Study Guide

IB MYP Year 2 (Class 7) Maths All Formulas: Complete Sheet

Every formula you need for MYP Year 2 grouped by the four strands: Number, Algebra, Geometry & Trigonometry, and Statistics & Probability.

IBClass 7
SparkEd Math9 April 202613 min read
IB MYP Year 2 maths formula reference sheet across four strands

A Formula Sheet That Works With the MYP Framework

A parent in Zurich once wrote to me asking for 'the IB equivalent of a CBSE formula sheet'. Her daughter had just moved to an MYP school in Year 2, which is roughly the same as Class 7 in the Indian system, and she could not find a single document that listed the maths formulas for the year. All the resources she found were either full textbooks or lesson plans. I promised her I would put one together, and here it is.

MYP mathematics is organised into four strands rather than chapters. The four strands are Number, Algebra, Geometry and Trigonometry, and Statistics and Probability. Each strand is assessed against four criteria: Criterion A (Knowing and Understanding), Criterion B (Investigating Patterns), Criterion C (Communicating), and Criterion D (Applying Mathematics in Real Life Contexts). This framework means that knowing a formula is only one quarter of the picture. You also need to investigate why it works, communicate your solution clearly, and apply it to real situations.

This sheet respects the MYP philosophy by grouping formulas under the four strands and, where appropriate, pointing out which assessment criterion tends to focus on that formula. Use it alongside your textbook and classroom resources to strengthen Criterion A recall, and use the practice links to develop the other three criteria through problem solving.

Strand 1: Number — Integer and Rational Operations

Integer sign rules

(+)×(+)=+,()×()=+(+) \times (+) = +, \quad (-) \times (-) = +

(+)×()=,()×(+)=(+) \times (-) = -, \quad (-) \times (+) = -

Order of operations (BIDMAS / PEMDAS): Brackets, Indices, Division and Multiplication (left to right), Addition and Subtraction (left to right).

Fraction arithmetic

ab+cd=ad+bcbd\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}

abcd=adbcbd\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}

ab×cd=acbd\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}

ab÷cd=ab×dc\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

Decimal to fraction: write the decimal as a numerator over a power of 10 and simplify.

Rational numbers: any number pq\frac{p}{q} with p,qZp, q \in \mathbb{Z} and q0q \ne 0.

The IB learner profile encourages students to be inquirers. When you meet a new number property, ask why it works rather than accepting it. For example, why does a negative times a negative give a positive? Ask your teacher to walk you through a number line based explanation.

Strand 1: Number — Percentages and Ratios

Percent to fraction: x%=x100x\% = \frac{x}{100}.

Percent of a quantity

x% of Q=x100×Qx\% \text{ of } Q = \frac{x}{100} \times Q

Percentage change

% change=newoldold×100\% \text{ change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100

Ratio and proportion: a ratio a:ba : b is equivalent to the fraction ab\frac{a}{b}. Four quantities a,b,c,da, b, c, d are in proportion if ab=cd\frac{a}{b} = \frac{c}{d}.

Direct proportion: y=kxy = kx for some constant kk.

Inverse proportion: y=kxy = \frac{k}{x} for some constant kk.

An application rich formulation tested in Criterion D: if you are baking a cake for six people and the recipe serves four, scale every ingredient by the factor 64=1.5\frac{6}{4} = 1.5. This direct proportion idea is tested in every MYP real world task.

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Strand 1: Number — Powers and Scientific Notation

Laws of indices for nonzero aa and positive integers mm, nn:

am×an=am+na^m \times a^n = a^{m+n}

am÷an=amna^m \div a^n = a^{m-n}

(am)n=amn(a^m)^n = a^{mn}

(ab)n=anbn(ab)^n = a^n b^n

(ab)n=anbn\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}

a0=1a^0 = 1

an=1ana^{-n} = \frac{1}{a^n}

Scientific notation (also called standard form): any number written as a×10na \times 10^n where 1a<101 \le a < 10 and nZn \in \mathbb{Z}.

Example: 3450000=3.45×1063450000 = 3.45 \times 10^6, and 0.00072=7.2×1040.00072 = 7.2 \times 10^{-4}.

IB MYP tests international unit conversions frequently, so knowing scientific notation is essential for handling very large or very small numbers like the mass of Earth in kilograms or the radius of a hydrogen atom in metres.

Strand 2: Algebra — Expressions and Identities

Terms and like terms: terms with the same variable part (including powers) can be added or subtracted. 3x+5x=8x3x + 5x = 8x but 3x+5y3x + 5y stays as is.

