Top 200 IB MYP Mathematics Vocabulary Words | Essential Word Pack

Use this IB MYP mathematics pack to understand a question, choose a method and explain why an answer is valid. The 200 entries below give contextual meanings and original examples across number, algebra, geometry, trigonometry, statistics and probability. Select the terms needed for your current lesson; this is an eduKate teaching bank, not an official IB prescribed vocabulary list.

The 200-word list: meanings and learning examples

1–20: Numbers and their structure · 21–40: Fractions, proportions and percentage calculations · 41–60: Operations, accuracy and checking a calculation · 61–80: Algebraic expressions, equations and solutions · 81–100: Functions, sequences and mathematical models · 101–120: Shapes, angles and geometric properties · 121–140: Lengths, areas, volumes and circular geometry · 141–160: Coordinates, transformations and right-triangle relationships · 161–180: Statistics, representations and careful interpretation · 181–200: Probability, investigation and mathematical justification

Assessment requirements · Starting check · Fencing Method · Practice and answers

1–20. Numbers and their structure

1. integer — A number with no fractional part: negative, zero or positive. Example: The temperature change of minus four degrees is represented by the integer −4.
2. natural number — A counting number beginning at one in this pack’s convention. Example: Seven is a natural number; check whether your course also includes zero.
3. whole number — Zero or a positive counting number in this pack. Example: The whole number zero represents an empty collection of counters.
4. rational number — A number expressible as a fraction of integers with a non-zero denominator. Example: The decimal 0.75 is a rational number because it equals 3/4.
5. irrational number — A real number that cannot be expressed as a fraction of integers. Example: The square root of two is an irrational number.
6. real number — A number represented by a point on the ordinary number line. Example: Both −3 and the square root of two are real numbers.
7. prime number — An integer greater than one with exactly two positive factors. Example: Thirteen is a prime number because only one and thirteen divide it exactly.
8. composite number — An integer greater than one with more than two positive factors. Example: Fifteen is a composite number because three and five are also factors.
9. factor — A non-zero integer that divides another integer exactly. Example: Six is a factor of twenty-four because 24 ÷ 6 = 4.
10. multiple — A number obtained by multiplying a given number by an integer. Example: Thirty-five is a multiple of seven because 7 × 5 = 35.
11. prime factorisation — Writing a positive integer greater than one as a product of primes. Example: The prime factorisation of forty-five is 3 × 3 × 5.
12. highest common factor — The greatest positive integer dividing each of the given positive integers. Example: The highest common factor of eighteen and thirty is six.
13. lowest common multiple — The smallest positive number that is a multiple of each given positive integer. Example: The lowest common multiple of six and eight is twenty-four.
14. absolute value — A real number’s distance from zero on the number line. Example: The absolute value of −9 is nine, which is non-negative.
15. reciprocal — The number that multiplies a given non-zero number to make one. Example: The reciprocal of 3/5 is 5/3; zero has no reciprocal.
16. exponent — The number indicating the power to which a base is raised. Example: In 2⁵, the exponent five tells us to multiply five twos.
17. square root — A real number whose square equals a given non-negative real number; √ denotes the non-negative root. Example: The square root written √49 is seven, although −7 also squares to forty-nine.
18. cube root — A number whose cube equals the given number. Example: The cube root of −27 is −3 because (−3)³ = −27.
19. standard form — Writing a non-zero number as a × 10ⁿ, with 1 ≤ absolute value of a < 10 and integer n. Example: The distance 6,200 metres becomes 6.2 × 10³ metres in standard form.
20. significant figure — A digit counted when stating a numerical value to a chosen precision. Example: The measurement 0.0472 has three significant figures: four, seven and two.

