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13 Cards in this Set
- Front
- Back
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1st Index Law |
When multiplying terms with the same base, add the powers. Example 2^3 * 2^5 = 2^3 + 5 = 2^8 |
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2nd Index Law |
When dividing the terms with the same base, subtract the powers. Example 6^8 / 6^6 = 6^8-6 = 6^2 |
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3rd Index Law |
When raising a term (letter) in index form to another power, keep the base and multiply the powers. Examples (x^2)^3 = x^2 * 3 =x^6 |
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Zero Power Law |
Any expression (except 0) raised to the power of zero is 1. Example (2a)^0 = 1 |
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4th Index Law |
When multiplying two or more powers raised to the power of 'm', raise each power in the brackets to 'm'. Example (a * b)^m = (ab)^m = a^m + b^m |
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5th Index Law |
When dividing two or more powers raised to the power of 'm', raise each power in the brackets to 'm'. (a/b)^m = a^m/b^m |
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Scientific Notation |
Used to express very large or small numbers, uses powers of 10 for large number and negative powers of 10 for small numbers. Examples 2,350,000 = 2.35 * 10^6 0.0005 = 5 * 10^4 |
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Binomial Expansion |
An expression with two terms (x+1, x+2), two binomial expressions can be multiplied (x+1) (x+2). Method x*x x*2 1*x 1*2 =x^2 + 3x + 2 |
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Pythagoras' Theorem |
To find the hypotenuse c^2(the hypotenuse) = a^2 + b^2 To find the shorter side c^2(shorter side) + b^2 = a^2 |
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Surface Area |
The TSA of a solid is the sum of the areas of all the surfaces. Rectangular prism 2lw + 2wh +2lh Square-based pyramid b^2 + 4 (1/2 bh) |
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Circumference |
Circle 2πr 2 x π x r (radius) Sector 2r + ϴ / 360 x 2πr 2x r (radius) + ϴ (angle of sector) / 360 x 2 x π x r (radius) |
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Area Formulas |
⃞ (square) = l^2
▭ (rectangle) = l * w △ (triangle) = 1/2 b * h ▱ (parallelogram) = b * h ⏢ (trapezium) = 1/2 (a + b) h ❐ (rhombus) = 1/2 x * y ♢ (kite) = 1/2 xy ◯ (circle) = πr^2 ⌔ (sector) = ϴ/360 * πr^2 |
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Index Laws |
Multiplication Law: a^m * a^n = a^m+n Division Law: a^m / a^n = a^m-n Raising Powers Law: (a^m)^n = a^mn (ab)^m = a^m b^m (a/b)^m = a^m / b^m Zero Index Law: a^0 = 1 Negative Power Law: a^-m = 1 / a^m |
