quantitative aptitude

Solve age problems using past, present, and future time relations to derive algebraic equations and determine the father's present age.

Represent work and unit work using a line-bar model, derive work per unit time, and solve time and work problems for two, four, and individual workers.

Model pipes and cisterns with work per unit time, using positive and negative work; compute A and B rates (1/24, 1/32) and set 18-minute fill equation to solve for x.

Explore how time, distance, and speed interrelate using cartesian coordinates, show that average speed from variable speeds is harmonic, and solve meeting-point problems for trains with different start times.

Master relative velocity and frames of reference through train problems. Learn to compute crossing times and speeds from ground, camera, and train perspectives.

Explores upstream and downstream velocities of a boat in a stream, deriving still-water speed and stream velocity by setting up velocity relations and total travel time.

Explore averages and weighted averages to measure central tendency, using mean concepts, sum, and fractions that sum to 1, and solve hostel expenditure problems with weights.

Explore how ratios are simple comparisons and how multiplying or dividing both terms preserves the ratio, illustrated with circles and squares in 2:1. Split 672 in the ratio 5:3.

Learn to compute partnership profits by deriving investment ratios from equivalent investments for unequal durations, and apply them to shared profits like 3:4:5.

Explore direct and inverse proportions by comparing ratios, recognizing direct proportion where y1/y2 = x1/x2 and inverse proportion where y1/y2 = x2/x1, with examples using work and time.

Explore percentages as 100-based ratios and solve a stepwise distribution where 40% goes to a wife, 20% to sons, and half remains for bank deposits to determine the initial amount.

Explore profit and loss by defining cost price and selling price, examining when selling above, below, or at cost, and deriving cost price from loss scenarios to find gain percentage.

Explore simple interest through a linear function, defining principal, interest, rate, and time while showing rate times principal as the slope and solving for principal in changing-rate scenarios.

Examine how compound interest behaves like an exponential function, unlike simple interest, as interest accrues on the total amount with each period. Compare 10 rs at 100% p/a.

Master mixture and alligation to compute mixing ratios that achieve a desired price by averaging component costs; explore examples with dots and milk to balance cost and gain.

Explore how logarithms serve as the inverse of exponential functions, apply base changes and exponent rules, and simplify expressions to evaluate a numeric result.

Define area using unit squares for square, rectangle, triangle, regular polygon, circle, parallelogram, rhombus, and trapezium. Apply area to tile a room and optimize tile size by highest common factor.

Explore how clocks use degrees and lead time to measure the angle between minute and hour hands, and compute right-angle occurrences and daily gains in 24 hours.

Explore permutations and combinations, with and without repetition, using factorials, nPr, and nCr, through practical examples and word formation.

Define events and the sample space, compute probability as favorable outcomes over total outcomes, and illustrate with coin tosses, ball draws, and card draws.

Explore how angles and lengths relate in right triangles through a unit circle model, defining sine and cosine as opp/hyp and adj/hyp, then use tan for height and distance problems.

Learn to interpret data across bar graphs, pie diagrams, line graphs, and tables using Cartesian coordinates, percentages, and averages to draw meaningful conclusions.