Bahria Admission Test cheat sheet

Subject-verb agreement: a singular subject takes a singular verb; a plural subject takes a plural verb; compound subjects joined by 'and' take a plural verb unless they name one idea.

Dangling modifier: an introductory participle phrase must modify the grammatical subject of the main clause, not some other noun.

Parallel structure: items joined by 'and', 'or', or 'but' must share the same grammatical form, such as all nouns, all infinitives, or all clauses.

'Fewer' modifies countable plural nouns such as books; 'less' modifies uncountable nouns such as water, time, or money.

A semicolon joins two independent clauses without a conjunction; a colon follows a complete clause and introduces a list, example, or explanation.

'Affect' is usually a verb meaning to influence; 'effect' is usually a noun meaning a result; 'effect' as a verb means to bring about.

Reading comprehension main idea: the correct main idea covers the whole passage, while a supporting detail answers only one part of it.

Inference: a valid inference must be logically supported by the passage, not merely plausible from personal opinion or outside knowledge.

Pronoun reference: a pronoun must agree with its antecedent in number and gender and must refer clearly to one stated noun.

Quadratic formula: x = [-b ± √(b²−4ac)]/(2a); discriminant D=b²−4ac gives D>0 two real roots, D=0 one repeated real root, and D<0 complex roots.

Slope: m=(y₂−y₁)/(x₂−x₁); parallel lines have equal slopes m₁=m₂; perpendicular lines have slopes whose product is −1.

Distance: d=√[(x₂−x₁)²+(y₂−y₁)²]; midpoint: ((x₁+x₂)/2, (y₁+y₂)/2).

Circle: area πr² and circumference 2πr; sphere: volume (4/3)πr³ and surface area 4πr².

Trigonometric identity: sin²θ+cos²θ=1; tanθ=sinθ/cosθ; sin30°=1/2, cos30°=√3/2, and tan45°=1.

Arithmetic sequence: a_n=a+(n−1)d and S_n=n/2[2a+(n−1)d]; geometric sequence: a_n=ar^(n−1) and S_n=a(1−r^n)/(1−r) for r≠1.

Probability: P(A∪B)=P(A)+P(B)−P(A∩B); for independent events, P(A∩B)=P(A)P(B).

Logarithms: log(ab)=log a+log b; log(a/b)=log a−log b; log(a^n)=n log a; log_b b=1 and log_b 1=0.

Percent change=(new−old)/old×100; compound interest A=P(1+r/n)^(nt), where n is the number of compounding periods per year.

Syllogism: 'All A are B' plus 'All B are C' implies 'All A are C'; 'Some A are B' does not imply 'All A are B'.

Conditional logic: A→B is equivalent to its contrapositive ¬B→¬A; the converse B→A and inverse ¬A→¬B are not equivalent.

Deductive validity concerns form, not factual truth: a valid argument can have false premises; soundness requires both validity and true premises.

Number series: test successive differences, ratios, squares or cubes, and alternating or two-step patterns before assuming a simple rule.

Letter coding: map A=1 through Z=26; reverse alphabet position=27−n; for word shifts, apply the same shift to each letter.

Blood relations: draw a family tree with gender and generation links, then trace the exact relationship from the stated person to the target person.

Direction sense: set north as +y and east as +x; a right turn is a 90° clockwise rotation; net displacement is the vector sum of all moves.

Analytical puzzles: convert each condition into a constraint; test 'if A then B' by eliminating cases where A is true and B is false.

Data sufficiency: evaluate each statement alone and then together; sufficient means exactly one answer follows, not that the statement is true.

Physics - Newton's second law: F_net=ma; weight W=mg; kinetic friction f_k=μ_kN; action-reaction pairs act on different bodies.

Physics - Constant-acceleration kinematics: v=u+at; s=ut+½at²; v²=u²+2as, where u is initial velocity, v final velocity, a acceleration, s displacement, and t time.

Physics - Ohm's law: V=IR; power P=VI=I²R=V²/R; series R_eq=R₁+R₂; parallel 1/R_eq=1/R₁+1/R₂.

Chemistry - Mole: n=m/M; 1 mol=6.022×10²³ particles; molar volume at STP is about 22.4 L for an ideal gas.

Chemistry - pH=−log[H+]; pH<7 acidic, pH=7 neutral at 25°C, pH>7 basic; strong acids ionize completely in water.

Chemistry - Periodic trends: atomic radius decreases across a period and increases down a group; electronegativity increases across and decreases down.

Biology - Photosynthesis: 6CO₂+6H₂O→C₆H₁₂O₆+6O₂ in chloroplasts; light reactions make ATP and NADPH; the Calvin cycle fixes CO₂.

Biology - DNA: A pairs with T by two hydrogen bonds, G pairs with C by three; replication is semi-conservative; transcription makes mRNA from a DNA template.

Biology - Mitosis produces two identical diploid cells; meiosis produces four haploid gametes with crossing over and independent assortment.