Prior Learning Formulae for IB Math AA SL & HL
This complete RevisionTown page gives IB Mathematics: Analysis and Approaches students a clean, searchable, calculator-supported guide to the prior learning formulae used by both AA SL and AA HL learners. Every key formula is rendered with MathJax, explained with examples, supported by a visual SVG diagram, and connected to exam strategy.
The prior learning section is small compared with the full AA syllabus, but it is not optional. These formulae support coordinate geometry, trigonometry, calculus, modelling, statistics, vectors, optimization, and exam-style problem solving. A student who cannot quickly identify \(A=\pi r^2\), \(V=\pi r^2h\), \(d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\), or the midpoint formula will lose time on questions where the actual challenge is meant to be deeper reasoning.
Core prior formulae
Area, circumference, volume, curved surface area, distance, and midpoint formulae collected in one revision-friendly page.
Same foundation
These formulae belong to the prior learning foundation for both Standard Level and Higher Level AA students.
Clean mathematics
All formulae are written in proper mathematical display form, including fractions, square roots, powers, and coordinate notation.
Interactive calculator
Select a formula, enter values, choose a unit, and see the result with substitution steps.
Prior Learning Formula Calculator
Use this tool to calculate the most common prior learning formulae. It is designed for revision, checking homework, and building speed with substitution. Choose the formula, enter the values, and the result will show the mathematical substitution in MathJax.
Result & Working
What Are Prior Learning Formulae in IB Math AA?
Prior learning formulae are the mathematical facts that IB Mathematics: Analysis and Approaches expects students to bring into the course from earlier mathematics. They are not advanced by themselves, but they are used constantly as building blocks. In an AA SL or AA HL exam, a question might appear to be about calculus, trigonometric modelling, vectors, functions, or probability, yet the first step may still require the area of a triangle, the volume of a cylinder, the distance between two coordinate points, or the midpoint of a segment.
This is why these formulae deserve a separate page. Many students revise the large topics first: differentiation, integration, functions, sequences, binomial theorem, complex numbers, vectors, probability distributions, and proof. That is logical, especially for HL students. However, marks are often lost through small errors in foundational formulae. A wrong radius, a missing square, a confused diameter, or a forgotten factor of \(\frac12\) can damage an otherwise correct solution.
The goal of this guide is not only to list formulae. It is to help you understand what each formula measures, when it applies, what every variable means, what units should be used, and how it connects to IB-style reasoning. In the IB Mathematics AA course, communication matters. A correct final answer is stronger when it is supported by correct notation, clear substitution, appropriate units, and a short explanation of why the formula applies.
Complete Prior Learning Formulae Table for AA SL & AA HL
| Formula | Mathematical form | Variables | Common use in AA |
|---|---|---|---|
| Area of a parallelogram | \(A=bh\) | \(b\) is base, \(h\) is height | Area modelling, vectors, geometry, integration context questions |
| Area of a triangle | \(A=\frac12 bh\) | \(b\) is base, \(h\) is perpendicular height | Coordinate geometry, trigonometry, optimization, vector geometry |
| Area of a trapezium | \(A=\frac12(a+b)h\) | \(a\) and \(b\) are parallel sides, \(h\) is height | Approximation, area under curves, modelling composite shapes |
| Area of a circle | \(A=\pi r^2\) | \(r\) is radius | Radians, sectors, rates of change, optimization |
| Circumference of a circle | \(C=2\pi r\) | \(r\) is radius | Arc length, circular motion, trigonometry, modelling |
| Volume of a cuboid | \(V=lwh\) | \(l\) is length, \(w\) is width, \(h\) is height | 3D geometry, optimization, practical modelling |
| Volume of a cylinder | \(V=\pi r^2h\) | \(r\) is radius, \(h\) is height | Optimization, related rates, modelling containers |
| Volume of a prism | \(V=Ah\) | \(A\) is cross-sectional area, \(h\) is length or height of prism | Composite solids, modelling, integration-based volume ideas |
| Curved surface area of a cylinder | \(A=2\pi rh\) | \(r\) is radius, \(h\) is height | Surface area optimization, packaging, rates of change |
| Distance between two points | \(d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\) | \((x_1,y_1)\) and \((x_2,y_2)\) are endpoints | Coordinate geometry, functions, circles, vectors |
| Midpoint of a line segment | \(\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\) | \((x_1,y_1)\) and \((x_2,y_2)\) are endpoints | Coordinate geometry, transformations, circles, proof |
Visual Map of Prior Learning Formulae
The diagram below groups the prior learning formulae into three families: two-dimensional measurement, three-dimensional measurement, and coordinate geometry. In revision, this grouping is useful because it helps you choose the correct formula faster. If a question asks for a flat region, think area. If it asks for a solid or container, think volume or surface area. If it gives coordinates, think distance, midpoint, gradient, circle equation, or vectors depending on the question.