21–40. Fractions, proportions and percentage calculations

21. numerator — The number above the fraction bar, counting the indicated parts. Example: In 5/8, the numerator five counts five eighths.
22. denominator — The non-zero number below a fraction bar, indicating the division. Example: The denominator eight in 5/8 means the whole is divided into eighths.
23. proper fraction — For non-negative fractions here, a fraction with numerator smaller than its positive denominator. Example: Three fifths is a proper fraction because three is smaller than five.
24. improper fraction — A fraction with positive numerator at least as large as its positive denominator. Example: Nine fourths is an improper fraction and is greater than two.
25. mixed number — A whole number combined with a proper fraction. Example: The mixed number 2 1/4 represents the same value as 9/4.
26. equivalent fraction — A fraction expressing the same value as another fraction. Example: Six eighths is an equivalent fraction to three quarters.
27. decimal — A number written using base-ten place value, usually with a decimal point here. Example: Write three quarters as the decimal 0.75.
28. recurring decimal — A decimal with a digit or block of digits repeating without end. Example: One third has the recurring decimal 0.333… .
29. terminating decimal — A decimal representation that ends after finitely many decimal places. Example: One eighth has the terminating decimal 0.125.
30. ratio — A comparison expressing the relative amounts of two or more quantities. Example: The ratio of red counters to blue counters is 2:3.
31. proportion — An equation stating that two ratios or fractions are equal. Example: The proportion 2/3 = 8/12 shows that the ratios are equivalent.
32. percentage — An amount expressed as a number of parts per hundred. Example: A percentage of twenty-five means twenty-five parts out of one hundred.
33. percentage point — The unit used for the difference between two percentages. Example: An increase from forty to fifty percent is ten percentage points.
34. percentage change — The change divided by the original non-zero value, multiplied by one hundred. Example: A price rising from twenty to twenty-five has a percentage change of twenty-five percent.
35. multiplier — A factor used to scale a quantity to its new value. Example: Use a multiplier of 1.15 for an increase of fifteen percent.
36. direct proportion — A relationship y = kx with a constant multiplier k. Example: With no fixed charge, total cost is in direct proportion to quantity at a constant card price.
37. inverse proportion — A relationship xy = k, with a constant product and non-zero quantities here. Example: For a fixed distance, average speed and journey time are in inverse proportion.
38. unit rate — A rate expressed for one unit of the comparison quantity. Example: Twelve dollars for three metres gives a unit rate of four dollars per metre.
39. simple interest — Interest calculated on the original principal alone over the stated periods. Example: At five percent yearly simple interest, one hundred dollars earns five dollars each year.
40. compound interest — Interest calculated on the principal and interest already added. Example: Two years of ten percent yearly compound interest turns one hundred into one hundred twenty-one.

41–60. Operations, accuracy and checking a calculation

41. sum — The result of adding quantities. Example: The sum of −3 and eight is five.
42. difference — The result of subtracting one quantity from another. Example: The difference 11 − 16 is −5, so the order matters.
43. product — The result of multiplying quantities. Example: The product of −4 and six is −24.
44. quotient — The result obtained by dividing one quantity by a non-zero quantity. Example: The quotient of twenty-one divided by seven is three.
45. remainder — The amount left after whole-number division into equal groups. Example: Dividing seventeen counters into groups of five leaves a remainder of two.
46. operation — A mathematical action such as addition, subtraction, multiplication or division. Example: Identify division as the operation in 18 ÷ 3 before calculating its value.
47. order of operations — The agreed priority for evaluating parts of an expression. Example: Following the order of operations gives 2 + 3 × 4 = 14.
48. inverse operation — An operation that reverses another within the relevant conditions. Example: Subtracting seven is the inverse operation for adding seven.
49. associative — Unchanged by regrouping three values under the same operation. Example: Addition is associative: (2 + 3) + 4 equals 2 + (3 + 4).
50. commutative — Unchanged when the order of two inputs to an operation is exchanged. Example: Multiplication is commutative, so 4 × 7 = 7 × 4.
51. distributive — Describing multiplication applied to each term of a sum or difference. Example: The distributive rule gives 5(x + 2) = 5x + 10.
52. estimate — Find a reasonable approximate value using available information. Example: Estimate 49 × 21 as about 50 × 20 before calculating exactly.
53. round — Replace a number with a nearby value at a stated level of precision. Example: Round 7.263 to two decimal places to obtain 7.26.
54. decimal place — A digit position to the right of the decimal point. Example: The second decimal place in 4.376 contains the digit seven.
55. lower bound — In rounding questions here, the lower endpoint of the allowed interval. Example: For 12.5 ≤ x < 13.5, the lower bound is 12.5.
56. upper bound — In rounding questions here, the upper endpoint of the allowed interval. Example: For 12.5 ≤ x < 13.5, the upper bound is 13.5 and is excluded.
57. error interval — An interval of possible values consistent with a stated rounded measurement. Example: Under the stated half-up rule, a length rounded to 13 cm has error interval 12.5 cm ≤ length < 13.5 cm.
58. exact value — A value expressed without rounding or approximation. Example: For a square of side one metre, the diagonal’s exact value is √2 metres.
59. approximation — A value or representation close enough for a stated purpose. Example: The decimal 3.14 is an approximation to pi, not its exact value.
60. unit conversion — Expressing the same quantity using a different measurement unit. Example: A unit conversion changes 250 centimetres to 2.5 metres without changing the length.

