Confirmed pattern: 4 sections, 50 questions, 60 marks, 60 minutes, no negative marking — Logical Reasoning (15×1=15), Mathematical Reasoning (20×1=20), Everyday Mathematics (10×1=10, same syllabus as Mathematical Reasoning), Achievers (5×3=15). Sections 2–3 mix ~60% Class 7 topics (below, full detail) with ~40% Class 6 revision (recap list at the end).
Each of the 14 Class 7 topics: What it is → 3–4 worked examples → How to teach it → Practice problems (with answers).
What it is: Whole numbers including negatives, added/subtracted/multiplied/divided with sign rules (same signs → positive result when multiplying/dividing; different signs → negative).
Examples: 1) (−8)+(−5)−(−12) = −8−5+12 = −1. 2) (−6)×(−3) = 18 (same signs → positive). 3) 20−(−7)+(−13) = 20+7−13 = 14.
How to teach it: Use a number line physically for addition/subtraction, and teach the sign-multiplication rule as "same signs make friends (positive), different signs make enemies (negative)" — a memorable shorthand for the rule.
Practice: (a) (−15)−(−9)+(−4) (b) (−7)×4 (c) 18÷(−3) Answers: (a) −10 (b) −28 (c) −6
What it is: Adding/subtracting fractions needs a common denominator; decimals are added/multiplied/divided using place value.
Examples: 1) 3/4 + 5/6 = 9/12+10/12 = 19/12 = 1 7/12. 2) 4.5 × 0.2 = 0.9. 3) 6.4 ÷ 0.8 = 8. 4) 5/8 − 1/4 = 5/8−2/8 = 3/8.
How to teach it: For fraction addition, always find the LCD (lowest common denominator) explicitly on the board before adding — skipping this step is the single biggest source of errors at this level.
Practice: (a) 7/9 + 2/3 (b) 12.5 × 0.4 (c) 6/8 − 1/4 Answers: (a) 13/9 = 1 4/9 (b) 5 (c) 6/8−2/8=4/8=1/2
What it is: A number multiplied by itself repeatedly (2³ = 2×2×2 = 8). Key rules: aᵐ×aⁿ=aᵐ⁺ⁿ, and (aᵐ)ⁿ=aᵐˣⁿ.
Examples: 1) 2³×2⁴ = 2⁷ = 128. 2) (3²)³ = 3⁶ = 729. 3) 5²×5³ = 5⁵ = 3125.
How to teach it: Physically expand 2 or 3 examples fully (2³×2⁴ = 2×2×2 × 2×2×2×2 = 2⁷) before introducing the shortcut rule "add the exponents" — showing why the rule works prevents it from being applied incorrectly later (e.g., mistakenly adding exponents when multiplying different bases).
Practice: (a) 4²×4³ (b) (2³)² (c) 10²×10⁴ Answers: (a) 4⁵=1024 (b) 2⁶=64 (c) 10⁶=1,000,000
What it is: Combining terms with the same variable ("like terms") by adding/subtracting their coefficients; unlike terms stay separate.
Examples: 1) 5x+3x−2x = 6x. 2) 7y−2y+5y = 10y. 3) 9a−4a+2a = 7a. 4) 3x+2y+5x = 8x+2y (x and y terms stay separate).
How to teach it: Use real objects as a metaphor — "3 apples + 2 apples = 5 apples, but 3 apples + 2 oranges can't combine into one term" — like terms vs. unlike terms becomes intuitive rather than a grammar rule to memorise.
Practice: (a) 6p−2p+4p (b) 8m+3n−2m (c) 10x−5x+2x Answers: (a) 8p (b) 6m+3n (c) 7x
What it is: Finding the unknown value (x) that makes an equation true, by performing the same operation on both sides.
Examples: 1) 3x+7=22 → 3x=15 → x=5. 2) 4x−5=19 → 4x=24 → x=6. 3) 2x+9=21 → 2x=12 → x=6.
How to teach it: Emphasise the "balance" metaphor — an equation is like a balanced scale, and whatever you do to one side (add, subtract, multiply, divide) you must do to the other to keep it balanced.
Practice: (a) 5x−3=17 (b) 2x+11=25 (c) 6x−4=20 Answers: (a) x=4 (b) x=7 (c) x=4
What it is: Complementary angles sum to 90°; supplementary angles sum to 180°; vertically opposite angles (formed by intersecting lines) are always equal.
