← HCS syllabus
HCS (Haryana)Stage 1: Preliminary Examination
Basic Numeracy (Class X Level)
What the official syllabus says
CSAT (Preliminary Examination, Paper II):
- Basic numeracy (numbers and their relations, order of magnitude, etc. -Class X level)
The level is Class X: the topics below are those of school mathematics up to that class, applied to word problems.
Topics in detail
Numbers and their relations
- Natural numbers, whole numbers, integers, rational and irrational numbers, real numbers
- Even and odd numbers, prime and composite numbers, co-primes
- Divisibility rules; remainders
- Factors and multiples; HCF and LCM and their word problems
- Fractions and decimals; recurring decimals; comparing fractions
- Powers, indices, square roots, cube roots and surds
- Simplification and the order of operations (BODMAS)
- Unit digit and number of zeros at the end of a product
Order of magnitude
- Place value, rounding off and approximation
- Estimating the result of a calculation before working it out
- Powers of ten and scientific notation
- Comparing large and small quantities; units and their conversion (lakh, crore, million, billion; metric units)
Arithmetic
- Percentages: percentage change, successive percentage changes
- Ratio and proportion; partnership; direct and inverse variation
- Averages, including weighted averages
- Profit, loss, discount and marked price
- Simple interest and compound interest
- Time and work; pipes and cisterns
- Time, speed and distance; relative speed; trains, boats and streams
- Mixtures and alligation
- Problems on ages
Algebra (Class X level)
- Linear equations in one and two variables; word problems
- Quadratic equations: roots by factorisation
- Arithmetic progressions: nth term and sum
- Simple inequalities
Geometry and mensuration
- Lines, angles, triangles (similarity, Pythagoras theorem) and circles
- Perimeter and area of triangles, quadrilaterals and circles
- Surface area and volume of cubes, cuboids, cylinders, cones and spheres
Counting, probability and statistics
- Simple counting: arrangements and selections by listing
- Probability of simple events (coins, dice, cards)
- Mean, median and mode
Relations worth knowing
| Topic | Relation |
|---|---|
| Percentage change | (new value minus old value) divided by old value, times 100 |
| Two successive changes of a% and b% | a + b + ab/100 per cent (use minus signs for decreases) |
| Simple interest | Principal times rate times time, divided by 100 |
| Compound interest (amount) | P(1 + R/100) to the power n |
| Speed | Distance divided by time; km/h times 5/18 gives m/s |
| Average | Sum of the observations divided by their number |
| HCF and LCM | For two numbers, HCF times LCM = product of the numbers |
| Arithmetic progression | nth term = a + (n minus 1)d; sum = n/2 times (2a + (n minus 1)d) |
Working method
At Class X level the difficulty lies less in the concepts than in speed and accuracy. Mental calculation, quick checks of divisibility, and estimating an answer before choosing an option save time, and an estimate also catches careless slips in a paper with a deduction for wrong answers.
Overlaps
Calculations with percentages, ratios and averages are what Data Interpretation questions need.