Formula Search Library
Search the library below by typing words such as circle, volume, coordinate, radius, area, midpoint, cylinder, triangle, or prism. Each card includes the formula, a short interpretation, and a button to load it into the calculator.
Area of a Parallelogram
\[A=bh\]
The area of a parallelogram is base multiplied by perpendicular height. The height is not usually the slanted side unless the slanted side is perpendicular to the base.
Area of a Triangle
\[A=\frac12 bh\]
The area of a triangle is half the area of a parallelogram with the same base and perpendicular height. The word perpendicular is important.
Area of a Trapezium
\[A=\frac12(a+b)h\]
Add the two parallel sides, multiply by the perpendicular height, then halve the result. This formula often appears in composite-area and approximation contexts.
Area of a Circle
\[A=\pi r^2\]
Use the radius, not the diameter. If a question gives diameter \(d\), first use \(r=\frac d2\), then substitute into \(A=\pi r^2\).
Circumference of a Circle
\[C=2\pi r\]
Circumference is the perimeter around a circle. It connects directly to arc length and radians later in the AA course.
Volume of a Cuboid
\[V=lwh\]
Multiply length, width, and height. A cuboid is a rectangular prism, so all three dimensions must be measured in the same unit before substitution.
Volume of a Cylinder
\[V=\pi r^2h\]
The base is a circle with area \(\pi r^2\). Multiplying by height gives the cylinder volume. This is common in optimization questions.
Volume of a Prism
\[V=Ah\]
A prism keeps the same cross-section along its length. Find the cross-sectional area first, then multiply by the prism length or height.
Curved Surface Area of a Cylinder
\[A=2\pi rh\]
The curved surface opens into a rectangle. Its width is the circumference \(2\pi r\), and its height is \(h\).
Distance Between Two Points
\[d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\]
This is Pythagoras applied to coordinate differences. It is essential for circles, vectors, gradients, and proof.
Midpoint of a Line Segment
\[\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\]
The midpoint is found by averaging the \(x\)-coordinates and averaging the \(y\)-coordinates separately.
How to Use These Formulae Correctly
The strongest way to revise formulae is not passive reading. You should practise four stages: identify, substitute, calculate, and interpret. First, identify what the question is asking for. Area, length, volume, surface area, distance, and midpoint are different outputs. Second, substitute the values clearly into the correct formula. Third, calculate using exact values when possible and round only when the question or context requires it. Fourth, interpret the answer with units and meaning.
For example, suppose a cylinder has radius \(4\text{ cm}\) and height \(9\text{ cm}\). The volume is not \(2\pi rh\), because that is curved surface area. The volume uses the area of the circular base:
\[V=\pi r^2h\]
\[V=\pi(4)^2(9)=144\pi\text{ cm}^3\]
The exact answer is \(144\pi\text{ cm}^3\). A decimal approximation is about \(452.39\text{ cm}^3\). In IB-style communication, leaving the answer exact may be preferred unless a decimal is requested or the context requires rounding.
A second example: suppose a question asks for the midpoint of \(A(-3,8)\) and \(B(7,-2)\). The midpoint is:
\[\left(\frac{-3+7}{2},\frac{8+(-2)}{2}\right)=\left(2,3\right)\]
Notice that the midpoint formula is not a distance formula. It does not square anything and it does not use a square root. It simply averages corresponding coordinates.
Detailed Formula Explanations and Examples
1. Area of a Parallelogram
The area of a parallelogram is:
\[A=bh\]
The base \(b\) can be any side chosen as the base, but the height \(h\) must be measured perpendicular to that base. Many students mistakenly multiply the base by a slanted side. That is only correct if the slanted side is perpendicular to the base, which is generally not true for a parallelogram. A useful way to remember this formula is to imagine cutting a triangular part from one side of the parallelogram and moving it to the other side. The shape becomes a rectangle with the same base and height.
