Topic-wise Quantitative Aptitude practice: number system, arithmetic, algebra, geometry and trigonometry, mensuration, data interpretation, statistics and probability. It is useful for OPSC ASO, OSSC, OSSSC, banking and other exams with a maths section. Each topic will get its own 30-question sets with worked solutions.
Number system and simplification
The base for every other chapter
Coming soonNumber system and divisibilityDivisibility, remainders, unit digit, consecutive numbers, largest and smallest numberQuestion types
- Types of numbers: natural, whole, integer, rational, irrational, prime, composite
- Divisibility rules for 2, 3, 4, 5, 6, 8, 9, 11
- Finding the missing digit for divisibility
- Remainder when a number or expression is divided
- Unit digit of a product or power
- Sum of consecutive odd, even and natural numbers
- Number of factors and sum of factors
- Largest and smallest number, ascending and descending order
Coming soonSimplification and BODMASBODMAS, squares and cubes, continued fractions, approximationQuestion types
- BODMAS expressions
- Squares, square roots, cubes and cube roots in expressions
- Continued fractions
- Expressions using algebraic identities
- Approximation and finding the nearest value
- Missing number in an expression
Coming soonFractions and decimalsComparing fractions, recurring decimals to fractionsQuestion types
- Comparing and ordering fractions
- Converting fractions, decimals and per cent
- Pure and mixed recurring decimals to fractions
- Operations on decimals
- Fraction of a number (word problems)
Coming soonHCF and LCMOnly LCM, only HCF, HCF × LCM = product, bells and remainder typesQuestion types
- LCM of numbers
- HCF of numbers
- HCF × LCM = product of two numbers
- HCF and LCM of fractions and decimals
- Least number which leaves a given remainder
- Greatest number which divides leaving remainders
- Bells ringing together, runners meeting
- Largest tile or container size
Coming soonIndices and surdsLaws of indices, rationalising, comparing surds, exponent equationsQuestion types
- Laws of indices; negative and fractional powers
- Solving exponent equations (find x)
- Simplifying surds
- Rationalising the denominator
- Comparing surds and finding the largest or smallest
- Unit digit and prime factors of powers
Coming soonSquare roots and cube rootsFinding roots quickly, perfect squaresQuestion types
- Square root by factorisation and division
- Cube root by factorisation
- Least number to multiply or divide to make a perfect square or cube
- Square roots of decimals and fractions
- Number of digits in a square root
Arithmetic
The core of most maths sections
Coming soonPercentageSuccessive change, price-consumption, income-saving, exam pass/fail, election, populationQuestion types
- Basic percentage of a number
- x is what per cent of y; A is x% more or less than B
- Successive percentage change and net change
- Effect on area and volume
- Price-consumption-expenditure
- Income, expenditure and savings
- Exam pass and fail marks
- Election votes and invalid votes
- Population growth and depreciation
- Venn diagram based percentage
- Commission and simple tax
Coming soonRatio and proportionProportionals, coins and rupees, income-expenditure ratioQuestion types
- Basic ratio and simplification
- Compound, duplicate and sub-duplicate ratio
- Mean, third and fourth proportional
- Dividing an amount in a ratio
- Adding a number to change the ratio
- Coins and rupees
- Income and expenditure ratio
- Ratio of ages, salaries and students
Coming soonPartnershipProfit sharing by capital and timeQuestion types
- Simple partnership (equal time)
- Compound partnership (different times)
- Partner joins or leaves midway
- Working partner's salary or share
- Finding capital or time from the profit share
Coming soonMixture and alligationAlligation rule, repeated replacement, profit on mixturesQuestion types
- Alligation rule: mixing two varieties
- Mean price of a mixture
- Milk and water ratio problems
- Repeated replacement (taking out and refilling)
- Profit or loss on a mixture
- Mixing at a given ratio of three items
Coming soonAveragesConsecutive numbers, wrong entry corrected, new member, cricket runsQuestion types
- Average of given numbers
- Average of consecutive odd, even and natural numbers
- A new member added or removed
- Wrong entry found and corrected
- Average age of a group, teacher included
- Cricket batting average and runs needed
- Combined average of two groups
- Average of first and last terms
- Monthly income and expenditure average
Coming soonProblems on agesPresent, past and future agesQuestion types
- Present age from a ratio
- Ages x years ago or hence
- Father and son, mother and daughter type
- Sum and difference of ages
- Average age based questions
Coming soonProfit and lossCP of x = SP of y, profit on SP, articles bought and sold, dishonest shopkeeperQuestion types
- CP, SP, profit and loss per cent
- Difference between SP and CP
- CP of x articles = SP of y articles
- Profit or loss on the selling price
- Bought at x per rupee, sold at y per rupee
- Two articles sold at the same price: one at profit, one at loss
- Selling in a chain (A to B to C)
- Dishonest shopkeeper and false weights
- Finding CP from the profit or loss given
