area, factorise where possible, and explain the meaning of each expression.