Inequalities · edition and printed answer key

Source metadata

The running header reads 2025 TJC H2 Math (9758) JC2 MSM: INEQUALITIES. The first pages also carry the title INEQUALITIES. The question compilation has four pages, printed 20,21,22,23; the worked compilation has sixteen pages, printed 1–16. “Answers” introduces the question-compilation key on printed 22. Question numbers, part labels, marks and original exam references are retained in each question article. Repeated headers and page numbers map to this edition record rather than requiring a PDF facsimile.

Printed answer key

This is the original compact key, including its Q4 general-range qualification. Full source workings and native diagrams appear in the linked question records.

Question	Key as printed
1	$x<-3$ or $0<x<5$; $0<x<e^{-3}$ or $1<x<e^5$
2	(a) $0\le x\le1/4$; (b) $1<x<2$ or $2<x<3$
3	(a) $1-\sqrt7<x<0$ or $x>1+\sqrt7$; $(-\infty,-1-\sqrt7]\cup[1+\sqrt7,\infty)$; (b) $x\in\mathbb R$
4	(a) $x<0$ or $x>1$; $x>0$; (b) $y\le(-1-\sqrt{1-k^2})/2$ or $y\ge(-1+\sqrt{1-k^2})/2$. The original omits exceptional k cases; the native working explicitly qualifies them.
5	$x\ge1+\sqrt2$ or $x=1$; $x\ge\sqrt2$ or $x=0$
6	$0<x<\pi/12$ or $5\pi/12<x<\pi/2$
7	$-6<a<2$
8	$0\le x<1$ or $4/3\le x\le2$
9	$-1-\sqrt2<x<-1+\sqrt2$, $x\ne-2,-1$; $x<\ln(\sqrt2-1)$
10	$x\le-5$ or $-2<x\le3$; $-\sqrt3\le x<0$ or $0<x\le\sqrt3$
11	(i) $-4\le x<-3$ or $x\ge1$; (ii) $-1/3<x\le-1/4$ or $0<x\le1$
12	(i) $x=5/3$ or $5/3\pm\sqrt{10}/3$; (ii) $x<5/3-\sqrt{10}/3$ or $5/3<x<2$ or $2<x<5/3+\sqrt{10}/3$
13	(i) $x=0$ or $2ab/(b+1)$; (ii)(a) $b<-1$; (ii)(b) $2ab/(b+1)\le x\le0$; $x\le\ln(-2ab/(b+1))$
14	(ii) $-3/2\le x\le-1$

Repeated key diagrams

The Q12 absolute-rational/line graph, Q13 V/line construction and Q14 absolute-exponential sketch repeat the same labelled content as their worked solutions. Each is redrawn once in its linked native question record; the page-item ledger maps both appearances to that canonical SVG.