SAT Math for IB Students — the gaps your syllabus doesn't cover

1. IB vs SAT — the philosophy gap

Why the SAT feels weirdly easy in places and awkwardly hard in others.

The SAT Math section assumes students have already mastered middle-school arithmetic — ratios, rates, percentages, unit conversions. The IB syllabus assumes the same, but treats it as Prior Learning and never actively teaches it again. The result: IB students lose easy marks on SAT questions that a well-prepared GCSE student would get in seconds.

Conversely, the SAT rewards structural algebra fluency: recognising that $y = a(x-h)^2 + k$ has vertex $(h, k)$, or that if $p(x)$ has factor $(x - r)$ then $p(r) = 0$. IB AA students eat this for breakfast. IB AI students — who lean heavily on their GDC — sometimes forget how to do this manually.

2. Content gaps by IB course

The table below is the entire analysis in one view. Bookmark it.

3. SL AA students — what to focus on

You're the best-placed of the four courses. Focus on the small stuff.

Algebra & Advanced Math (70% of SAT)

You're solid here. Skim these to make sure you're fluent in SAT phrasing:

Problem-solving & Data Analysis (your weak spot)

Get fluent with these — they're not in AA active syllabus:

• Ratios, rates, unit conversions. "A car travels $60$ km in $45$ minutes. What's its speed in m/s?"
• Percentages & proportions. "A price rose $20\%$ then fell $20\%$. Net change?" (Answer: $-4\%$.)
• One-variable statistics. Reading medians, quartiles and box plots quickly.
• Two-variable data & evaluating claims. Scatterplots and whether a claim is supported by the data.

Geometry & Trigonometry

• Lines, angles, triangles — SOHCAHTOA, similar triangles, angle-sum properties
• Right-triangle trig, circles (area, circumference, arcs, sectors)
• Area, surface area, volume — cones, spheres, cylinders (formulas given on SAT)

4. SL AI students — what to focus on

You need manual algebra practice more than the others. That's the honest truth.

Priority #1 — Manual algebra fluency

The Digital SAT gives you Desmos, but structural questions still need you to see patterns:

• Given $f(x) = x^2 + 6x + 9$, express as $(x + a)^2$. (Answer: $(x + 3)^2$.)
• If $\dfrac{x^2 - 4}{x - 2} = ?$, simplify. (Answer: $x + 2$, for $x \ne 2$.)
• For what value of $c$ does $x^2 - 8x + c$ have a double root? (Answer: $c = 16$.)

Priority #2 — Middle-school arithmetic

Same as SL AA — see section 3 above.

What you're strong at (relative to SL AA)

• Two-variable data & scatterplot modelling — this is your bread and butter
• Exponential growth/decay word problems — you've done these in units 4-5
• Real-world statistical reasoning — reading tables, understanding sampling bias

5. HL AA students — what to focus on

You are mathematically over-prepared. Don't let that make you complacent.

Every SAT algebra/advanced math topic is well within your comfort zone. Your risk is silly errors on easy questions:

• Rushed percentage calculations ("$15\%$ of $80$" without a calculator, in 15 seconds)
• Unit conversion mistakes ($1$ km = $1000$ m; $1$ hour = $60$ min = $3600$ s)
• Reading scatterplot axes correctly under time pressure

Do the SL AA focus list above, but focus your time on timed sets of 20 middle-school arithmetic questions — you should aim for 30 seconds each.

6. HL AI students — what to focus on

Best-prepared for stats. Weakest for polynomial manipulation.

Where HL AI shines

• Statistics & probability — you've done confidence intervals, chi-squared, correlation and regression. The SAT stats questions will feel easy.
• Modelling — exponentials, logistic, piecewise. The SAT variants are simpler than what you're used to.
• Matrices — not on the SAT, but the algebraic thinking transfers.

Priority — manual polynomial algebra

Same as SL AI, but the SAT will push you slightly further with rational expressions:

• Simplify $\dfrac{x^2 - 5x + 6}{x - 2}$. (Factor numerator: $(x-2)(x-3) \to$ answer $x - 3$.)
• Combine: $\dfrac{2}{x} + \dfrac{3}{x + 1}$. (Common denominator $x(x+1)$ $\to$ $\dfrac{5x + 2}{x(x+1)}$.)
• Solve: $\dfrac{x + 1}{x - 2} = 3 \Rightarrow x + 1 = 3(x - 2) \Rightarrow x = \tfrac{7}{2}$.

7. Use the built-in Desmos calculator

The Digital SAT includes a full graphing Desmos calculator throughout the entire 44-question section.

This is transformational for IB AI students (who are already GDC-fluent) and undersold for IB AA students (who don't practise graphing calculators as heavily). What Desmos does for you on the SAT:

• Systems of equations — type both equations, read intersection off the graph in 5 seconds.
• Quadratic vertex & roots — graph the parabola, click the vertex/roots for exact coordinates.
• Function evaluation — type $f(x) = 2x^2 - 3x + 1$, then evaluate $f(5)$ by typing $f(5)$ directly.
• Solving equations — graph both sides as separate functions and read the intersection.

The site student.desmos.com or the Bluebook practice app both give you access to the exact SAT-issue version.

8. A 3-week SAT plan for IB students

Assumes ~5 hours per week alongside your IB studies.

Week 1 — Diagnostic + gap identification

• Take one full official Bluebook practice test (2h 14min for Math + Reading)
• Score it and identify your two weakest sub-domains
• Read the two relevant sub-topic notes above in detail

Week 2 — Targeted fluency practice

• 4 × 30-minute focused fluency sets on your weakest sub-domain (10-15 questions each)
• 2 × 30-minute focused fluency sets on your second-weakest sub-domain
• 1 × 45-minute Desmos speed session (mixed topics, aim for < 60s per question)

Week 3 — Full-length simulation + review

• Take another full Bluebook practice test under real timing
• Score it; compare to Week 1 diagnostic
• Spend the remaining time reviewing your mistakes: annotate why each mistake happened (setup error, arithmetic slip, misread, ran out of time)