61–80. Algebraic expressions, equations and solutions

61. variable — A symbol representing a quantity that may take different values. Example: Let the variable n represent the number of cards ordered.
62. constant — A fixed value within the expression or situation being considered. Example: In 4x + 9, the constant term is nine.
63. term — One part of an expression separated by addition or subtraction. Example: The expression 3x² + 2x − 5 has three terms.
64. coefficient — The numerical factor multiplying a variable or variable expression. Example: The coefficient of x in −6x + 4 is −6.
65. expression — A mathematical combination of values, symbols and operations without a relation sign. Example: The expression 2n + 5 gives a value once n is known.
66. equation — A mathematical statement that two expressions have equal values. Example: Solve the equation 2x + 5 = 13 to find x.
67. identity — An equality true for every permitted value of its variables. Example: The identity 2(x + 3) = 2x + 6 holds for every real x.
68. inequality — A statement comparing values using less-than or greater-than relations, possibly including equality. Example: The inequality n ≤ 12 allows twelve but excludes thirteen.
69. formula — An equation expressing a relationship between quantities. Example: The formula A = lw gives the area of a rectangle.
70. substitute — Replace a variable with a specified value or expression. Example: Substitute x = 4 into 3x − 2 to obtain ten.
71. simplify — Rewrite an expression in an equivalent, more manageable form. Example: Simplify 3x + 2x to 5x, keeping the same value.
72. expand — Remove brackets by applying multiplication to the enclosed terms. Example: Expand 4(x − 3) to obtain 4x − 12.
73. factorise — Rewrite an expression as a product of factors. Example: Factorise x² + 5x as x(x + 5).
74. solution — A value or set of values satisfying the original equation or conditions. Example: The solution x = 4 makes both sides of 2x + 5 = 13 equal.
75. linear equation — In one variable here, an equation that can be written ax + b = 0, where a is non-zero. Example: The linear equation 3x − 4 = 11 has solution x = 5.
76. quadratic equation — An equation in one variable that can be written ax² + bx + c = 0, with a non-zero. Example: The quadratic equation x² − 9 = 0 has solutions three and minus three.
77. simultaneous equations — Equations whose shared variables must satisfy all the equations together. Example: The simultaneous equations x + y = 7 and x − y = 1 give x = 4, y = 3.
78. algebraic fraction — A fraction containing algebraic expressions, with a non-zero denominator. Example: The algebraic fraction (x + 2)/x is undefined when x equals zero.
79. subject — The variable isolated on one side of a formula. Example: In A = lw, A is the subject of the formula.
80. rearrange — Transform an equation to an equivalent form while preserving its conditions. Example: Rearrange v = d/t to d = vt, retaining the condition that t is non-zero.

