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\fancyfoot[L]{\small May 2026}
\fancyfoot[R]{\small\itshape J.\ Murphy --- EOY Skills Checklist}
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\begin{document}

\begin{center}
{\LARGE\bfseries\color{tealmain} EOY Cumulative --- Skills Checklist}\\[2pt]
{\small Year 11 Extended\;$\cdot$\;June 2026 EOY\;$\cdot$\;Probability $\cdot$ Functions $\cdot$ Exp/Log $\cdot$ Trigonometry}\\[2pt]
{\footnotesize\itshape\color{rulegray}v.\ \today}
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\vspace{4pt}

\begin{headerbox}
\textbf{\textcolor{tealdark}{How to use this sheet.}} Each skill below maps to a Dr Frost code where one exists. Tick a box once you can do that skill confidently without help. Skills are organised by EOY pack so you can work through them as you go. Codes are clickable on the DFM site for direct practice.

\smallskip
\textit{For deeper trigonometry practice, see the four-packet \textbf{Trigonometry Review Booklet} and its dedicated checklist. The trig section here covers the cumulative essentials.}
\end{headerbox}

% =============================================================
% PACK 1 — PROBABILITY
% =============================================================
\section{Pack 1 --- Probability (Sets, Venn \& Probability)}

\noindent\textbf{Haese chapter references:} \haese{10E:3} (Sets \& set notation), \haese{10E:17} (Probability and tree diagrams), \haese{10E:17H} (Conditional probability --- Extended only).

\medskip

\begin{topic}{Sets \& set notation \skillcode{384, 387}}
\begin{skilllist}
  \skill{384a}{Use set notation for union, intersection, complement, subset.}
  \skill{384b}{List elements of a set defined by a property; use $n(A)$.}
  \skill{387a}{Use interval notation for subsets of $\mathbb{R}$.}
\end{skilllist}
\end{topic}

\begin{topic}{Venn diagrams \skillcode{395}}
\begin{skilllist}
  \skill{395a}{Place elements correctly in a two-set Venn diagram.}
  \skill{395b}{Use a two-set Venn to find probabilities.}
  \skill{395c}{Place elements correctly in a three-set Venn diagram.}
  \skill{395d}{Apply inclusion--exclusion to find $|A\cup B \cup C|$.}
\end{skilllist}
\end{topic}

\begin{topic}{Theoretical probability \skillcode{396}}
\begin{skilllist}
  \skill{396a}{Find probabilities from sample spaces and outcome grids.}
  \skill{396b}{Use $P(A') = 1 - P(A)$.}
  \skill{396c}{Apply $P(A\cup B) = P(A) + P(B) - P(A\cap B)$.}
\end{skilllist}
\end{topic}

\begin{topic}{Conditional probability \skillcode{397}}
\begin{skilllist}
  \skill{397a}{Compute $P(A|B) = \dfrac{P(A\cap B)}{P(B)}$ from a Venn or table.}
  \skill{397b}{Use a tree diagram to find compound and conditional probabilities.}
  \skill{397c}{Recognise sampling without replacement and adjust the second-stage probabilities.}
\end{skilllist}
\end{topic}

\begin{topic}{Independence \& mutual exclusivity \skillcode{398}}
\begin{skilllist}
  \skill{398a}{Test whether $A$ and $B$ are independent using $P(A\cap B) = P(A)\,P(B)$.}
  \skill{398b}{Test whether $A$ and $B$ are mutually exclusive using $P(A\cap B) = 0$.}
  \skill{398c}{Solve for an unknown using a probability equation (e.g.\ find $n$ given $P$).}
\end{skilllist}
\end{topic}

% =============================================================
% PACK 2 — FUNCTIONS
% =============================================================
\section{Pack 2 --- Functions}

\noindent\textbf{Haese chapter references:} \haese{10E:15A--E,G} (Composite, Inverse), \haese{10E:20} (Functions Review --- relations, domain, range), \haese{10E:9} \& \haese{10E:21} (Quadratics, vertex form, factoring), \haese{10E:6} (Lines \& gradients --- Y10 carryover).

\medskip

\begin{topic}{Definition, domain \& range \skillcode{225}}
\begin{skilllist}
  \skill{225a}{Determine whether a relation defines $y$ as a function of $x$ (vertical line test).}
  \skill{225b}{State the natural domain of a function (e.g.\ excluding $\sqrt{\text{neg}}$ or $\div 0$).}
  \skill{225c}{State the range from a graph or vertex form.}
  \skill{225d}{Evaluate $f(a)$ and solve $f(x) = k$.}
\end{skilllist}
\end{topic}

\begin{topic}{Composite functions \skillcode{227}}
\begin{skilllist}
  \skill{227a}{Compute $f(g(a))$ for a numeric input.}
  \skill{227b}{Find an algebraic expression for $(f\circ g)(x)$ and simplify.}
  \skill{227c}{State the domain of a composite function.}
\end{skilllist}
\end{topic}

