Y9 Booklet 10 – Algebra and Proportion | Original 17-page PDF

Exact unchanged original Y9 Booklet 10 – Algebra and Proportion | Original 17-page PDF.

Keep the original page, question and subpart numbers when following the matching lesson recordings. Each recording may cover selected examples; the complete PDF includes additional practice. This is the original teaching booklet, with its original historical labels and layout.

Spiral learning connection: connect these skills to earlier number, algebra and modelling ideas, then return to them in later problems.

Original-edition clarifications (the PDF itself is unchanged):

• Page 3: direct proportion is defined by a constant ratio, not just by two quantities changing in the same direction. The inverse-proportion example’s target variable should be x: z = 6/x = 6x⁻¹.

• Page 8, Q7: (x − 4)³ + 3ˣ⁻⁴ = 100 has x ≈ 7.611869, hence 7.6 to one decimal place. The printed 3.2 is incorrect; the recording correctly replaces it with 7.6.

• Page 12, Q10: the value 5π(11³)/4 rounds to 5,227 cubic centimetres, rather than the printed linear-centimetre unit.

• Pages 12–14, Q11(a,b): unless x is restricted to nonnegative values, include both branches: x = ±√(5t + 35) and x = ±√(3u − 12).

• For real-valued answers, Q12 requires x ≥ 20, with just y = 0 at x = 20. Q13 requires x greater than 2 because its square root is in the denominator; x = 2 is also excluded.

• Page 17’s suggested 225–249 kg price band assumes continuation of the last two 25 kg bands. The banded table is not strict direct proportionality between mass and price.