BCSE (Class X) cheat sheet

Reading comprehension questions: locate the specific sentence or paragraph that supports the answer; an option that is true in general but unsupported by the passage is incorrect.

Main-idea questions ask for the whole passage's central claim; detail questions ask for one stated fact. Match the question type before choosing.

Grammar: a subject and verb must agree in number; intervening prepositional phrases do not change the subject's number ("The box of pens is heavy").

Punctuation rule: a comma splice (two independent clauses joined only by a comma) is an error; use a period, semicolon, or coordinating conjunction.

Vocabulary in context: substitute each candidate word into the original sentence and test whether the sentence's meaning stays intact.

Percent change = (new value - old value) / old value x 100; a decrease gives a negative result, and successive percentage changes multiply rather than add.

Ratio and proportion: set up a/b = c/d and cross-multiply (ad = bc); for unit rates, divide the quantity by the unit count to get per-unit value.

Area formulas: rectangle = length x width; triangle = 1/2 x base x height; circle = pi x r^2; circumference = 2 x pi x r.

Science method rule: an experiment tests one independent variable at a time; the control group receives no treatment and establishes the baseline for comparison.

Mean = sum of values / number of values; median = middle value when ordered; mode = most frequent value. An outlier shifts the mean most and the median least.

Probability of a single event = favorable outcomes / total equally likely outcomes; probabilities range from 0 (impossible) to 1 (certain).

Unit conversion chains: multiply by fractions equal to 1 (e.g., 1000 mL / 1 L) so unwanted units cancel; check that the final unit matches the question.

Scientific notation: a number is written as a x 10^n with 1 <= a < 10; a positive exponent means a large number, a negative exponent a small one.

Graph reading rule: read the axis labels and units before the data; slope on a distance-time graph is speed, and a flat segment means no motion.

Significant figures: nonzero digits count; zeros between nonzero digits count; leading zeros never count; trailing zeros count only when a decimal point is present.

Rounding decision rule: if the digit after the target place is 5 or greater, round up; otherwise keep the digit unchanged.

Cause vs correlation: two variables changing together does not prove one causes the other; a controlled experiment is needed to establish causation.