Coming soonDiscountSuccessive discount, marked price above cost, discount with profitQuestion types
- Marked price, discount and SP
- Successive discounts and their single equivalent
- Marked x% above cost and discount y%: profit or loss
- Discount with a profit target
- Buy x get y free offers
Coming soonSimple interestSum becomes n times, rate and time, difference in interestQuestion types
- Basic SI = PRT/100
- Find principal, rate or time
- Sum becomes n times in t years
- Difference in SI for two rates or times
- Amount after given years
- Money lent in parts at different rates
Coming soonCompound interestYearly and half-yearly, CI − SI, instalments, growthQuestion types
- CI compounded yearly
- Half-yearly and quarterly compounding
- Difference between CI and SI for 2 and 3 years
- Sum becomes n times at CI
- Equal annual instalments
- Population growth and depreciation
- Different rates for different years
Coming soonTime and workEfficiency, M1D1 = M2D2, worker leaves or joins, men-women-boysQuestion types
- Work per day (A alone, B alone, together)
- A + B, B + C, C + A type
- Efficiency ratio
- M1D1H1 = M2D2H2
- Worker leaves or joins midway
- Men, women and boys
- Alternate days working
- Work and wages shared by work done
Coming soonPipes and cisternsFilling and emptying, taps opened alternately, leaksQuestion types
- Two pipes filling together
- Filling pipe with an emptying pipe or leak
- Fraction of the tank filled
- Pipes opened alternately
- Pipe closed after some time
Coming soonUnitary method, work and wagesProvisions, wages by work doneQuestion types
- Direct and inverse variation
- Provisions lasting for soldiers or students
- Men-days-hours with wages
- Wages divided by work done
Coming soonSpeed, time and distanceAverage speed, relative speed, arriving late or earlyQuestion types
- Conversion between km/h and m/s
- Basic speed, time, distance
- Average speed of a journey
- Relative speed: same and opposite direction
- Arriving late or early by changing speed
- Ratio of speeds and times
- Man on a bicycle or walking problems
Coming soonTrainsCrossing poles, platforms, bridges and other trainsQuestion types
- Train crossing a pole or man
- Train crossing a platform, bridge or tunnel
- Two trains crossing in the same or opposite direction
- Train crossing a moving man
- Finding the length of a train
Coming soonBoats and streamsUpstream and downstreamQuestion types
- Upstream and downstream speed
- Speed of the boat and stream
- Time to go and return
- Distance from total time
Coming soonRaces and clocksRaces, circular tracks, angle between clock handsQuestion types
- A beats B by x metres or seconds
- Dead heat and head start
- Circular track meeting time
- Angle between hands at a given time
- When the hands coincide, are opposite or at right angles
- Clock gaining or losing time
Algebra
Class 10 algebra and a little more
Coming soonPolynomials and identitiesAlgebraic identities, remainder and factor theoremQuestion types
- Algebraic identities: (a + b)², (a − b)², a² − b², a³ ± b³
- Find x³ + 1/x³ from x + 1/x
- Remainder theorem
- Factor theorem: find k
- Zeros of a polynomial; sum and product
- Degree and value of a polynomial
Coming soonLinear equations in two variablesSolving, consistency, word problemsQuestion types
- Solve by substitution or elimination
- Consistent, inconsistent and dependent pairs
- Condition for unique, no or infinite solutions
- Word problems: numbers, ages, fractions, money
Coming soonQuadratic equationsRoots, discriminant, forming equationsQuestion types
- Roots by factorisation
- Roots by the quadratic formula
- Discriminant and nature of roots
- Sum and product of roots
- Forming the equation from its roots
- Word problems on quadratic equations
Coming soonArithmetic and geometric progressionnth term, sum, means, sequencesQuestion types
- nth term of an AP
- Sum of n terms of an AP
- Three or four numbers in AP
- Which term is a given number
- nth term and sum of a GP
- Arithmetic and geometric mean
- Finding the series from Sn
Coming soonSetsOperations and Venn diagramsQuestion types
- Types of sets; roster and set-builder form
- Union, intersection, difference, complement
- Number of subsets and power set
- n(A ∪ B) formula
- Venn diagram word problems
Coming soonMatricesAddition, multiplication, equalityQuestion types
- Order and types of matrices
- Addition and scalar multiplication
- Multiplication of matrices
- Equality of matrices: find x, y
- Transpose and 2 × 2 determinant
Coming soonLogarithmLaws of logarithm, simplificationQuestion types
- Laws of logarithm
- Simplifying log expressions
- Solving for x in log equations
- Change of base and common values
Geometry, trigonometry and mensuration
Shapes, angles, areas and volumes
Coming soonGeometry: lines, triangles and circlesAngles, similar triangles, Pythagoras, circle theorems, tangentsQuestion types
- Angles made by parallel lines and a transversal
- Angle sum and exterior angle of a triangle
- Similar triangles and the basic proportionality theorem
- Pythagoras theorem and triplets
- Centres of a triangle
- Circle theorems: chords and angles
- Tangents from an external point
Coming soonTrigonometryRatios, standard angles, identities, complementary anglesQuestion types
- Trigonometric ratios from a right triangle
- Values at 0°, 30°, 45°, 60°, 90°
- Identities: sin²θ + cos²θ = 1 etc.