\begin{topic}{Inverse functions \skillcode{228}}
\begin{skilllist}
  \skill{228a}{Find $f^{-1}(x)$ algebraically (swap and solve).}
  \skill{228b}{State the domain of $f^{-1}$ as the range of $f$.}
  \skill{228c}{Verify $f(f^{-1}(x)) = x$ algebraically.}
  \skill{228d}{Recognise that the graph of $f^{-1}$ is the reflection of $f$ in $y = x$.}
\end{skilllist}
\end{topic}

\begin{topic}{Quadratic functions \skillcode{279, 281}}
\begin{skilllist}
  \skill{279a}{Complete the square to convert to vertex form.}
  \skill{279b}{Identify vertex, axis of symmetry, and minimum/maximum value.}
  \skill{281a}{Solve a quadratic equation by factorising.}
  \skill{281b}{Solve a quadratic by the quadratic formula (give exact answers in surd form).}
  \skill{281c}{Use the discriminant to determine the number of real roots.}
\end{skilllist}
\end{topic}

\begin{topic}{Cross-skill: lines \& quadratics (Y10 carryover) \skillcode{198, 256}}
\begin{skilllist}
  \skill{198a}{Find the equation of a line through two points.}
  \skill{198b}{Find the perpendicular bisector of a line segment.}
  \skill{198c}{Find the midpoint and length of a segment.}
  \skill{256a}{Find the intersection of a line and a quadratic algebraically (using surds when needed).}
\end{skilllist}
\end{topic}

% =============================================================
% PACK 3 — EXPONENTIALS & LOGS
% =============================================================
\section{Pack 3 --- Exponentials \& Logarithms}

\noindent\textbf{Haese chapter references:} \haese{10E:15A--C} (Index laws --- Y10 carryover prerequisite), \haese{10E:18} (Exponential and logarithmic functions, including all of: graphs, log definitions, equations, growth and decay).

\medskip

\begin{topic}{Index laws (Y10 carryover) \skillcode{120}}
\begin{skilllist}
  \skill{120a}{Apply $a^m \cdot a^n = a^{m+n}$, $a^m / a^n = a^{m-n}$, $(a^m)^n = a^{mn}$.}
  \skill{120b}{Use $a^{-n} = 1/a^n$ and $a^{1/n} = \sqrt[n]{a}$.}
  \skill{120c}{Simplify expressions involving fractional and negative indices.}
\end{skilllist}
\end{topic}

\begin{topic}{Exponential graphs \skillcode{305}}
\begin{skilllist}
  \skill{305a}{Sketch $y = b^x$ and $y = a\cdot b^x$, including the $y$-intercept and asymptote $y=0$.}
  \skill{305b}{Solve $a\cdot b^x = k$ when the answer is a clean integer (no logs needed).}
\end{skilllist}
\end{topic}

\begin{topic}{Logarithm definitions \skillcode{310}}
\begin{skilllist}
  \skill{310a}{Convert between $\log_b a = c$ and $b^c = a$.}
  \skill{310b}{Evaluate logarithms with integer arguments and bases.}
  \skill{310c}{Use $\log_b 1 = 0$, $\log_b b = 1$, and $\log_b b^x = x$.}
\end{skilllist}
\end{topic}

\begin{topic}{Log laws \skillcode{311}}
\begin{skilllist}
  \skill{311a}{Apply $\log(xy) = \log x + \log y$.}
  \skill{311b}{Apply $\log(x/y) = \log x - \log y$.}
  \skill{311c}{Apply $\log(x^n) = n\log x$.}
  \skill{311d}{Combine multiple log expressions into a single log.}
\end{skilllist}
\end{topic}

\begin{topic}{Exponential \& log equations \skillcode{312, 313}}
\begin{skilllist}
  \skill{312a}{Solve $a^x = k$ by taking logs of both sides.}
  \skill{312b}{Solve equations using a common base (e.g.\ $4^{2x+1} = 8^{x-2}$).}
  \skill{313a}{Solve a log equation by combining logs and exponentiating.}
  \skill{313b}{Check solutions for validity (argument of log must be $> 0$).}
\end{skilllist}
\end{topic}

\begin{topic}{Growth \& decay applications \skillcode{306}}
\begin{skilllist}
  \skill{306a}{Set up a model $A = A_0\,b^{\,t}$ from a percentage rate.}
  \skill{306b}{Solve for time using logs.}
  \skill{306c}{Find the smallest integer $t$ for an inequality.}
\end{skilllist}
\end{topic}

\begin{topic}{Cross-skill: substitution \& surds (Y10 carryover)}
\begin{skilllist}
  \skillnocode{Use a substitution $u = a^x$ to convert an exponential equation into a quadratic.}
  \skillnocode{Simplify a logarithm of a surd using $\log(a^{p/q}) = (p/q)\log a$.}
  \skillnocode{Solve $\log_x k = c$ by writing $x^c = k$.}
\end{skilllist}
\end{topic}

% =============================================================
% PACK 4 — TRIGONOMETRY
% =============================================================
\section{Pack 4 --- Trigonometry (Cumulative Essentials)}

\noindent\textbf{Haese chapter references:} \haese{10E:12A--D} (Right-angle trig and bearings, Y10 carryover), \haese{10E:12E--I} (Sine rule, cosine rule, area), \haese{10E:21A--D,H} (Unit circle, exact values, equations), \haese{DP Core 6A} (Radians, arcs, sectors --- introduced in Y11).

