Basic Numeracy

What the official syllabus says

Preliminary Examination, General Studies Paper II:

• Basic numeracy (numbers and their relations, orders of magnitude, etc.) (Class X level), ...

The level is fixed by the syllabus itself: Class X mathematics. The questions are arithmetic and elementary algebra and geometry, solved without a calculator. Speed comes from knowing the methods well, not from advanced mathematics.

Topics in detail

Numbers and their relations

• Types of numbers: natural, whole, integers, rational and irrational, real; even and odd; prime and composite.
• Place value and face value; the decimal system.
• Divisibility rules for 2, 3, 4, 5, 6, 8, 9, 10 and 11.
• Factors and multiples; number of factors; prime factorisation.
• HCF and LCM, and their word problems (bells ringing together, largest tile for a floor).
• Remainders: division algorithm; remainders of sums and products.
• Unit digit of powers and products; cyclicity of last digits.
• Fractions and decimals: conversion, comparison and ordering; recurring decimals.
• Simplification and the order of operations (BODMAS).
• Squares, cubes, square roots and cube roots; indices and surds.

Orders of magnitude

• Comparing the size of numbers, fractions and powers.
• Scientific notation; thousands, lakhs, crores, millions and billions and conversion between them.
• Approximation and rounding; estimating an answer before calculating.
• Units and their conversion: length, area, volume, mass and time.

Percentages, ratios and averages

• Percentages: percentage change, successive changes, percentage points.
• Ratio and proportion; direct and inverse proportion; partnership.
• Averages; weighted averages; effect of adding or removing an item.
• Mixtures and alligation.
• Profit, loss and discount; marked price and cost price.
• Simple and compound interest; growth and depreciation.

Arithmetic word problems

• Time and work; work and wages; pipes and cisterns.
• Time, speed and distance; relative speed; trains; boats and streams; races.
• Problems on ages.
• Linear equations in one and two variables and their word problems.
• Quadratic equations (Class X): roots by factorisation and the formula.
• Arithmetic progressions: nth term and sum of n terms.

Geometry and mensuration (Class X)

• Lines and angles; triangles (congruence, similarity, the Pythagoras theorem); quadrilaterals; circles.
• Coordinate geometry: distance between two points; section formula.
• Perimeter and area of triangles, rectangles, squares, circles and combinations of figures.
• Surface area and volume of cubes, cuboids, cylinders, cones and spheres.

Counting and chance

• Simple counting by listing cases: arrangements and selections of a few items.
• Elementary probability: the probability of an event as favourable outcomes over possible outcomes (coins, dice, cards).
• Sets and Venn diagrams for counting.

Useful equivalents

Method

• Mental arithmetic: tables, squares up to 30, cubes up to 15, fraction and percentage equivalents.
• Using options to check answers; eliminating by unit digit, divisibility or estimation.

Overlaps

• Data Interpretation applies percentages, ratios and averages to tables and charts.
• Number puzzles, clocks and calendars are on the General Mental Ability page.