- Complementary angles
- Simplifying trigonometric expressions
Coming soonHeights and distancesAngles of elevation and depressionQuestion types
- Angle of elevation: height of a tower or tree
- Angle of depression from a tower or building
- Shadow length problems
- Ladder against a wall
- Two positions of the observer
Coming soonMensuration: plane figuresTriangle, quadrilaterals, circle, sectorQuestion types
- Area and perimeter of triangle, rectangle, square
- Parallelogram, rhombus, trapezium
- Circle: area, circumference
- Sector, arc and segment
- Wheel revolutions
- Path around a field, cost of fencing or flooring
Coming soonMensuration: solidsCube, cuboid, cylinder, cone, sphere, melting and recastingQuestion types
- Cube and cuboid: volume, surface area, diagonal
- Cylinder: volume, curved and total surface area
- Cone and frustum basics
- Sphere and hemisphere
- Melting and recasting
- Water level rise and filling tanks
Statistics, data interpretation and probability
Reading data and working out chances
Coming soonStatistics: mean, median, modeGrouped data, missing frequency, variance and standard deviationQuestion types
- Mean of ungrouped and grouped data
- Finding a missing value or frequency
- Median of ungrouped and grouped data
- Mode of a frequency table
- Relation: mode = 3 median − 2 mean
- Variance and standard deviation
- Range, quartiles, GM and HM basics
Coming soonData interpretationTables, bar graphs, pie charts, line graphsQuestion types
- Table
- Simple bar graph
- Multiple and divided bar graph
- Pie chart (degrees and per cent)
- Line graph
- Histogram
- Mixed graphs
Coming soonProbability I: coins, dice, cardsSimple eventsQuestion types
- Probability of a simple event; P(E) + P(not E) = 1
- One, two or three coins
- One or two dice: sums and doubles
- A pack of 52 cards
- Numbers 1 to 100: primes, multiples
- Letters of a word, days and leap year
Coming soonProbability II: balls, eventsDrawing objects, combined eventsQuestion types
- Drawing balls of a colour from a bag
- Drawing two or more objects together
- With and without replacement
- Socks, marbles and tickets
- P(A ∪ B), mutually exclusive and independent events
Previous year papers
OPSC ASO Mathematics sections, attempted as tests with answers
50 questions2025-26 ASO (Advocate General office)Mathematics, attempt as a testQuestion types
- Paper II maths, Q51–100
- Arithmetic and number system heavy
- Answers and worked solutions by EduSaint
49 questions2021-22 ASOMathematics, attempt as a testQuestion types
- Paper II maths, Q51–100
- Algebra, probability and statistics heavy
- Answers and worked solutions by EduSaint
50 questions2015-16 ASOMathematics, attempt as a testQuestion types
- Full Mathematics paper
- Polynomials, mensuration, probability
- Answers and worked solutions by EduSaint
50 questions2012-13 ASOMathematics, attempt as a testQuestion types
- Full Mathematics paper
- Number system, A.P., mensuration, statistics
- Answers and worked solutions by EduSaint
The tests open topic by topic. Each one will have a timer, scoring and explanations as the other tests on this site.