Classwise Practice Tests

Q1. Describe the geometric figure formed by all points in a plane situated exactly 4 cm from a fixed point P.📘 Playing with Constructions📕 Provided book — p. 188, 8.1 · Circles & Curved Constructions

Q2. For a square with corners P, Q, R, S, determine which cyclic permutations are valid names and which are invalid.📘 Playing with Constructions📕 Provided book — p. 193, 8.2 · Constructing Squares

Q1. Add integers using positive and negative tokens: (+6)+(+4), (-3)+(-2), (+5)+(-7), (-2)+(+6).📘 The Other Side of Zero📕 Provided book — p. 257, 10.2 · Additive Inverses & Zero Pairs

Q2. Explain why angle APB cannot simply be named angle P when multiple rays emanate from vertex P.📘 Lines and Angles📕 Provided book — p. 20, 2.5 · Angles & Notation

Q3. Determine missing room dimensions and total built-up floor area (1050 sq ft) for Charan's house layout.📘 Perimeter and Area📕 Provided book — p. 146, 6.3 · Area of Rectangles and Squares

Q4. Calculate the area of composite polygons by partitioning them into right triangles and rectangles.📘 Perimeter and Area📕 Provided book — p. 144, 6.3 · Area of Triangles

Q1. Determine whether line b or line c is parallel to line a by testing constant perpendicular distance.📘 Parallel and Intersecting Lines📕 Provided book — p. 114, Figure it Out 5.2 · Concept of Parallel Lines

Q2. Write improper decimal quantities: 234 hundredths as 2.34 and 105 tenths as 10.5.📘 A Peek Beyond the Point📕 Provided book — p. 64, In-Text Exploration · Decimal Place Value System

Q1. Calculate unknown angles from transversal diagrams: e = 69°, f = 48°, g = 122°, and h = 75°.📘 Parallel and Intersecting Lines📕 Provided book — p. 123, Figure it Out 5.4 · Angle Calculations in Parallel Lines

Q2. Prove using parallel lines that when base angles sum to 180° or more, arms are parallel or diverge, so no triangle can exist.📘 A Tale of Three Intersecting Lines📕 Provided book — p. 162-163, In-Text Exploration · Angle Sum Property of Triangle

Q3. Subtract algebraic expressions: (a) -3a+15b-32, (b) 16y+18x-23, (c) 10h-27g+2, (d) -(3a+3b+32), (e) -13y-13x+6, (f) 3h-16g+30.📘 Expressions Using Letter-Numbers📕 Provided book — p. 103, Figure it Out 4.3 · Addition & Subtraction of Expressions

Q4. In parallelogram ABCD with AB||CD and AD||BC, angle DAC=65°, ADC=60°; calculate CAB (55°), ABC (60°), and BCD (120°).📘 Parallel and Intersecting Lines📕 Provided book — p. 122, In-Text Exploration · Angle Calculations in Parallel Lines

Q1. Prove the three fundamental magic square constraints: magic sum must be 15, center number must be 5, and 1 and 9 must be on edge centers.📘 Number Play📕 Provided book — p. 134-136, In-Text Exploration · Magic Squares

Q1. Evaluate (-1)^5 and (-1)^56, and determine if (-2)^4 equals 16.📘 Power Play📕 Provided book — p. 22, In-Text Exploration · Concept of Powers & Exponents

Q2. Investigate quadrilaterals formed by joining two equilateral, isosceles, or scalene triangles.📘 Quadrilaterals📕 Provided book — p. 104, In-Text Exploration · Constructions & Theorems

Q3. Describe the Mayan vertical place value system (base 20/360) and its seashell zero placeholder.📘 A Story of Numbers📕 Provided book — p. 75, In-Text Exploration · Ancient Positional Systems

Q4. Analyze how Gumulgal, Bakairi, and Bushmen developed independent equivalent counting in 2s.📘 A Story of Numbers📕 Provided book — p. 56, In-Text Exploration · Base-n Number Systems

Q1. Expand (a-b)(a+b), (a-b)(a^2+ab+b^2), and (a-b)(a^3+a^2b+ab^2+b^3), identifying the general pattern.📘 We Distribute, Yet Things Multiply📕 Provided book — p. 143, Figure it Out 6.1 · Distributive Property & Polynomial Products

Q2. Prove the alternating sum test for 11 using place values being alternatingly 1 more/less than 11.📘 Number Play📕 Provided book — p. 128, In-Text Exploration · Divisibility Rules for 9 and 11

Q1. The diameter of a circle is AB. Point C is on the circumference. What is the measure of ∠ACB? Explain your reasoning.📘 I'm Up and Down, and Round and Round📕 Provided book — p. 114, End-of-Chapter · Angles Subtended by Chords & Arcs