81–100. Functions, sequences and mathematical models

81. function — A rule assigning exactly one output to each allowed input. Example: The function f(x) = 2x + 1 gives seven when x is three.
82. input — A value supplied to a function or mathematical process. Example: The input four produces the output nine under f(x) = 2x + 1.
83. output — The value a function or process produces from a given input. Example: For f(x) = x², the output is sixteen when the input is −4.
84. domain — The set of input values allowed for a function. Example: The real-number domain of f(x) = 1/x excludes zero.
85. piecewise function — A function using different rules on different parts of its domain. Example: A piecewise function may use f(x) = x for x ≤ 2 and f(x) = 2 otherwise.
86. sequence — An ordered list of numbers or other mathematical objects. Example: The sequence 4, 7, 10, 13 continues by adding three.
87. term number — The position of a term in a sequence. Example: The term number of thirteen in 4, 7, 10, 13 is four.
88. arithmetic sequence — A sequence with a constant difference between consecutive terms. Example: The numbers 9, 5, 1, −3 form an arithmetic sequence.
89. common difference — The constant amount added between consecutive terms of an arithmetic sequence. Example: The common difference in 9, 5, 1, −3 is −4.
90. geometric sequence — A sequence formed by multiplying each term by a fixed ratio. Example: The geometric sequence 3, 6, 12, 24 uses repeated multiplication by two.
91. common ratio — The fixed multiplier between consecutive terms of a geometric sequence. Example: The common ratio in 16, 8, 4, 2 is one half.
92. nth term — The term at position n, often expressed by a formula in n. Example: The nth term 3n + 1 gives four, seven and ten for n = 1, 2, 3.
93. recursive rule — A rule defining a term using earlier terms, with starting values supplied. Example: Start at five and add two each time: this recursive rule produces 5, 7, 9.
94. linear model — A model using a relationship with a constant rate of change. Example: The linear model C = 12 + 0.80n includes a fixed charge and a card charge.
95. quadratic model — A model using a variable squared as its highest power. Example: The quadratic model A = x² represents the area of a square of side x.
96. exponential growth — Repeated change by a constant multiplier greater than one over equal intervals. Example: Doubling a model population each hour describes exponential growth under that assumption.
97. exponential decay — Repeated change by a constant multiplier between zero and one over equal intervals. Example: Keeping eighty percent of a quantity each period models exponential decay.
98. parameter — A fixed value chosen to specify a particular model or function. Example: Changing the parameter m in y = mx + 2 changes the line’s gradient.
99. assumption — A condition accepted when building or using a model. Example: Our assumption is that every printed card has the same unit price.
100. constraint — A condition restricting the permitted values or choices. Example: A budget of thirty-eight dollars is a constraint on the order.

101–120. Shapes, angles and geometric properties

101. point — An exact position with no length, width or thickness. Example: Mark the point where the two drawn lines intersect.
102. line — A straight path extending indefinitely in both directions. Example: The line through two distinct points continues beyond the marks on the page.
103. line segment — The straight part of a line between two endpoints. Example: The line segment AB has a measured length of six centimetres.
104. ray — A straight path beginning at one endpoint and extending indefinitely in one direction. Example: Draw a ray starting at A and passing through B.
105. vertex — A point where edges or sides meet. Example: Label the vertex shared by the two sides forming the angle.
106. angle — The measure of turn between two rays with a common endpoint. Example: The angle from the first ray to the second is thirty degrees.
107. acute angle — An angle greater than zero degrees and smaller than ninety degrees. Example: A forty-degree angle is an acute angle.
108. right angle — An angle measuring exactly ninety degrees. Example: The corner of the rectangle is a right angle.
109. obtuse angle — An angle greater than ninety degrees and smaller than one hundred eighty degrees. Example: A one hundred twenty-degree angle is an obtuse angle.
110. reflex angle — An angle greater than one hundred eighty degrees and smaller than three hundred sixty degrees. Example: The longer turn of two hundred seventy degrees is a reflex angle.
111. perpendicular — Meeting at a right angle. Example: The horizontal and vertical axes are perpendicular on this coordinate grid.
112. parallel — In a plane, remaining the same distance apart and never intersecting. Example: The opposite sides of a rectangle are parallel.
113. polygon — A closed flat figure formed by straight line segments. Example: A five-sided polygon is called a pentagon.
114. regular polygon — A polygon with all sides equal and all interior angles equal. Example: A square is a regular polygon, but a non-square rectangle is not.
115. triangle — A polygon with exactly three sides. Example: The triangle’s three interior angles total one hundred eighty degrees in plane geometry.
116. parallelogram — A four-sided polygon with both pairs of opposite sides parallel. Example: A rectangle is a parallelogram because both pairs of opposite sides are parallel.
117. rectangle — A four-sided polygon with four right angles. Example: A square is also a rectangle because it has four right angles.
118. rhombus — A four-sided polygon with all four sides equal in length. Example: A rhombus need not have right angles, but a square does.
119. square — A four-sided polygon with four equal sides and four right angles. Example: The square has side length three centimetres and perimeter twelve centimetres.
120. circle — The set of points in a plane at a fixed positive distance from a centre. Example: Every point on this circle is five centimetres from its centre.

