PAC Cadet Scholarship Exam cheat sheet

Subject-verb agreement: a singular subject takes a singular verb; compound subjects joined by 'and' take a plural verb, but 'each', 'every', and 'either' take a singular verb.

Active to passive conversion: move the object to subject position, use the correct form of 'be' plus the past participle, and add 'by' plus the original subject only when it matters.

Direct to indirect speech: shift present tense to past, change pronouns to match the reporter, and change time words (now becomes then, today becomes that day, tomorrow becomes the next day).

Articles: 'a' before consonant sounds, 'an' before vowel sounds (an hour, a university), 'the' for specific or previously mentioned nouns and for unique things.

Prepositions of time: 'in' for months, years, and long periods; 'on' for days and dates; 'at' for clock times and specific points (at noon, at night).

Commonly confused pairs: affect (verb) versus effect (noun); its (possessive) versus it's (it is); principal (main/head) versus principle (rule).

Conditional sentences: first conditional uses present simple plus 'will'; second uses past simple plus 'would'; third uses had plus past participle plus 'would have'.

Punctuation: a comma splice joins two independent clauses with only a comma; fix it with a full stop, semicolon, or coordinating conjunction.

Area and perimeter: rectangle area = length x width, perimeter = 2(l + w); triangle area = 1/2 x base x height; circle area = pi r squared, circumference = 2 pi r.

Pythagoras theorem: in a right triangle, a squared + b squared = c squared, where c is the hypotenuse. Common triples: 3-4-5, 5-12-13, 8-15-17.

Average speed = total distance divided by total time; convert km/h to m/s by multiplying by 5/18.

Percentage change = (new value - old value) / old value x 100; a 20% increase followed by a 20% decrease leaves a net 4% decrease, not zero.

Algebra: (a + b) squared = a squared + 2ab + b squared; (a - b)(a + b) = a squared - b squared.

Ratio and proportion: if a : b = c : d then ad = bc; divide a quantity in ratio m : n by splitting it into m + n equal parts.

Simple interest = principal x rate x time / 100; compound amount = principal x (1 + r)^n for annual compounding.

Angles: angles on a straight line sum to 180 degrees, angles at a point sum to 360 degrees, and interior angles of a triangle sum to 180 degrees.

Pakistan's provinces: Punjab (Lahore), Sindh (Karachi), Khyber Pakhtunkhwa (Peshawar), Balochistan (Quetta); Islamabad is the federal capital territory.

Pakistan's neighbours: India to the east, China to the north, Afghanistan to the northwest, Iran to the southwest; the Arabian Sea lies to the south.

Highest peaks: K2 (Godwin-Austen), 8,611 m, is the second-highest mountain in the world and lies in the Karakoram range.

Rivers of Pakistan: the Indus is the longest, rising in Tibet and flowing into the Arabian Sea; the Jhelum, Chenab, Ravi, and Sutlej are its main tributaries.

International organisations: the UN was founded in 1945 with headquarters in New York; the OIC has its secretariat in Jeddah; SAARC's secretariat is in Kathmandu.

Nobel and global firsts: Malala Yousafzai is the youngest Nobel laureate (Peace, 2014); Abdus Salam won the Physics Nobel in 1979.

Current affairs method: verify the date, the office-holder, and the source before answering; office-holders and rankings change, so rely on the most recent verified fact.

Space and science landmarks: the first artificial satellite was Sputnik 1 (1957); the first human in space was Yuri Gagarin (1961).

Five Pillars of Islam: Shahadah (declaration of faith), Salah (prayer), Sawm (fasting in Ramadan), Zakat (almsgiving), and Hajj (pilgrimage to Makkah).

Salah: five daily obligatory prayers are Fajr, Zuhr, Asr, Maghrib, and Isha; each has a fixed time window, and Fajr ends at sunrise.

Zakat is due at 2.5% of qualifying wealth held for one lunar year above the nisab threshold; it is obligatory for eligible Muslims.

Sawm: fasting from dawn (Fajr) to sunset (Maghrib) in Ramadan; it is obligatory for able adults and excused for the ill, travellers, and others specified in Islamic law.

Hajj: performed in the month of Dhul Hijjah; core rites include ihram, tawaf of the Kaaba, standing at Arafah on 9 Dhul Hijjah, and the farewell tawaf.

Sources of Islamic guidance: the Quran (revealed to Prophet Muhammad over about 23 years) and the Sunnah (the Prophet's practice recorded in hadith).

Ethics: honesty (sidq), trustworthiness (amanah), justice (adl), and kindness to parents and neighbours are core Islamic moral values.

Comparative religion: Islam, Christianity, and Judaism are Abrahamic faiths sharing belief in one God; each has its own scripture and key figures, and accurate comparison avoids misrepresenting other faiths.

Pakistan Movement timeline: All-India Muslim League founded 1906 at Dhaka; Lahore Resolution passed 23 March 1940; independence on 14 August 1947.

Key figures: Muhammad Ali Jinnah (Quaid-e-Azam) was the first Governor-General; Allama Iqbal's Allahabad Address (1930) proposed a separate Muslim state in northwest India.

Constitution: Pakistan's current Constitution was adopted in 1973; it establishes a parliamentary system, and the Prime Minister is the chief executive.

Geography: the Indus Plain is the most fertile and densely populated region; the Thar Desert lies in southeastern Sindh; the Potwar Plateau lies in northern Punjab.

Economy and resources: agriculture employs a large share of the workforce; major crops include wheat, rice, cotton, and sugarcane; the textile sector is a leading export industry.

Social studies: culture includes regional languages (Punjabi, Sindhi, Pashto, Balochi, Urdu), and Urdu is the national language while English is widely used officially.

Government structure: the Parliament has the National Assembly and the Senate; provinces are headed by a Chief Minister, and the President is head of state.

Landmarks: Badshahi Mosque and Lahore Fort are in Lahore; Mohenjo-daro in Sindh is an Indus Valley Civilisation site; Faisal Mosque is in Islamabad.