Q1. In ΔABC, D is the midpoint of AB. P is any point on BC, and Q on AB is such that CQ || PD. Prove that Area(ΔBPQ) = 1/2 Area(ΔABC).📘 Measuring Space: Perimeter and Area📕 Provided book — p. 143, 6.2 · Area of Quadrilaterals & Polygons

Q2. A chord of a circle of radius r subtends 60° at the centre. Show that the area of the minor segment is equal to πr²(1/6 - √3/4).📘 Measuring Space: Perimeter and Area📕 Provided book — p. 148, 6.3 · Area Related to Circles & Segments

Q3. Simplify the rational expression (assuming non-zero denominator): (w³ - v³ + x³ + 3wvx) / (w² + v² + x² - 2wv - 2vx + 2wx)📘 Exploring Algebraic Identities📕 Provided book — p. 87, 4.5 · Cubic Identities

Q1. Sponges lack true tissues and organs. Which cellular feature confirms their taxonomic placement in Animalia? (Presence of cell membrane / lack of cell wall).📘 Patterns in Life: Diversity and Classification📕 Provided book — p. 249, Revise, Reflect, Refine · Animalia: Non-Chordates to Chordates

Q2. An object is moving with a strictly constant velocity in a straight line. Is there any net external force acting upon it? (No, net force is zero)📘 How Forces Affect Motion📕 Provided book — p. 101, Pause and Ponder · Balanced & Unbalanced Forces

Q3. In the taxonomic hierarchy, which rank - class or genus - contains fewer species but exhibits a significantly higher degree of shared characteristics? (Genus)📘 Patterns in Life: Diversity and Classification📕 Provided book — p. 250, Revise, Reflect, Refine · Basis of Biological Classification

Q4. Which option defines the core function of biogeochemical cycles? (To recycle essential chemical nutrients continuously between biotic and abiotic spheres).📘 Earth as a System: Energy, Matter, and Life📕 Provided book — p. 267, Revise, Reflect, Refine · Biogeochemical Cycles (Carbon, Nitrogen, Water)

Q1. Observe two different animals in your school campus. List diagnostic anatomical features that place them into separate phyla or classes.📘 Patterns in Life: Diversity and Classification📕 Provided book — p. 249, Revise, Reflect, Refine · Animalia: Non-Chordates to Chordates

Q2. A motorbike moving at 28 m/s with constant acceleration stops after travelling 98 m. Find its acceleration (-4 m/s²) and time taken to come to a stop (7 s).📘 Describing Motion Around Us📕 Provided book — p. 69, Revise, Reflect, Refine · Acceleration & Kinematic Equations

Q3. Define albedo (reflectivity) and explain the positive feedback loop: global warming melts high-albedo ice, exposing low-albedo ocean, accelerating warming.📘 Earth as a System: Energy, Matter, and Life📕 Provided book — p. 267, Revise, Reflect, Refine · Anthropogenic Impacts & Climate Change

Q1. True/False: sin θ = 4/3 for some angle θ. Justify your answer.📘 Introduction to Trigonometry📕 Provided book — p. 121, Ex 8.1 · Algebraic & Monotonic Properties of Trig Ratios

Q2. In triangle ABC, DE || BC. Find AD if DB=7.2cm, AE=1.8cm, EC=5.4cm.📘 Triangles📕 Provided book — p. 84, Ex 6.2 · Basic Proportionality Theorem (Thales)

Q1. Vertical pole of length 6 m casts shadow 4 m; at same time tower casts shadow 28 m. Find height of tower.📘 Triangles📕 Provided book — p. 97, Ex 6.3 · Applications & Proofs of Similarity

Q2. Product of two consecutive positive integers is 306. Represent in the form of a quadratic equation.📘 Quadratic Equations📕 Provided book — p. 42, Ex 4.1 · Applied Word Problems on Quadratics

Q3. E is on CB produced of isosceles ABC (AB=AC). If AD perp BC and EF perp AC, prove triangle ABD ~ ECF.📘 Triangles📕 Provided book — p. 97, Ex 6.3 · Applications & Proofs of Similarity

Q4. Train travels 480 km at uniform speed. If speed was 8 km/h less, it takes 3 hours more. Represent as quadratic equation.📘 Quadratic Equations📕 Provided book — p. 42, Ex 4.1 · Applied Word Problems on Quadratics

Q1. Triangle ABC circumscribes circle of radius 4 cm, BD=8 cm, DC=6 cm. Find the sides AB and AC.📘 Circles📕 Provided book — p. 152, Ex 10.2 · Theorems & Proofs on Tangents