121–140. Lengths, areas, volumes and circular geometry

121. perimeter — The total distance around a closed flat figure’s boundary. Example: A rectangle measuring six by four metres has perimeter twenty metres.
122. area — The measure of a flat region, expressed in square units. Example: The area of a six-by-four-metre rectangle is twenty-four square metres.
123. circumference — The perimeter of a circle. Example: A circle of radius three centimetres has circumference 6π centimetres.
124. radius — A segment from a circle’s centre to its boundary, or its length. Example: The radius is four centimetres when the diameter is eight centimetres.
125. diameter — A chord passing through a circle’s centre, or its length. Example: The diameter of a circle is twice its radius.
126. chord — A line segment joining two points on a circle. Example: The chord need not pass through the circle’s centre.
127. tangent — A straight line meeting a circle at exactly one point. Example: The tangent is perpendicular to the radius at the point of contact.
128. arc — A continuous portion of a circle’s circumference. Example: The marked arc covers a quarter of the circle’s boundary.
129. sector — The region bounded by two radii and their connecting arc. Example: A ninety-degree sector occupies one quarter of a circle’s area.
130. circular segment — The region bounded by a chord and its corresponding arc. Example: Shade the circular segment between the chord and the smaller arc.
131. volume — The measure of three-dimensional space occupied or enclosed, expressed in cubic units. Example: The cuboid’s volume is 3 × 4 × 5 = 60 cubic centimetres.
132. surface area — The total area of a three-dimensional figure’s outer surfaces. Example: Include all six faces when calculating a closed cuboid’s surface area.
133. capacity — The maximum internal volume a container can hold under the stated conditions. Example: The container’s capacity is two litres, although it currently holds one litre.
134. prism — A solid with congruent parallel polygonal ends and parallelogram side faces. Example: A triangular prism has two congruent triangular ends.
135. cylinder — A solid with congruent parallel circular ends and a constant circular cross-section parallel to them. Example: For this right cylinder, multiply base area by perpendicular height to find volume.
136. pyramid — A solid with a polygonal base and triangular faces meeting at one vertex. Example: A square-based pyramid has four triangular side faces.
137. cone — A solid with a circular base and a curved surface meeting at one vertex. Example: For a right cone, its slant height is greater than its perpendicular height.
138. sphere — A round three-dimensional figure whose surface stays a fixed distance from its centre. Example: The radius of a sphere measures from its centre to its surface.
139. net — A flat arrangement of faces that can fold into a solid. Example: Check that the six squares in the net fold into a cube without overlap.
140. scale factor — A number describing a change of scale; its absolute value multiplies corresponding lengths. Example: A scale factor of three makes each corresponding length three times as large.

