Exam Skills & Year-8 Bridges

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.