Distributive law: a(b+c)=ab+aca(b + c) = ab + ac.

Expanding double brackets: (a+b)(c+d)=ac+ad+bc+bd(a + b)(c + d) = ac + ad + bc + bd.

Simple algebraic identities (introduced informally in MYP Year 2):

(a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2

(ab)2=a22ab+b2(a - b)^2 = a^2 - 2ab + b^2

(a+b)(ab)=a2b2(a + b)(a - b) = a^2 - b^2

Substitution: to evaluate an expression, replace each variable with the given value, using brackets around negative substitutions.

Strand 2: Algebra — Linear Equations and Inequalities

Solving linear equations: isolate the variable using inverse operations.

Balance principle: whatever operation you apply to one side, you must apply to the other.

Word problem translation:
* 'sum' means addition
* 'difference' means subtraction
* 'product' means multiplication
* 'quotient' means division
* 'is' or 'equals' means the equal sign

Simple inequalities: x>ax > a, x<ax < a, xax \ge a, xax \le a represent ranges of values. When multiplying or dividing both sides by a negative number, reverse the inequality sign.

Pattern to formula: given a sequence like 3,7,11,15,3, 7, 11, 15, \ldots, the general term is Tn=4n1T_n = 4n - 1. Finding a rule from a pattern is a staple of Criterion B (investigating patterns).

Strand 2: Algebra — Coordinates and Linear Graphs

Cartesian coordinates: a point in a plane has the form (x,y)(x, y) where xx is measured along the horizontal axis and yy along the vertical axis.

Distance between two points (informal in MYP Year 2):

d=(x2x1)2+(y2y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

This is derived from the Pythagoras theorem.

Linear equation: y=mx+cy = mx + c where mm is the slope (gradient) and cc is the y intercept.

Gradient between two points:

m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}

Horizontal line: y=ky = k for some constant kk.

Vertical line: x=kx = k for some constant kk.

A classic Criterion D application: given two data points, find the line that passes through them and use it to predict a third value.

Strand 3: Geometry and Trigonometry — Angles and Triangles

Angle sum of a triangle: 180°180°.

Exterior angle theorem: the exterior angle equals the sum of the two opposite interior angles.

**Sum of interior angles of a polygon with nn sides**:

S=(n2)×180°S = (n - 2) \times 180°

Regular polygon interior angle:

each angle=(n2)×180°n\text{each angle} = \frac{(n - 2) \times 180°}{n}

Pythagoras theorem: in a right angled triangle, c2=a2+b2c^2 = a^2 + b^2 where cc is the hypotenuse.

Triangle classification
* By sides: equilateral, isosceles, scalene
* By angles: acute, right, obtuse

Parallel lines and transversal
* Corresponding angles are equal
* Alternate interior angles are equal
* Co interior angles sum to 180°180°

Strand 3: Geometry and Trigonometry — Perimeter, Area and Volume

Perimeter of a polygon: sum of all sides.

Area formulas

square: A=s2\text{square: } A = s^2

rectangle: A=l×w\text{rectangle: } A = l \times w

triangle: A=12×b×h\text{triangle: } A = \frac{1}{2} \times b \times h

parallelogram: A=b×h\text{parallelogram: } A = b \times h

trapezium: A=12(a+b)×h\text{trapezium: } A = \frac{1}{2}(a + b) \times h

circle: A=πr2\text{circle: } A = \pi r^2

Circumference of a circle: C=2πr=πdC = 2\pi r = \pi d.

Volume formulas for prisms: V=base area×heightV = \text{base area} \times \text{height}.

Specific volumes

cube: V=s3\text{cube: } V = s^3

cuboid: V=l×w×h\text{cuboid: } V = l \times w \times h

cylinder: V=πr2h\text{cylinder: } V = \pi r^2 h

Surface areas (basic)
* Cube: 6s26s^2
* Cuboid: 2(lw+lh+wh)2(lw + lh + wh)
* Cylinder: 2πr2+2πrh2\pi r^2 + 2\pi rh

Unit conversions (important for international contexts)
* 1 m =100= 100 cm =1000= 1000 mm
* 1 km =1000= 1000 m
* 1 litre =1000= 1000 cm3^3
* 1 kg =1000= 1000 g
* 1 hectare =10000= 10000 m2^2

Use π3.14\pi \approx 3.14 or π=227\pi = \frac{22}{7} as specified by the question.

Strand 3: Geometry and Trigonometry — Transformations

MYP introduces four basic transformations in Year 2.

Reflection: a mirror image of a figure across a line. The distance from any point to the line equals the distance from its image to the line.