Q2. Prove: tan θ / (1 - cot θ) + cot θ / (1 - tan θ) = 1 + sec θ cosec θ.📘 Introduction to Trigonometry📕 Provided book — p. 131, Ex 8.3 · Trigonometric Identities & Proofs

Q3. Spiral made of 13 successive semicircles with alternating centres, radii 0.5, 1.0, 1.5, 2.0 cm. Find total length (π=22/7).📘 Arithmetic Progressions📕 Provided book — p. 69, Ex 5.3 · Word Problems & Real-Life AP Models

Q1. Why does dry HCl gas not change the colour of dry litmus paper?📘 Acids, Bases and Salts📕 Provided book — p. 25, In-Text 3 · Aqueous Solutions & Ionisation (pH Scale)

Q2. What criteria do we use to decide whether something is living or non-living?📘 Life Processes📕 Provided book — p. 81, In-Text 1 · Autotrophic & Heterotrophic Nutrition

Q1. Describe the microscopic structure and filtration mechanism of nephrons in the human kidney.📘 Life Processes📕 Provided book — p. 98, In-Text 5 · Excretion in Animals and Plants

Q1. In a group of 100 sports car buyers, 40 bought alarm systems, 30 purchased bucket seats, and 20 purchased an alarm system and bucket seats. If a car buyer chosen at random, bought an alarm system, what is the probability they also bought bucket seats?📘 Probability📕 Provided book — p. 318, 9.4 · Conditional Probability - Sports Car Options

Q2. A manufacturer reckons that the value of a machine, which costs him Rs. 56200, will depreciate each year by 20%. Find the estimated value at the end of 3 years.📘 Sequences and Series📕 Provided book — p. 154-155, 5.4 · Depreciation Application - GP

Q3. In a clinic, 10% of patients have liver disease and 5% are alcoholics. Among those patients diagnosed with liver disease, 7% are alcoholics. Find the probability that a patient has liver disease given that they are an alcoholic.📘 Probability📕 Provided book — p. 322-323, 9.6 · Bayes' Theorem - Diagnostic Screening

Q4. If (-1, 1), (2, 3), (1, 0), (2, 1) are some of the elements of A x B, then find A and B. Also find the remaining elements of A x B.📘 Relations📕 Provided book — p. 112, 4.3 · Cartesian Product Elements

Q1. In a factory manufacturing bulbs, units A, B and C manufacture 25%, 35% and 40% of bulbs respectively. Of their outputs, 5%, 4% and 2% are defective. A bulb drawn at random is found to be defective. What is the probability that it was manufactured by unit B?📘 Probability📕 Provided book — p. 326, 9.6 · Bayes' Theorem - Multi-Unit Factory Output

Q2. A car repair manager identifies starting troubles: Battery (A1, 0.4, start prob 0.3), No petrol (A2, 0.3, start 0), Flooded (A3, 0.1, start 0.8), Other (A4, 0.2, start 0.5). Find: (a) Probability that the car starts upon instructions (b) If it starts, probability that the car had a battery problem.📘 Probability📕 Provided book — p. 325, 9.6 · Bayes' Theorem - Workshop Diagnosis

Q1. Evaluate the principal value of cos^-1(-1/2).📘 Inverse Trigonometric Functions📕 Provided book — p. 26, 2.1 · Principal Value Branches

Q1. Discuss the continuity of f(x) = {x+2 for x<=1; x-2 for x>1} at x=1.📘 Continuity and Differentiability📕 Provided book — p. 110, Ex. · Continuity of Functions at a Point/Interval

Q2. Find the anti-derivative F(x) of f(x) = 4x^3 - 6 where F(0) = 3.📘 Integrals📕 Provided book — p. 233, Ex. · Indefinite Integrals & Elementary Forms

Q3. Find the relationship between a and b so that f(x) = {ax+1 for x<=3; bx+3 for x>3} is continuous at x=3.📘 Continuity and Differentiability📕 Provided book — p. 117, 5.1 · Continuity of Functions at a Point/Interval

Q4. Evaluate the definite integral from -1 to 2 of |x^3 - x| dx.📘 Integrals📕 Provided book — p. 276, Ex. · Definite Integrals & Properties

Q1. Evaluate the integral of (3x - 2) / [(x + 1)^2 * (x + 3)] dx.📘 Integrals📕 Provided book — p. 255, Ex. · Integration by Partial Fractions

Q2. Find the indefinite integral of (x + 3) / sqrt(5 - 4x - x^2) dx.📘 Integrals📕 Provided book — p. 250, Ex. · Integration by Substitution

Q3. Evaluate the definite integral from 0 to pi of log(1 + cos x) dx.📘 Integrals📕 Provided book — p. 280, 7.1 · Definite Integrals & Properties