1
Numbers
Natural, whole, integers; even & odd; prime & composite; divisibility rules; factors & multiples. Skills: number logic, factorization speed, basic number manipulation.
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Learning objectives:
• Understand natural, whole, integers
• Identify even & odd, prime & composite numbers
• Apply divisibility rules
• Work with factors & multiples
• Develop number logic and factorization speed
2
Problems on Numbers
Digit-based problems, remainder concepts, cyclicity, unit digit problems, number formation.
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Learning objectives:
• Solve digit-based problems
• Apply remainder concepts
• Use cyclicity
• Solve unit digit problems
• Handle number formation
3
Problems on H.C.F and L.C.M
Prime factorization and division methods, applications in word problems, LCM in recurring events, HCF in grouping.
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Learning objectives:
• Apply prime factorization method
• Use division method
• Solve word problems with LCM/HCF
• Apply LCM in recurring events
• Apply HCF in grouping problems
4
Decimal Fraction
Decimal operations, fraction–decimal conversion, recurring decimals, word problems.
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Learning objectives:
• Perform decimal operations
• Convert between fraction and decimal
• Handle recurring decimals
• Solve word problems
5
Simplification
BODMAS rule, fraction and percentage simplification, approximation methods, shortcut calculations.
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Learning objectives:
• Apply BODMAS rule
• Simplify fractions and percentages
• Use approximation methods
• Apply shortcut calculations
6
Square Root and Cube Root
Prime factor and long division methods, approximation, perfect squares & cubes recognition.
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Learning objectives:
• Use prime factor method
• Apply long division method
• Use approximation
• Recognize perfect squares & cubes
7
Surds and Indices
Laws of exponents, rationalization, simplifying surds, fractional powers.
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Learning objectives:
• Apply laws of exponents
• Rationalize expressions
• Simplify surds
• Work with fractional powers
8
Logarithm
Laws of logarithms, change of base, solving logarithmic equations, simplification problems.
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Learning objectives:
• Apply laws of logarithms
• Use change of base
• Solve logarithmic equations
• Simplify using logarithms
9
Percentage
Basic percentage, increase & decrease, successive percentage, reverse percentage, real-life applications.
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Learning objectives:
• Calculate basic percentage
• Handle increase & decrease
• Apply successive percentage
• Apply reverse percentage
• Solve real-life applications
10
Ratio and Proportion
Basic ratio, proportion equations, continued proportion, comparison problems.
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Learning objectives:
• Understand basic ratio
• Solve proportion equations
• Apply continued proportion
• Solve comparison problems
11
Chain Rule
Direct and inverse proportion, work-rate applications.
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Learning objectives:
• Apply direct proportion
• Apply inverse proportion
• Solve work-rate applications
12
Average
Simple average, weighted average, combined average, missing value problems.
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Learning objectives:
• Calculate simple average
• Apply weighted average
• Find combined average
• Solve missing value problems
13
Partnership
Profit sharing, time-weighted partnership, capital variation problems.
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Learning objectives:
• Apply profit sharing
• Handle time-weighted partnership
• Solve capital variation problems
14
Alligation or Mixture
Alligation rule, replacement problems, weighted mixing, two & three variable mixtures.
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Learning objectives:
• Apply alligation rule
• Solve replacement problems
• Handle weighted mixing
• Solve two & three variable mixtures
15
Time and Distance
Speed, distance, time relation; relative speed; unit conversions; meeting problems.
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Learning objectives:
• Apply speed-distance-time relation
• Calculate relative speed
• Convert units
• Solve meeting problems
16
Problems on Trains
Platform crossing, pole crossing, train overtaking, opposite direction problems.
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Learning objectives:
• Solve platform crossing
• Solve pole crossing
• Handle train overtaking
• Solve opposite direction problems
17
Boats and Streams
Upstream & downstream, effective speed, current calculation.
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Learning objectives:
• Solve upstream & downstream problems
• Calculate effective speed
• Find current
18
Races and Games
Head start, dead heat, relative speed comparison.
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Learning objectives:
• Handle head start problems
• Solve dead heat problems
• Compare relative speed
19
Height and Distance
Trigonometric ratios, angle of elevation and depression, shadow problems.
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Learning objectives:
• Apply trigonometric ratios
• Use angle of elevation
• Use angle of depression
• Solve shadow problems
20
Time and Work
Work efficiency, LCM method, alternate day work, combined work problems.
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Learning objectives:
• Calculate work efficiency
• Apply LCM method
• Solve alternate day work
• Solve combined work problems
21
Pipes and Cistern
Filling & emptying, leak problems, efficiency comparison.
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Learning objectives:
• Solve filling & emptying problems
• Handle leak problems
• Compare efficiency
22
Profit and Loss
Cost price & selling price, marked price & discount, successive discount, profit percentage comparison.
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Learning objectives:
• Apply CP & SP
• Handle marked price & discount
• Apply successive discount
• Compare profit percentage
23
Simple Interest
SI formula, principal calculation, time calculation, real-life problems.
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Learning objectives:
• Apply SI formula
• Calculate principal and time
• Solve real-life problems
24
Compound Interest
CI formula, difference between SI & CI, half-yearly & quarterly compounding, growth problems.
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Learning objectives:
• Apply CI formula
• Find difference between SI & CI
• Apply half-yearly & quarterly compounding
• Solve growth problems
25
True Discount
Present worth, banker's formula, application-based problems.
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Learning objectives:
• Calculate present worth
• Apply banker's formula
• Solve application-based problems
26
Banker's Discount
Banker's gain, present value, comparison with true discount.
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Learning objectives:
• Calculate banker's gain
• Find present value
• Compare with true discount
27
Stocks and Shares
Face value, market value, dividend calculation, yield problems.
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Learning objectives:
• Understand face value and market value
• Calculate dividend
• Solve yield problems
28
Problems on Ages
Age ratio problems, past & future age, linear age equations.
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Learning objectives:
• Solve age ratio problems
• Handle past & future age
• Form and solve linear age equations
29
Calendar
Leap year logic, odd days method, day calculation.
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Learning objectives:
• Apply leap year logic
• Use odd days method
• Calculate day of week
30
Clock
Angle between hands, coinciding positions, time calculation problems.
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Learning objectives:
• Find angle between hands
• Determine coinciding positions
• Solve time calculation problems
31
Area
Triangles, quadrilaterals, circles, composite figures.
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Learning objectives:
• Calculate area of triangles, quadrilaterals, circles
• Solve composite figures
32
Volume and Surface Area
Cube, cuboid, cylinder, cone, sphere, frustum.
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Learning objectives:
• Calculate volume and surface area of cube, cuboid, cylinder, cone, sphere, frustum
33
Permutation and Combination
nPr, nCr, circular permutations, selection problems.
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Learning objectives:
• Apply nPr and nCr
• Solve circular permutations
• Solve selection problems
34
Probability
Basic probability, complement rule, independent events, conditional probability.
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Learning objectives:
• Apply basic probability
• Use complement rule
• Handle independent events
• Apply conditional probability
35
Odd Man Out and Series
Number series, alphabet series, pattern detection, missing term.
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Learning objectives:
• Identify number and alphabet series
• Detect patterns
• Find missing term