Example: If \(b=12\) and \(h=7\), then:
\[A=12\times7=84\]
If the unit is centimetres, the answer is \(84\text{ cm}^2\). The square unit matters because area measures a two-dimensional region.
2. Area of a Triangle
The area of a triangle is:
\[A=\frac12 bh\]
This formula comes from the fact that a triangle is half of a parallelogram with the same base and height. The height must again be perpendicular to the base. In IB Mathematics AA, triangle area appears in coordinate geometry, vectors, trigonometry, and modelling. Later, students may also use \(A=\frac12 ab\sin C\), but the prior learning version is the base-height formula.
Example: If \(b=10\) and \(h=6\), then:
\[A=\frac12(10)(6)=30\]
If the dimensions are in metres, the area is \(30\text{ m}^2\).
3. Area of a Trapezium
The area of a trapezium is:
\[A=\frac12(a+b)h\]
Here, \(a\) and \(b\) are the two parallel sides, and \(h\) is the perpendicular height between them. The formula works by averaging the two parallel sides and multiplying by height. This is also why it connects well to approximation methods and the trapezoidal idea used when estimating areas under curves.
Example: If \(a=8\), \(b=14\), and \(h=5\), then:
\[A=\frac12(8+14)(5)=55\]
The answer is \(55\) square units.
4. Area of a Circle
The area of a circle is:
\[A=\pi r^2\]
The variable \(r\) is the radius. The radius is the distance from the centre of the circle to the edge. If a question gives the diameter, use \(r=\frac d2\). A common mistake is to substitute the diameter directly into \(A=\pi r^2\), which makes the area four times too large.
Example: If \(r=5\), then:
\[A=\pi(5)^2=25\pi\]
If the radius is in centimetres, the exact area is \(25\pi\text{ cm}^2\), approximately \(78.54\text{ cm}^2\).
5. Circumference of a Circle
The circumference of a circle is:
\[C=2\pi r\]
Circumference means the perimeter around the circle. This formula is directly connected to arc length, radians, and circular modelling. Since \(d=2r\), the formula can also be written as \(C=\pi d\), but the prior learning table usually presents it in radius form.
Example: If \(r=9\), then:
\[C=2\pi(9)=18\pi\]
If the radius is in metres, the circumference is \(18\pi\text{ m}\), approximately \(56.55\text{ m}\).
6. Volume of a Cuboid
The volume of a cuboid is:
\[V=lwh\]
A cuboid is a box-like rectangular solid. The formula multiplies length, width, and height. The dimensions must be measured in the same unit. If one dimension is in centimetres and another is in metres, convert before multiplying. In modelling and optimization, a cuboid might represent packaging, a tank, a room, or a rectangular container.
Example: If \(l=8\), \(w=5\), and \(h=3\), then:
\[V=8\times5\times3=120\]
If the dimensions are in centimetres, the volume is \(120\text{ cm}^3\).
7. Volume of a Cylinder
The volume of a cylinder is:
\[V=\pi r^2h\]
This formula comes from the prism idea \(V=Ah\), where the cross-sectional area \(A\) is the circle area \(\pi r^2\). Therefore:
\[V=(\pi r^2)h=\pi r^2h\]
In IB AA, cylinder volume is useful in optimization questions, where a fixed volume or fixed surface area is used to create an equation. Students may need to differentiate a volume or surface area expression after substituting one variable in terms of another.
Example: If \(r=3\) and \(h=10\), then:
\[V=\pi(3)^2(10)=90\pi\]
The exact volume is \(90\pi\) cubic units.
8. Volume of a Prism
The volume of a prism is:
\[V=Ah\]
A prism has the same cross-section throughout its length. The variable \(A\) means the area of that cross-section, and \(h\) means the length or height through which the cross-section extends. This is a general formula. Cuboids and cylinders are special types of prisms because their cross-sections are rectangles and circles.