Examples: 1) Two supplementary angles, one is 65° → other is 115°. 2) Two complementary angles, one is 35° → other is 55°. 3) Two intersecting lines create two pairs of vertically opposite, equal angles.
How to teach it: Draw two intersecting lines on the board and have students measure all four resulting angles with a protractor themselves — discovering the "opposite angles are equal" rule firsthand is far more memorable than being told it.
Practice: (a) One of two supplementary angles is 78°. Find the other. (b) One of two complementary angles is 22°. Find the other. (c) If one angle at an intersection is 50°, what is its vertically opposite angle? Answers: (a) 102° (b) 68° (c) 50° (equal)
What it is: Percentage = a fraction out of 100. Profit/Loss % = (profit or loss ÷ cost price) × 100. Simple Interest = (Principal × Rate × Time) ÷ 100.
Examples: 1) 25% of 160 = 40. 2) Bought for ₹250, sold for ₹300: profit=₹50, profit%=50/250×100=20%. 3) SI on ₹2000 at 5% for 3 years = (2000×5×3)/100 = ₹300.
How to teach it: Always write out the three quantities (cost price, selling price, profit/loss) in a small table before calculating — organizing the given information prevents plugging numbers into the wrong part of the formula.
Practice: (a) 40% of 250 (b) Bought for ₹400, sold for ₹460 — find profit%. (c) SI on ₹3000 at 6% for 2 years. Answers: (a) 100 (b) profit=₹60, 60/400×100=15% (c) (3000×6×2)/100=₹360
What it is: The interior angles of any triangle always sum to 180°. The sum of any two sides must always exceed the third side (triangle inequality). An exterior angle equals the sum of the two non-adjacent interior angles.
Examples: 1) If two angles are 50° and 60°, the third is 180−50−60=70°. 2) Sides of 3cm, 4cm, 5cm: 3+4=7>5 ✓ valid triangle. 3) Sides of 2cm, 3cm, 6cm: 2+3=5<6 ✗ NOT a valid triangle.
How to teach it: Give students strips of paper/string cut to specific lengths and have them physically try to form a triangle — some combinations simply won't close into a triangle, making the inequality rule a hands-on discovery.
Practice: (a) Two angles of a triangle are 40° and 90°. Find the third. (b) Can sides of 5cm, 5cm, 11cm form a triangle? (c) An exterior angle is formed at one vertex; the two opposite interior angles are 55° and 65°. Find the exterior angle. Answers: (a) 50° (b) No — 5+5=10 < 11 (c) 120°
What it is: Two triangles are congruent (identical in shape and size) if they satisfy one of these rules: SSS (all 3 sides equal), SAS (2 sides + included angle equal), ASA (2 angles + included side equal), or RHS (right angle, hypotenuse, and one side equal, for right triangles only).
Examples: 1) Two triangles with all three sides matching → congruent by SSS. 2) Two triangles sharing two equal sides and the angle between them → congruent by SAS. 3) Two right triangles with equal hypotenuse and one equal leg → congruent by RHS.
How to teach it: Physically cut out two paper triangles built to the same SSS measurements and overlay them — seeing them match exactly, corner to corner, makes "congruent" a visual fact rather than an abstract rule.
Practice: (a) Which rule applies when all three sides of two triangles match? (b) Which rule applies specifically to right-angled triangles? (c) If two sides and the included angle of one triangle match another, which rule proves congruence? Answers: (a) SSS (b) RHS (c) SAS
What it is: A shape has line symmetry if it can be folded along a line so both halves match exactly. It has rotational symmetry if it looks the same after being rotated less than a full turn.
Examples: 1) A square has 4 lines of symmetry (2 diagonals + 2 through the midpoints of opposite sides). 2) A circle has infinite lines of symmetry. 3) A regular pentagon has rotational symmetry of order 5 (looks the same after each 72° turn).
How to teach it: Have students fold paper cutouts of different shapes to physically find lines of symmetry — folding either matches perfectly or it doesn't, which is more convincing than looking at a printed shape and guessing.