141–160. Coordinates, transformations and right-triangle relationships

141. coordinate — A value locating a point relative to reference axes or a grid. Example: The first coordinate in (−2, 5) gives the horizontal position.
142. origin — The point where coordinate axes meet, labelled zero on each axis. Example: The origin of the usual two-dimensional grid is (0, 0).
143. axis — A reference line used to locate positions or display values. Example: Label the horizontal axis with time in minutes.
144. gradient — For a non-vertical straight line, vertical change divided by horizontal change. Example: A rise of six over a run of three gives gradient two.
145. intercept — A point where a graph crosses or meets a coordinate axis. Example: The graph y = 2x + 3 has a vertical intercept at (0, 3).
146. midpoint — The point halfway along a line segment. Example: The midpoint of (2, 4) and (6, 8) is (4, 6).
147. distance — The length of the straight segment joining two points. Example: The distance from (0, 0) to (3, 4) is five units.
148. vector — A quantity described by magnitude and direction. Example: The displacement vector moves a point three units right and two units up.
149. translation — Moving every point of a figure by the same vector. Example: A translation by two units right leaves the figure’s size and orientation unchanged.
150. reflection — Mapping points across a mirror line along perpendiculars, preserving their distance from that line. Example: A reflection in the vertical axis maps (3, 2) to (−3, 2).
151. rotation — Turning every point through a specified angle about a fixed centre. Example: A ninety-degree anticlockwise rotation about the origin maps (2, 0) to (0, 2).
152. enlargement — Scaling positions relative to a centre by a stated scale factor. Example: An enlargement with scale factor two doubles corresponding lengths, not their areas.
153. congruent — Having the same shape and size, allowing movement, turning or reflection. Example: The two congruent triangles still match after one is rotated.
154. similar — Having the same shape, with corresponding lengths in one common ratio. Example: Rectangles measuring 3 by 2 and 6 by 4 are similar.
155. bearing — A clockwise angle from north, conventionally written as three digits in degrees. Example: A bearing of 090° points east.
156. hypotenuse — The side opposite the right angle in a right-angled triangle. Example: The hypotenuse is the longest side of this right-angled triangle.
157. Pythagoras’ theorem — In a right-angled triangle, the hypotenuse squared equals the sum of the other sides squared. Example: Pythagoras’ theorem gives c² = 3² + 4², so c = 5 for the length.
158. sine — For an acute angle in a right triangle, opposite-side length divided by hypotenuse length. Example: The sine of the marked angle is 3/5 when its opposite side is three and hypotenuse five.
159. cosine — For an acute angle in a right triangle, adjacent non-hypotenuse side length divided by hypotenuse length. Example: The cosine of the marked angle is 4/5 when its adjacent side is four and hypotenuse five.
160. tangent ratio — For an acute angle in a right triangle, opposite-side length divided by adjacent non-hypotenuse side length. Example: The tangent ratio is 3/4 when the opposite side is three and adjacent side four.

161–180. Statistics, representations and careful interpretation

161. data — Recorded observations or values collected for a purpose. Example: Keep the original data before arranging the journey times in order.
162. population — The complete group of cases an investigation aims to describe. Example: All students in the school form the population for this stated survey question.
163. sample — The selected part of a population examined in an investigation. Example: Our sample includes thirty students, not everyone in the school.
164. random sample — A sample selected through a specified process involving chance. Example: A random sample can still differ from the population by chance.
165. bias — A systematic tendency for a method to favour particular results or groups. Example: Surveying only club members risks bias when describing the whole school.
166. frequency — The number of times a value or category occurs. Example: The frequency of five is three in the data 5, 5, 5, 8.
167. relative frequency — The frequency divided by the total number of observations. Example: Eight red outcomes in twenty trials gives a relative frequency of 0.4.
168. mean — For a non-empty numerical data set, the sum of the values divided by the number of values. Example: The mean of two, four and nine is five.
169. median — The middle ordered value, or the mean of the two middle values for an even count. Example: The median of 2, 4, 7 and 11 is (4 + 7) ÷ 2 = 5.5.
170. mode — A value occurring with the highest frequency in the data. Example: The mode of 2, 3, 3 and 8 is three.
171. range — In statistics here, the largest value minus the smallest value. Example: The range of 2, 4 and 9 is seven.
172. quartile — One of three cut points separating ordered data into four approximately equal-sized parts. Example: Use the stated course method to find the lower quartile.
173. interquartile range — The upper quartile minus the lower quartile. Example: If the quartiles are four and ten, the interquartile range is six.
174. outlier — A value unusually distant from the main pattern under a stated judgement or rule. Example: Sixty is a possible outlier beside the values four, five, five and six.
175. histogram — A graph of numerical intervals with bar areas proportional to their frequencies. Example: Unequal class widths require frequency density on this histogram’s vertical axis.
176. box plot — A diagram displaying the median, quartiles and whiskers under a stated convention. Example: Read the median from the line inside the box plot’s central box.
177. scatter plot — A graph showing paired numerical observations as points. Example: Use a scatter plot to examine the relationship between height and arm span.
178. correlation — A statistical association between the values of variables. Example: A correlation in this sample does not identify its cause.
179. interpolation — Estimating within the observed input range using a model or pattern. Example: Predicting a value at twelve minutes from observations at ten and fifteen is interpolation.
180. extrapolation — Estimating beyond the observed input range using a model or pattern. Example: A prediction for thirty minutes from observations ending at fifteen is extrapolation.