Example: If a prism has cross-sectional area \(A=18\text{ cm}^2\) and length \(h=12\text{ cm}\), then:
\[V=18\times12=216\text{ cm}^3\]
9. Curved Surface Area of a Cylinder
The curved surface area of a cylinder is:
\[A=2\pi rh\]
This formula does not include the two circular ends. It only measures the curved side. A helpful visual method is to imagine cutting the cylinder vertically and unrolling it. The curved surface becomes a rectangle. The rectangle has height \(h\), and its width is the circumference of the circular base, \(2\pi r\). Therefore:
\[A=(2\pi r)h=2\pi rh\]
If a question asks for total surface area of a closed cylinder, you must add the two circular ends:
\[\text{Total surface area}=2\pi rh+2\pi r^2\]
However, the prior learning formula listed here is specifically the curved surface area.
10. Distance Between Two Points
The distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is:
\[d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\]
This is the Pythagorean theorem written in coordinate form. The horizontal difference is \(x_1-x_2\), and the vertical difference is \(y_1-y_2\). Squaring removes the sign, so it does not matter whether you use \(x_1-x_2\) or \(x_2-x_1\), as long as the expression is squared. The same applies to the \(y\)-difference.
Example: Find the distance between \(A(2,3)\) and \(B(8,11)\).
\[d=\sqrt{(2-8)^2+(3-11)^2}\]
\[d=\sqrt{(-6)^2+(-8)^2}=\sqrt{36+64}=\sqrt{100}=10\]
11. Midpoint of a Line Segment
The midpoint of the line segment with endpoints \((x_1,y_1)\) and \((x_2,y_2)\) is:
\[\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\]
The midpoint is the average position of the two endpoints. Average the \(x\)-coordinates to find the midpoint’s \(x\)-coordinate, and average the \(y\)-coordinates to find the midpoint’s \(y\)-coordinate. This formula is frequently used with circle questions. For example, if the endpoints of a diameter are known, the centre of the circle is the midpoint of those endpoints.
Example: Find the midpoint of \(A(-4,9)\) and \(B(10,1)\).
\[\left(\frac{-4+10}{2},\frac{9+1}{2}\right)=\left(3,5\right)\]
IB Math AA SL & HL Course Context
Mathematics: Analysis and Approaches is one of the DP mathematics routes. It is designed for students who need strong algebraic, analytical, and mathematical argument skills. It is especially suitable for students considering mathematics-heavy university pathways such as mathematics, engineering, computer science, physics, economics, statistics, data science, and related fields. The course is available at Standard Level and Higher Level. HL includes greater depth and additional content, but the prior learning formulae on this page apply to both levels.
In the current DP mathematics structure, students take one DP mathematics course as part of the diploma. The available mathematics routes are Mathematics: Analysis and Approaches SL, Mathematics: Analysis and Approaches HL, Mathematics: Applications and Interpretation SL, and Mathematics: Applications and Interpretation HL. AA focuses more strongly on algebraic manipulation, proof-like reasoning, functions, calculus, and exact mathematical structure. AI focuses more strongly on applied modelling, statistics, technology, and interpretation. Both courses require mathematical thinking, but the emphasis is different.
For AA students, prior formulae are not isolated early-school facts. They are the language through which many advanced questions begin. A calculus question about maximizing the volume of a cylinder still depends on \(V=\pi r^2h\). A coordinate geometry question about the equation of a circle may begin with distance or midpoint. A modelling question about material cost may use curved surface area. A trigonometry question may use circle circumference or area as a bridge to radians.
Current AA Assessment Overview and Score Weighting
The assessment structure matters because it tells you where formula fluency affects marks. Paper 1 is non-technology, so students must be comfortable with exact values, algebraic manipulation, and hand calculations. Paper 2 allows technology, but students still need to show suitable working and choose correct mathematical methods. HL students also sit Paper 3, which focuses on extended problem solving and often requires connecting different topics.
| Level | Component | Technology | Duration | Weighting | Formula fluency impact |
|---|---|---|---|---|---|
| AA SL | Paper 1 | No technology | 1 hour 30 minutes | 40% | High: exact substitution and clean algebra are essential. |
| AA SL | Paper 2 | Technology allowed | 1 hour 30 minutes | 40% | High: calculator use helps, but formula choice and interpretation still matter. |
| AA SL | Internal assessment exploration | Varies by exploration | Independent coursework | 20% | High: modelling, measurement, and mathematical communication need correct formula use. |
| AA HL | Paper 1 | No technology | 2 hours | 30% | Very high: HL questions often combine basic formulae with advanced methods. |
| AA HL | Paper 2 | Technology allowed | 2 hours | 30% | Very high: students must use technology efficiently and communicate mathematics clearly. |
| AA HL | Paper 3 | Technology allowed | 1 hour | 20% | Very high: extended problem solving rewards strong foundations and flexible thinking. |
| AA HL | Internal assessment exploration | Varies by exploration | Independent coursework | 20% | High: precise formula use supports modelling, analysis, and interpretation. |
Upcoming May 2026 IB Math AA Exam Timetable
For the May 2026 session, Mathematics: Analysis and Approaches papers are scheduled during Week 3 and Week 4 of the IB examination period. Schools must follow their allocated exam zone and local session start times. Students should always confirm the final local timetable with their IB coordinator, because schools manage local logistics, seating, candidate instructions, and any timetable adjustments.
