IB Math AA SL Paper 1 practice questions (non-calculator)

What Paper 1 actually tests — and how to improve fast

Paper 1 (non-calculator) at SL AA is deliberately narrow. Under exam pressure and no calculator, the mistakes that cost marks are almost always mechanical: bad algebra, wrong sign, or reaching for a shortcut that isn't in your toolkit.

The five skills you must have automatic

• Exact-value trigonometry. $\sin ,\cos ,\tan$ of $0,\frac{\pi }{6},\frac{\pi }{4},\frac{\pi }{3},\frac{\pi }{2}$ (and their multiples across all four quadrants) should come out of your fingers in under 3 seconds. The identity ${\sin }^2\theta +{\cos }^2\theta =1$ must be used both forwards and backwards.
• Log rules under pressure. ${\log }_a(xy)={\log }_{a}x+{\log }_{a}y$, ${\log }_a{x}^n=n{\log }_{a}x$, change of base. Practise combining and expanding in both directions. Never leave ${\log }_{2}8$ as anything but $3$.
• Quadratics without formula-panic. Completing the square, discriminant $b^2-4ac$, sum and product of roots ($-b/a$ and $c/a$), and knowing when a substitution turns a quartic into a quadratic.
• Derivative fluency. Chain, product, quotient rules and ${\displaystyle \frac{d}{dx}}[\sin ,\cos ,e^x,\ln x]$. Reasonably clean simplification is expected — leaving unsimplified ${\displaystyle \frac{f^{\prime }(x)g(x)-f(x)g^{\prime }(x)}{[g(x){]}^2}}$ often loses A marks.
• Integration by inspection. Reversing the chain rule on $\int \sin (ax+b)dx$, $\int (2x+3{)}^{5}dx$, $\int \frac{1}{x-2}dx$. Substitution appears in Paper 1 but expect the substitution to be either obvious or hinted.

How to actually improve

1. Twenty-minute mechanical fluency reps. Every day, 20 minutes of pure calculation — no notes, no calculator. Not full past papers; just the five mechanical skills above rotated across the week.
2. Redo your worst mistake three times. Whenever you drop a mark on Paper 1, write the error, then redo the exact question a day later, a week later, and a month later. Never let the same mistake happen twice.
3. Show every method line. M marks are the biggest hidden points reservoir. Write the substitution, the rule name, the identity used — even one word ("chain") next to a derivative earns method credit.
4. Time yourself on part (a). Paper 1 has short parts (2-4 marks) that must be done at ~1 min per mark. If part (a) drags past 4 minutes, move on. This is a Paper 1-specific pacing skill.
5. Practise "reverse engineering" answers. Given an integral, differentiate it back. Given a quadratic's roots, verify by expansion. Fast self-checking on Paper 1 is where the top grades win.