181–200. Probability, investigation and mathematical justification

181. probability — A numerical measure of likelihood between zero and one inclusive. Example: The probability of heads is one half for the stated fair coin.
182. outcome — One possible result of a chance process. Example: Rolling a four is one outcome of a six-sided die roll.
183. event — A set of outcomes satisfying a specified condition. Example: Rolling an even number is the event containing two, four and six.
184. sample space — The set of all possible outcomes of the stated chance process. Example: For one ordinary six-sided die, the sample space is {1, 2, 3, 4, 5, 6}.
185. equally likely — Having the same probability under the stated model. Example: The six faces are equally likely only when the die is modelled as fair.
186. complement — The event containing all outcomes outside a specified event within the sample space. Example: Not rolling a six is the complement of rolling a six.
187. union — The event containing outcomes in either of two events, including their overlap. Example: The union of {1, 2} and {2, 3} is {1, 2, 3}.
188. intersection — The event containing outcomes shared by both events. Example: The intersection of {1, 2} and {2, 3} contains only two.
189. independent events — Events for which knowing one occurs does not change the probability of the other. Example: For independently tossed fair coins, heads on the first coin and heads on the second are independent events.
190. mutually exclusive events — Events that cannot both occur in the same trial. Example: Odd and even outcomes are mutually exclusive events on one die roll.
191. conditional probability — The probability of an event when specified additional information is given. Example: Find the conditional probability of red given that the chosen card is a triangle.
192. tree diagram — A branching representation of possible stages and outcomes. Example: Label each branch probability on the tree diagram before multiplying along a path.
193. experimental probability — An estimate of probability based on observed relative frequency. Example: Twelve successes in forty trials gives experimental probability 0.3.
194. expected frequency — For trials with the same event probability, the number of trials multiplied by that probability. Example: With probability 0.3 over one hundred trials, the expected frequency is thirty.
195. conjecture — A mathematical claim suggested by evidence but not yet proved. Example: The first few cases suggest a conjecture about the sum of consecutive odd numbers.
196. counterexample — One case showing that a claim about every case is false. Example: The number two is a counterexample to the claim that every prime is odd.
197. proof — A logical argument establishing a mathematical claim from accepted facts and assumptions. Example: A proof must explain why the claim holds for all permitted cases.
198. justify — Give valid mathematical reasons supporting a result or decision. Example: Justify the even result by expressing it as twice an integer.
199. verify — Check that a proposed result satisfies the relevant conditions. Example: Verify x = 4 by substituting it into the original equation.
200. limitation — A restriction on what a method, model or conclusion can support. Example: The missing delivery fee is a limitation of this incomplete cost model.

List check: 200 distinct entries in 10 groups of 20. This is a reference bank for learning and application, not a quota for one response.

The MYP spans approximately ages 11–16, so one learner may need fraction language while another is working with functions or conditional probability. Begin with familiar quantities and diagrams, then move to relationships and justification when ready. Your school’s actual course, standard or extended mathematics provision, task criteria and permitted tools determine the next step.

Guide contents

Sections 1–4: Understand the stage and use words accurately

1. What does IB MYP mathematics actually require?
2. Start with a short task and find the real difficulty
3. Use mathematical words with their conditions
4. Apply the Fencing Method to mathematical explanations

Sections 5–6: Worked examples and practice

5. Worked task: compare two printing models
6. Six practice tasks with reasoned answers

Sections 7–11: Review, revise and continue

7. Repair the reasoning behind common errors
8. An optional five-session practice plan
9. Check progress through independent use
10. Questions learners and families ask
11. Sources and the scope of this teaching pack

Continue with vocabulary for your stage

The IB programme overview places PYP at ages 3–12, MYP at 11–16 and DP at 16–19. Schools use different year and grade labels. In this eduKate series, School Years 1–13 are an illustrative school-year route; your school’s programme placement takes priority.

Age 12 vocabulary reference · Fencing Method for vocabulary · Vocabulary Learning Hub

Related subject Essential Word Packs

• PYP Mathematics — 200 words
• PYP Science — 200 words
• MYP Mathematics — 200 words — this guide
• MYP Sciences — 200 words

General Essential Word Packs by school year

School Year 7 · School Year 8 · School Year 9 · School Year 10 · School Year 11

Return to the 200-word bank · Return to guide contents