Practice Flashcards
What is the 2D distance formula between (x1,y1) and (x2,y2)?
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All Flashcards in Topic 3.1
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3.1.14 cards
What is the 2D distance formula between (x1,y1) and (x2,y2)?
d = sqrt((x2-x1)^2 + (y2-y1)^2)
Subtract coordinates first, then square.
What is the midpoint formula in 2D?
M = ((x1+x2)/2, (y1+y2)/2)
Average x-coordinates and y-coordinates separately.
When do we use the 3D distance formula?
When points have x, y, and z coordinates.
Add the z-difference squared as well.
Common IB trap with distance questions?
Mixing up subtraction order before squaring and arithmetic slips.
Squaring removes sign, but arithmetic still matters.
3.1.26 cards
3D distance formula?
d = √[(x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²] — the 2D formula plus a z-term.
3D midpoint formula?
M = ((x₁+x₂)/2, (y₁+y₂)/2, (z₁+z₂)/2) — average all three coordinates.
What is a space diagonal?
The line from one corner of a cuboid to the opposite corner — found with the 3D distance formula.
Distance from (0,0,0) to (2,3,6)?
√(4+9+36) = √49 = 7.
Given the 3D midpoint M and one end A, find the other end B?
B = 2M − A (double the midpoint, subtract the known end), coordinate by coordinate.
Most common 3D-distance error?
Adding the gaps before squaring: √(6+4+3) instead of √(36+16+9). Square each gap first.
3.1.34 cards
Volume of a prism formula?
Volume = cross-sectional area x length
Use consistent units (e.g., cm^3).
Volume of a cylinder formula?
V = pi r^2 h
Radius must be squared, not diameter.
Surface area vs volume: key difference?
Surface area measures outside covering; volume measures inside space.
Units: area in square units, volume in cubic units.
IB context cue for surface area?
Material needed to cover an object.
Look for paint, wrapping, or tin-sheet contexts.
Topic 3.1 study notes
Full notes & explanations for 3D space, volume, angles, and midpoints
Math AI exam skills
Paper structures, command terms & tips
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