| Date | Session | AA SL | AA HL | Duration |
|---|---|---|---|---|
| Thursday 14 May 2026 | Afternoon session | Analysis and approaches SL Paper 1 | Analysis and approaches HL Paper 1 | SL: 1h 30m; HL: 2h |
| Friday 15 May 2026 | Morning session | Analysis and approaches SL Paper 2 | Analysis and approaches HL Paper 2 | SL: 1h 30m; HL: 2h |
| Wednesday 20 May 2026 | Afternoon session | Not applicable | Analysis and approaches HL Paper 3 | HL: 1h 15m in the May 2026 schedule |
Future Curriculum Update Note for First Assessment 2029
IB has announced an updated Mathematics: Analysis and Approaches course launching for first teaching in August 2027, with first assessment in May 2029. The update is described as refinement rather than a complete reinvention. The announced changes include reduced content in selected areas and reduced mark totals for future assessment papers. For students sitting the current course before the updated first assessment, the current subject guide and school instructions remain the immediate reference.
For future AA cohorts, the announced assessment changes include Paper 1 and Paper 2 at SL moving to 75 marks each, Paper 1 and Paper 2 at HL moving to 100 marks each, and Paper 3 at HL moving to 50 marks with a one-hour duration. This matters for page freshness because students and parents may see both current and future course information online. Always check which assessment year applies to your cohort.
IB Math AA Score Guidelines: What Grades Mean
IB subject grades use the 1–7 scale. A grade is not produced by a permanently fixed percentage table that applies every year. Grade boundaries can change by session because exam papers differ in difficulty and candidate performance changes. The safest revision approach is therefore not to chase one fixed percentage, but to develop the qualities that match the higher grade descriptors: strong syllabus knowledge, accurate mathematical processes, clear communication, efficient technology use where allowed, and the ability to solve unfamiliar problems.
| IB Grade | Practical AA meaning | Formula fluency target |
|---|---|---|
| 7 | Excellent command of concepts, sophisticated mathematical arguments, strong problem-solving in challenging and unfamiliar contexts. | Formulae are automatic; student uses them accurately inside multi-step reasoning. |
| 6 | Very strong understanding, good communication, and reliable problem-solving across a wide variety of questions. | Formula use is mostly automatic with minor slips only under pressure. |
| 5 | Good knowledge and understanding, successful routine problem-solving, and generally effective communication. | Formulae are known, but complex contexts may still cause hesitation. |
| 4 | Satisfactory knowledge and performance in straightforward contexts, with some gaps in unfamiliar questions. | Basic formula substitution works, but errors appear when wording changes. |
| 3 | Partial knowledge and limited understanding, with some success on routine tasks. | Student recognizes some formulae but may confuse area, volume, surface area, distance, and midpoint. |
| 2 | Limited knowledge and basic mathematical processes, often with weak notation or method choice. | Formula recall is inconsistent and substitution errors are common. |
| 1 | Minimal mathematical knowledge and very limited use of correct processes or notation. | Formulae are not yet secure enough for exam conditions. |
How Prior Learning Formulae Connect to the Five AA Topics
IB Mathematics AA is organized around five broad mathematical areas: number and algebra, functions, geometry and trigonometry, statistics and probability, and calculus. Prior learning formulae connect most directly to geometry and trigonometry, but they also appear across the other topics.
In number and algebra, formulae train students to rearrange, substitute, simplify, and maintain unit consistency. For example, using \(V=\pi r^2h\) in an optimization problem often requires rearranging to express \(h\) in terms of \(r\). This is algebraic fluency, not just measurement.