Practice: (a) How many lines of symmetry does an equilateral triangle have? (b) Does a scalene triangle (all sides different) have any line symmetry? (c) What is the order of rotational symmetry of a square? Answers: (a) 3 (b) No (c) 4 (matches itself every 90°)
What it is: Numbers that can be written as a fraction p/q (q≠0), including negative fractions. Comparing them requires converting to a common denominator or decimal form.
Examples: 1) −3/4 = −0.75 and −2/3 ≈ −0.667; since −0.667 is closer to zero, −2/3 is greater. 2) The additive inverse of −5/7 is 5/7 (they sum to zero). 3) 3/4 and 6/8 are equivalent rational numbers.
How to teach it: For comparing negative fractions, convert both to decimals first — most students find comparing −0.75 vs. −0.667 far more intuitive than comparing the fractions directly, since "closer to zero is greater" is easy to see in decimal form.
Practice: (a) Which is greater: −1/2 or −1/3? (b) Find the additive inverse of −4/9. (c) Are 2/3 and 8/12 equivalent? Answers: (a) −1/3 (closer to zero) (b) 4/9 (c) Yes (both simplify to 2/3)
What it is: Perimeter = the total distance around a shape's boundary. Area = the space inside a shape. Rectangle area = length×breadth; triangle area = ½×base×height.
Examples: 1) Rectangle 8cm×5cm: perimeter=2(8+5)=26cm, area=8×5=40cm². 2) Triangle with base 12cm, height 7cm: area=½×12×7=42cm². 3) Square of side 9cm: perimeter=4×9=36cm.
How to teach it: Have students physically measure and calculate the perimeter and area of their own textbook cover or desk — applying the formula to a real, familiar object cements it better than only using diagrams.
Practice: (a) Perimeter of a rectangle with length 15cm, breadth 9cm. (b) Area of a triangle with base 10cm, height 6cm. (c) Area of a square with side 7cm. Answers: (a) 48cm (b) 30cm² (c) 49cm²
What it is: Organising and interpreting data using tables, bar graphs, and simple measures like the average (mean) = sum of values ÷ number of values.
Examples: 1) Average of 12,18,24,30,36: sum=120, ÷5=24. 2) A bar graph with a taller bar for "Cricket" than "Football" shows more students prefer cricket. 3) A pictograph where each symbol=5 units, showing 4 symbols, represents 20 units.
How to teach it: Have the class generate their own small dataset (e.g., favourite subject, by show of hands) and build a bar graph from it themselves — creating a graph from scratch makes reading someone else's graph much easier afterward.
Practice: (a) Find the average of 14,18,22,26,30. (b) If each pictograph symbol=4 units and a row shows 5 symbols, what total does it represent? (c) In a bar graph, one bar reaches 18 and another reaches 12 — which is greater and by how much? Answers: (a) sum=110,÷5=22 (b) 20 units (c) The first, by 6
What it is: Recognising 3D shapes (cube, cuboid, cylinder, cone, sphere, pyramid) from 2D nets/drawings, and basic construction skills (drawing a specific triangle or line using a ruler and compass).
Examples: 1) A cube's net (unfolded flat shape) is 6 connected squares. 2) A cylinder has 2 flat circular faces and 1 curved surface. 3) Constructing a triangle when all 3 side lengths are known uses a compass to mark each side's length from a base line.
How to teach it: Give students an actual paper net to fold into a 3D shape (a cube net is easiest) — physically folding it from flat to solid makes the abstract "faces, edges, vertices" concept concrete.
Practice: (a) How many flat faces does a cylinder have? (b) What is a "net" of a 3D shape? (c) What tool is essential for constructing a triangle from given side lengths? Answers: (a) 2 (the two circular ends) (b) The 2D unfolded/flattened version of a 3D shape's surface (c) A compass (to mark exact lengths)
Knowing Our Numbers, Whole Numbers, Playing with Numbers (factors, multiples, HCF, LCM), Basic Geometrical Ideas, Understanding Elementary Shapes, Integers (introduction), Fractions (introduction), Decimals (introduction), Data Handling (introduction), Mensuration (perimeter basics), Algebra (introduction), Ratio and Proportion, Symmetry (introduction), Practical Geometry (introduction).
Pair this with the Class 7 Logical Reasoning notes and the IMO Class 7 mock exams built earlier in this conversation.