Exam Skills & Year-8 Bridges

2 h · 110 marks. Exact form required: fractions, surds, $\pi$-multiples — never decimals. Section A short, Section B extended.

2 h · 110 marks. GDC allowed and expected — state the GDC step ('using GDC, ...') for the M1 mark. Solutions to 3 s.f. unless told otherwise.

1 h · 55 marks. Two long extension-style problems guiding you through unfamiliar territory. Read part (e) before starting part (a) — it tells you where you're going.

Method mark — awarded for the correct formula or set-up appearing on the page. Quote the rule explicitly to bank this.

Accuracy mark — awarded for a correct intermediate or final value arising from correct method.

Reason mark — awarded for the justifying sentence ('by the principle of induction...', 'since $f'(x) > 0$ on $[a,b]$, $f$ is increasing...').

Show working; give the answer. Working can earn M1 even if the final A1 is wrong.

FULL algebraic trail required. No shortcuts. You must end at the stated result.

Like 'find' but with a justification line — give the value AND a reason ('therefore...').

'Hence' = use the previous part's result. 'Hence or otherwise' = use it OR start fresh.

Final value only; no working expected. Often 1 mark, no partial credit.

Label every asymptote, intercept, and turning point with coordinates. Unlabelled features score 0.

(1) Quote the formula. (2) Show every algebra step on its own line. (3) Use exact form on Paper 1. (4) Check the requested interval for second solutions. (5) Write the closing sentence on proofs.

Paper 1/2: ~65 sec/mark. Paper 3: ~65 sec/mark. If a question is taking >2× the budget, flag it and move on.

UK Year-8 students sometimes skip GCSE-level rational, exponential, and trig fluency. These bridges replay the key Year-8/9 concepts with question-led discovery, then drop you straight into a real IB Paper 1 question.

$b \ne 0$. The zero comes from the numerator; the vertical asymptote comes from the denominator hitting 0.

$x = c$ where denominator $= 0$ AND numerator $\ne 0$. Curve shoots to $\pm\infty$ as $x \to c$.

For $f(x) = \dfrac{ax+b}{cx+d}$ with $a, c \ne 0$: HA at $y = a/c$ (ratio of leading coefficients).

Step 1: write $y = f(x)$. Step 2: swap $x \leftrightarrow y$. Step 3: solve for $y$. Step 4: rename $y = f^{-1}(x)$. Step 5: state the domain (= range of $f$).

$f(x) = \dfrac{9x+9}{3x-12}$ — find the zero, the asymptotes, the inverse. Bridge ends here so you can sit a real exam question with confidence.

Six real-IB-style Paper 1 questions modelled on 2023 May TZ1: rational function, frequency table & expected value, $\cos 2\theta = \sin\theta$, exponential range, sine transformation, related rates.

No calculator. Exact form everywhere. Show every line of working. Time yourself: ~50 minutes total.

Review the per-mark reveals on every question. Identify which marks you LEFT on the table — those are the highest-leverage areas to drill next.

Ten encounter decks — one per math topic. Each pairs a Paper 1 (no-calc, exact form) question with a Paper 2 (GDC-active) question, modelled on 2022-2023 AA HL May papers. Take them after the corresponding chapter quizzes.

Question setup → guided per-mark solve → topic-specific traps slide → wrap. Every explanation uses the Per-mark scheme [n]: format so you see which line earns which IB mark.

ONE encounter per study session. 22 minutes each. Don't rush — the trap-spotting slide at the end is the highest-leverage 90 seconds in this topic.

Each chosen question represents a high-frequency archetype in AA HL May 2018-2023. Mastering all 20 patterns covers ~70% of historical mark distribution.