In functions, formulae can define models. A circle’s area as a function of radius is \(A(r)=\pi r^2\). A cylinder’s volume with fixed height can be written as \(V(r)=\pi r^2h\). A cuboid’s volume can become a multivariable function \(V(l,w,h)=lwh\). These connections help students understand domains, variables, and rates of change.
In geometry and trigonometry, prior formulae are direct tools. The circle formulae connect to radians, sectors, arcs, and trigonometric modelling. Distance and midpoint are central to coordinate geometry. Areas of triangles, trapezia, and parallelograms support proof, construction, and problem solving.
In statistics and probability, geometry formulae appear less often, but the same habits matter: identify variables, substitute accurately, and interpret units. Coordinate geometry can also appear in data visualization, regression context, and modelling discussions.
In calculus, prior formulae become functions to differentiate or integrate. A container optimization question may combine surface area and volume. A related rates question may involve \(A=\pi r^2\), \(C=2\pi r\), or \(V=\pi r^2h\). Students who know these formulae instantly can focus on the calculus rather than wasting time reconstructing geometry.
Revision Strategy for AA SL and AA HL Students
A strong revision plan should separate formula memorization from formula application. Memorization means you can write the formula correctly. Application means you can choose it in a new context, substitute values accurately, handle units, and explain the result. IB questions tend to reward application more than memorization alone.
Formula Fluency Checklist
- Can you write each formula from memory without looking?
- Can you explain what every variable means?
- Can you identify whether the answer should be in units, square units, or cubic units?
- Can you avoid confusing radius and diameter?
- Can you distinguish curved surface area from total surface area?
- Can you use distance and midpoint formulae with negative coordinates?
- Can you use exact answers such as \(25\pi\) before rounding?
- Can you connect a formula to an AA topic such as calculus, functions, or trigonometry?
For SL students, these formulae support the speed needed in Paper 1 and Paper 2. For HL students, they also reduce cognitive load in longer questions where the challenge is not the formula itself but the surrounding reasoning. In both cases, the best method is short, repeated practice. Spend ten minutes daily on five formula substitutions, then spend another ten minutes on one exam-style problem that uses a prior formula in context.
Common Mistakes Students Make
| Mistake | Why it happens | Correct method |
|---|---|---|
| Using diameter instead of radius in circle formulae | The question gives diameter and the student substitutes too quickly. | Use \(r=\frac d2\), then apply \(A=\pi r^2\) or \(C=2\pi r\). |
| Forgetting the \(\frac12\) in triangle or trapezium area | The student remembers base times height but not the geometric relationship. | Triangle: \(A=\frac12 bh\). Trapezium: \(A=\frac12(a+b)h\). |
| Using slanted side as height | The student does not check perpendicular height. | Height must be perpendicular to the base or parallel sides. |
| Confusing volume and surface area of a cylinder | Both formulae contain \(\pi\), \(r\), and \(h\). | Volume: \(V=\pi r^2h\). Curved surface area: \(A=2\pi rh\). |
| Dropping negative signs in coordinate geometry | Coordinates such as \((-4,7)\) are substituted without brackets. | Use brackets: \((x_1-x_2)^2\) and \((y_1-y_2)^2\). |
| Writing area units for volume | The student calculates correctly but labels incorrectly. | Length uses units, area uses square units, volume uses cubic units. |
Practice Drill Generator
Click the button below to generate a quick set of practice questions. Try them first without opening the answers. Then check your work and repeat until the formula choice becomes automatic.
Practice Questions with Answers
- Find the area of a parallelogram with base \(14\text{ cm}\) and height \(9\text{ cm}\).
- Find the area of a triangle with base \(18\text{ m}\) and height \(7\text{ m}\).
- Find the area of a trapezium with parallel sides \(6\text{ cm}\) and \(16\text{ cm}\), and height \(5\text{ cm}\).
- Find the area and circumference of a circle with radius \(8\text{ cm}\).
- Find the volume of a cuboid with dimensions \(7\text{ cm}\), \(4\text{ cm}\), and \(12\text{ cm}\).
- Find the volume of a cylinder with radius \(5\text{ m}\) and height \(11\text{ m}\).
- Find the curved surface area of a cylinder with radius \(3\text{ cm}\) and height \(20\text{ cm}\).
- Find the distance between \(A(-2,5)\) and \(B(10,-4)\).
- Find the midpoint of \(A(6,-8)\) and \(B(-2,12)\).
