These numbers come up again and again. Knowing them saves minutes in every quantitative section. Review them daily for a week.
These numbers come up again and again. Knowing them saves minutes in every quantitative section. Review them daily for a week.
| Formula | In plain words | How to remember it |
|---|
| % التغير = (الجديد − القديم) / القديم × 100 | Percent increase or decrease. | Always divide by the old value. |
| خصمان a% ثم b% = a + b − ab/100 | Total of two discounts in a row (not a + b). | 20% then 10% = 28%, not 30%. |
| السعر بعد زيادة p% = السعر × (1 + p/100) | Increases and decreases by one multiplication. | Up 25% = × 1.25; down 25% = × 0.75. |
| الربح = البيع − التكلفة, % الربح = الربح / التكلفة × 100 | Profit and profit percent of cost. | The percent is always of the cost. |
| I = P × r × t | Simple interest = principal × rate × years. | “P-r-t.” |
| d = v × t | Distance = speed × time. | Triangle: d on top, v and t below. |
| متوسط السرعة = المسافة الكلية / الزمن الكلي | Not the average of the two speeds. | Same distance there and back: 2v₁v₂ / (v₁ + v₂). |
| معًا: 1/t = 1/a + 1/b ⇒ t = ab / (a + b) | Time for two workers together. | “Product over sum.” 3 h and 6 h → 18 ÷ 9 = 2 h. |
| المجموع = المتوسط × العدد | The key to every average question. | When a number is added or removed, work with totals, not averages. |
| النسبة a: b من المجموع N ⇒ aN / (a + b) | Sharing an amount in a ratio. | Add the parts; one part = total ÷ number of parts. |
| زاوية الساعة = |30H − 5.5M| | Angle between the clock hands. | Each hour is 30°; the hour hand moves half a degree per minute. |
| n(n − 1) / 2 | Handshakes or games among n people. | Each meets n − 1 others; halve because a handshake has two people. |
| (a + b)² = a² + 2ab + b², (a − b)² = a² − 2ab + b² | Square of a sum and a difference. | Never forget the middle term 2ab. |
| a² − b² = (a − b)(a + b) | Difference of two squares. | Gets 51² − 49² = 2 × 100 = 200 in a second. |
| aᵐ · aⁿ = aᵐ⁺ⁿ, aᵐ / aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁰ = 1, a⁻ⁿ = 1/aⁿ | Power laws. | Multiply → add, divide → subtract, power of a power → multiply. |
| مساحة المستطيل = ط × ع, المثلث = ½ × ق × ع | Basic areas. | A triangle is half the rectangle around it. |
| متوازي الأضلاع = ق × ع, شبه المنحرف = ½(أ + ب) × ع, المعين = ½ × ق₁ × ق₂ | Areas of quadrilaterals. | Trapezoid = average of the bases × height. |
| المثلث المتطابق الأضلاع = (√3 / 4) s² | Area of an equilateral triangle; its height is (√3 / 2) s. | Comes up with the regular hexagon = 6 equilateral triangles. |
| قطر المربع = s√2, قطر المكعب = s√3 | Diagonals. | “A square has 2 dimensions → √2; a cube 3 → √3.” |
| محيط الدائرة = 2πr, مساحتها = πr² | The circle. | Double the radius: double the circumference, four times the area. |
| المكعب s³, متوازي المستطيلات ط × ع × ر, الأسطوانة πr²h | Basic volumes. | Prism or cylinder: base area × height. |
| المخروط ⅓ πr²h, الكرة (4/3) πr³ | Cone and sphere. | A cone is a third of its cylinder; a pyramid a third of its prism. |
| مساحة سطح المكعب 6s², الكرة 4πr² | Surface areas. | A cube has 6 faces of s² each. |
| الاحتمال = عدد الحالات المطلوبة / عدد الحالات الكلية | Simple probability, between 0 and 1. | The chance it does not happen = 1 − the chance it does. |
| الوسيط, المنوال, المدى | Median: the middle after sorting. Mode: the most common. Range: largest − smallest. | Always sort before finding the median. |
| + k لكل القيم | × k لكل القيم | Adding k to all: mean and median rise by k, range and spread stay. Multiplying by k: everything is multiplied. | Adding shifts the data; multiplying stretches it. |
