Mathematics (IGCSE, Grade 9) · Textbook Exercise 2.1, Q1–26

Math Exercise 2.1 — Simultaneous Equations

Graded 2026-06-17 · Sys4Ethan (Claude Opus 4.8 vision, human-verified)

81%

✅ Correct 21 ◐ Partial 1 ✗ Needs fixing 3 ○ Not attempted 1 Total 26

To fix & review (5)Q2 Q3 Q14 Q19 Q23

Q1 ✓ Correct substitution into $y=x^2$

Roots right. Habit tip: also write the matching $y$, i.e. the full coordinate pairs.

Q2 ✗ Needs fixing substitution + factorising

Try this → Your factorisation $(2x+2)(x-4)=0$ is correct. Re-check the root from $2x+2=0$ — what sign should $x$ be? You wrote $x=1$.

Q3 ✗ Needs fixing line meets circle

Try this → $x^2+y^2=25$ is not the same as $x+y=5$ — you cannot square-root a sum term by term. Substitute $y=x-1$ into $x^2+y^2$, keep the squares and expand; you should get a quadratic with two solutions.

Q4 ✓ Correct solving in $y$

Neat — factorised in $y$ and got both pairs.

Q5 ✓ Correct common factor

Q6 ✓ Correct eliminating $3xy$

Q7 ✓ Correct substitution + quadratic

Q8 ✓ Correct substitution + quadratic

Factorising to $(x-3)(x-9)=0$ is right — just double-check the $y$ value when $x=3$.

Q9 ✓ Correct substitution + quadratic

Q10 ✓ Correct line through origin meets circle

Q11 ✓ Correct sum/product

Q12 ✓ Correct parabola meets line

Q13 ✓ Correct substitution + quadratic

Q14 ✗ Needs fixing wrong question copied

Try this → The working under Q14 is actually Q15 ($y=3x$). Q14 is a different pair: $x+y=4$ and $x^2+y^2=10$. Redo it against the correct equations.

Q15 ✓ Correct $y=3x$ into quadratic

Q16 ✓ Correct substitution + quadratic

Q17 ✓ Correct substitution + quadratic

Q18 ✓ Correct expand $(x-1)(y+2)$

Q19 ○ Not attempted line meets circle

Try this → Skipped. Find where the line $y=1-2x$ cuts the curve $x^2+y^2=2$ — same substitution method you used elsewhere.

Q20 ✓ Correct sum & product word problem

Both equations and the solution are correct.

Q21 ✓ Correct two squares word problem

Nice use of $(x+y)^2$ to get $xy$.

Q22 ✓ Correct length of chord $AB$

Q23 ◐ Partial midpoint of chord

Try this → You found the two intersection points, but the question asks for the MIDPOINT of $AB$ — take the average of the two points. Also re-check the $x$-coordinate of the first point by substituting back into $2x+5y=1$.

Q24 ✓ Correct length of chord $AB$

Q25 ✓ Correct section ratio on a chord

Section ratio $AP:PB=3:1$ handled correctly — strong work.

Q26 ✓ Correct perpendicular bisector

Perpendicular bisector found correctly — excellent.

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