- A cylinder has volume \(200\pi\text{ cm}^3\) and radius \(5\text{ cm}\). Find its height.
Answers
- \(A=14\times9=126\text{ cm}^2\)
- \(A=\frac12(18)(7)=63\text{ m}^2\)
- \(A=\frac12(6+16)(5)=55\text{ cm}^2\)
- \(A=64\pi\text{ cm}^2\), \(C=16\pi\text{ cm}\)
- \(V=7\times4\times12=336\text{ cm}^3\)
- \(V=\pi(5)^2(11)=275\pi\text{ m}^3\)
- \(A=2\pi(3)(20)=120\pi\text{ cm}^2\)
- \(d=\sqrt{(-2-10)^2+(5-(-4))^2}=\sqrt{225}=15\)
- \(\left(\frac{6+(-2)}2,\frac{-8+12}2\right)=(2,2)\)
- \(200\pi=\pi(5)^2h\Rightarrow 200=25h\Rightarrow h=8\text{ cm}\)
Study Plan: 7-Day Formula Mastery Routine
A short, focused study plan is more effective than trying to memorize everything in one sitting. Use this seven-day routine before mocks, unit tests, or final exam revision.
| Day | Focus | Task |
|---|---|---|
| Day 1 | 2D area formulae | Write and use \(A=bh\), \(A=\frac12 bh\), and \(A=\frac12(a+b)h\). |
| Day 2 | Circle formulae | Practise \(A=\pi r^2\), \(C=2\pi r\), radius-diameter conversion, exact answers. |
| Day 3 | 3D volume formulae | Practise \(V=lwh\), \(V=\pi r^2h\), and \(V=Ah\). |
| Day 4 | Cylinder surface area | Compare \(A=2\pi rh\), \(V=\pi r^2h\), and total surface area \(2\pi rh+2\pi r^2\). |
| Day 5 | Coordinate geometry | Practise distance and midpoint with negative coordinates. |
| Day 6 | Mixed word problems | Do ten mixed questions where you must choose the formula yourself. |
| Day 7 | Exam simulation | Complete a timed 20-minute formula drill and review every error. |
Frequently Asked Questions
What are prior learning formulae in IB Math AA?
They are foundational formulae that students are expected to know before and during the Mathematics: Analysis and Approaches course. They include area, circumference, volume, surface area, distance, and midpoint formulae.
Are these formulae for both AA SL and AA HL?
Yes. The prior learning formulae listed on this page are useful for both AA SL and AA HL students. HL students go deeper in the course, but these formulae remain part of the same foundation.
Do I need to memorize these formulae?
Students should know them fluently. Even when formula booklets are available, memorizing these basic formulae saves time and improves accuracy in multi-step questions.
Why is the radius so important in circle formulae?
Circle formulae use radius. If a question gives diameter, first divide by two to get the radius. Using diameter directly in \(A=\pi r^2\) is a common error.
What is the difference between curved surface area and total surface area of a cylinder?
Curved surface area is \(A=2\pi rh\), which measures only the side surface. Total surface area of a closed cylinder includes the two circular ends: \(2\pi rh+2\pi r^2\).
How do prior learning formulae help with calculus?
Many calculus questions use area, volume, or surface area formulae as the starting model. For example, optimization questions may require differentiating a cylinder volume or surface area expression.
Are grade boundaries fixed for IB Math AA?
No. IB grade boundaries can change by session. Students should focus on strong mathematical understanding, clear working, accurate formula use, and problem-solving skill rather than relying on one fixed percentage.
What is the best way to revise these formulae?
Use active recall, mixed practice, and timed substitution drills. Practise choosing the formula from the context, not only applying it after someone tells you which formula to use.
Can this calculator replace exam practice?
No. The calculator helps with fluency and checking, but exam preparation requires written working, reasoning, interpretation, and past-paper-style practice.
Should answers be exact or rounded?
Use exact values such as \(25\pi\) when possible unless the question asks for a decimal or the context requires rounding. When rounding, keep enough accuracy during working.
Reference Notes for Students
This RevisionTown page is an educational study guide. Students should confirm final assessment instructions, permitted technology, local exam start times, and official course requirements with their IB coordinator and teacher.
Helpful official references: IB DP Mathematics curriculum, IB Mathematics AA updates, IB May 2026 examination schedule.