Rotation: turn about a fixed point by a given angle. Specify the centre, angle and direction (clockwise or anticlockwise).

Translation: slide a figure by a fixed vector (ab)\binom{a}{b}. Every point moves aa units horizontally and bb units vertically.

Enlargement (scaling): a figure is multiplied in size by a scale factor kk from a centre of enlargement.
* If k>1k > 1, the figure gets bigger.
* If 0<k<10 < k < 1, the figure gets smaller.
* If k<0k < 0, the figure is also reflected through the centre.

Congruent vs similar
* Congruent: same size and same shape (scale factor 1).
* Similar: same shape, possibly different size.

Strand 4: Statistics and Probability — Measures of Centre and Spread

Mean: xˉ=xin\bar{x} = \dfrac{\sum x_i}{n}

Median: the middle value when data is arranged in order. For an even count, average the two middle values.

Mode: the most frequently occurring value. A dataset may have one mode, no mode, or multiple modes.

Range: maximum value minus minimum value.

Frequency table summarises data by listing each value (or class interval) alongside its frequency.

Histogram and bar chart: visual representations. Use a histogram for continuous data, a bar chart for categorical data.

Stem and leaf plot: a compact way to show data while preserving individual values.

Criterion D tip: whenever you compute a statistic, ask whether it accurately represents the data. Outliers can distort the mean but leave the median unaffected. Explaining this in your write up shows strong application of mathematics in real contexts.

Strand 4: Statistics and Probability — Basic Probability

Probability of an event

P(E)=number of favourable outcomestotal number of outcomesP(E) = \frac{\text{number of favourable outcomes}}{\text{total number of outcomes}}

Probability range: 0P(E)10 \le P(E) \le 1.
* P(E)=0P(E) = 0 means the event is impossible.
* P(E)=1P(E) = 1 means the event is certain.

Complementary events: P(not E)=1P(E)P(\text{not } E) = 1 - P(E).

Sample space: the set of all possible outcomes. For a single die, the sample space has 6 elements {1,2,3,4,5,6}\{1, 2, 3, 4, 5, 6\}.

Independent events: for two independent events AA and BB:

P(A and B)=P(A)×P(B)P(A \text{ and } B) = P(A) \times P(B)

Mutually exclusive events: events that cannot happen at the same time. For mutually exclusive AA and BB:

P(A or B)=P(A)+P(B)P(A \text{ or } B) = P(A) + P(B)

The MYP learner profile encourages students to be reflective. When solving probability problems, check whether events are really independent or whether you need a tree diagram to map the outcomes properly.

The MYP Assessment Criteria: Why Formulas Alone Are Not Enough

Unlike CBSE and ICSE, the MYP grades students on four separate criteria. Here is what each one looks for, and how to use this formula sheet for each.

Criterion A — Knowing and Understanding
This is pure recall and direct application. Test questions ask 'calculate', 'evaluate', 'find'. This formula sheet is directly helpful for Criterion A.

Criterion B — Investigating Patterns
Tasks ask you to spot a pattern in a sequence or diagram, describe the rule, generalise it algebraically, and verify it. This sheet helps less here; you need actual investigation tasks. The formulas you derive in an investigation often get added to your personal formula sheet at the end.

Criterion C — Communicating
You must write mathematics clearly, using correct notation, complete sentences and appropriate diagrams. Using the correct symbols from this sheet (for example \subseteq not 'subset of') is part of Criterion C.

Criterion D — Applying Mathematics in Real Life Contexts
You take a real world scenario and apply maths to make a decision or prediction. This sheet gives you the tools; Criterion D asks you to choose the right tool and use it well.

A student aiming for a level 7 or 8 on MYP mathematics needs to practise all four criteria, not just one. Use this sheet for Criterion A revision, and use dedicated investigation tasks for the other three.

How to Use This Sheet

Here is a practical two week revision plan before any summative assessment.

Two weeks out: read each strand section carefully. For every formula you do not recognise immediately, mark it with a star.

One week out: make flashcards of starred formulas. Review them twice a day for five minutes each.

Four days out: attempt practice questions for each strand on the SparkEd Class 7 IB practice hub. Whenever a formula comes up that you did not have memorised, mark the flashcard for extra review.

Two days out: do a mixed mock task covering all four strands. Time yourself.

Exam day: scan the relevant strand sections ten minutes before walking in. Do not try to learn anything new on the day of the test. Trust your preparation.

For structured investigation practice aligned to Criterion B, and communication exercises for Criterion C, ask your teacher for past MYP tasks from your school's shared resources.

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