\medskip

\begin{topic}{Right-angle trig \& bearings (Y10 carryover) \skillcode{327}}
\begin{skilllist}
  \skill{327a}{Use SOHCAHTOA to find a side or angle in a right-angled triangle.}
  \skill{327b}{Solve angle-of-elevation/depression problems.}
  \skill{327c}{Use three-figure bearings; compute back-bearings.}
\end{skilllist}
\end{topic}

\begin{topic}{Sine \& cosine rule \skillcode{465, 466}}
\begin{skilllist}
  \skill{465a}{Use the sine rule to find an unknown side (ASA).}
  \skill{465b}{Use the sine rule to find an unknown angle.}
  \skill{466a}{Use the cosine rule to find an unknown side (SAS).}
  \skill{466c}{Use the cosine rule to find an unknown angle (SSS).}
  \skill{466e}{Combine sine and cosine rules across linked triangles.}
\end{skilllist}
\end{topic}

\begin{topic}{Triangle area \skillcode{467}}
\begin{skilllist}
  \skill{467a}{Use Area $= \tfrac{1}{2}ab\sin C$.}
  \skill{467f}{Find a length given the area and an included angle.}
  \skill{467o}{Find the area of a quadrilateral by splitting into triangles.}
\end{skilllist}
\end{topic}

\begin{topic}{Radians, arcs \& sectors \skillcode{584, 318, 319}}
\begin{skilllist}
  \skill{584a}{Convert between degrees and radians.}
  \skill{318a}{Calculate arc length $s = r\theta$.}
  \skill{318b}{Find the perimeter of a sector.}
  \skill{319a}{Calculate sector area $A = \tfrac{1}{2}r^2\theta$.}
  \skill{467i}{Find the area of a segment.}
\end{skilllist}
\end{topic}

\begin{topic}{Unit circle, exact values \& equations \skillcode{412, 430, 503}}
\begin{skilllist}
  \skill{412a}{Recall exact values at $0\degree, 30\degree, 45\degree, 60\degree, 90\degree$.}
  \skill{430a}{Use the unit circle to find $\sin/\cos$ at multiples of $90\degree$.}
  \skill{430c}{Find $\sin$ or $\cos$ of an angle in any quadrant using symmetry.}
  \skill{503a}{Solve $\sin x = k$, $\cos x = k$, or $\tan x = k$ in a given range.}
\end{skilllist}
\end{topic}

\begin{topic}{Cross-skill: 3D \& exact-value triangles (Y10 carryover)}
\begin{skilllist}
  \skillnocode{Identify the right ground triangle in a 3D bearings/elevation problem.}
  \skillnocode{Use sine/cosine rule on a ground triangle, then RA trig for vertical heights.}
  \skillnocode{Combine exact ratios with cosine rule to give surd answers (e.g.\ $AC = 2\sqrt{7}$).}
\end{skilllist}
\end{topic}

% =============================================================
% PROGRESS SUMMARY
% =============================================================
\section{Self-Assessment Summary}
\textit{When you've worked through a pack, rate your confidence and decide what to revisit.}

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\begin{tabular}{|p{0.31\linewidth}|c|c|c|p{0.32\linewidth}|}
\hline
\textbf{Pack} &
\textbf{\,\large\color{teallight}$\square$\,} &
\textbf{\,\large\color{teallight}$\square$\,} &
\textbf{\,\large\color{teallight}$\square$\,} &
\textbf{Topics to revisit} \\
& {\footnotesize shaky} & {\footnotesize ok} & {\footnotesize confident} & \\\hline
P1: Probability & & & & \\\hline
P2: Functions & & & & \\\hline
P3: Exp \& Logs & & & & \\\hline
P4: Trigonometry & & & & \\\hline
\end{tabular}

% =============================================================
% TIPS
% =============================================================
\section{Working Strategy}
\begin{enumerate}[leftmargin=1.4em, itemsep=2pt, topsep=2pt]
  \item Work through the question booklet pack by pack, in order. Each pack starts gentle and builds.
  \item For each skill code you found tricky, log into Dr Frost and practise that exact code.
  \item Use the Summary Sheet for formulas, but try to recall them from memory first.
  \item Re-attempt any question you got wrong from scratch a few days later --- not just by reading the solution.
  \item For trigonometry: always check the angle units on your calculator (DEG vs RAD).
  \item Time yourself on Pack 4 questions in particular --- the EOY paper is time-pressured.
\end{enumerate}

\smallskip
\textit{DFM course: \href{https://drfrost.org/explorer.php?coid=13372}{drfrost.org/explorer.php?coid=13372} (11 NAT Course).}

\end{document}