Important Notes and FormulasNumbers
Test of Divisibility
Standard formThis is a convenient way to write very large or very small numbers, using the from a x 10^{n}, where n is a positive or negative integer, and a s between 1 to 10 inclusive.An example: More examples: 123 400 written as standard form is 1.234 x 10^{5}0.0000987 written as standard form is 9.87 x 10^{-5}Multiplying numbers in standard form Dividing numbers in standard form Adding and Subtracting numbers in standard form - Make the index between the 2 numbers the same so that it is easier to factorise the numbers before adding eg Scales and MapsGiven that a map has a scale of 1:10 000, this means that 1cm on the map represents 10,000cm on the actual ground.1cm : 200m = 1cm : 0.2km = 1cm^{2} : 0.04km^{2} ProportionA. Direct ProportionThis means that when y increases, x increases, and vice versa. Use this equation: y = kx B. Indirect Proportion This means that when y increases, x decreases, and vice versa. Use this equation: y=k/x Percentage ChangePercentage Profit and LossSimple Interest and Compound InterestA. Simple Interest FormulaB. Compound Interest Formula C. Compound interest compounded MONTHLY Formula: S = P(1 + r/k)^{n} S = final value P = principal r = interest rate (expressed as decimal eg 4% = 0.04) k = number of compounding periods Note:
If $4000 is invested at an annual rate of 6.0% compounded monthly, what will be the final value of the investment after 10 years? Since the interest is compounded monthly, there are 12 periods per year, so, k = 12. Since the investment is for 10 years, or 120 months, there are 120 investment periods, so, n = 120. S = P(1 + r/k)^{n} S = 4000(1 + 0.06/12)^{120} S = 4000(1.005)^{120} S = 4000(1.819396734) S = $7277.59 Coordinate Geometry FormulasFrom: http://www.dummies.com/how-to/content/coordinate-geometry-formulas.htmlAlgebraic Manipulation
ax + bx = x(a+b) ax + bx + kay + kby = x(a+b) + ky(a+b) = (a+b)(x+ky) (a+b)^{2} = a^{2} + 2ab + b^{2}(a-b)^{2 }= a^{2} - 2ab + b^{2-}a^{2} - b^{2} = (a + b)(a - b) Solving algebraic fractional equationsAvoid these common mistakes!Solution of Quadratic EquationsCompleting the SquareStep 1: Take the number or coefficient before x and square itStep 2: Divide the square of the number by 4 Eg. y = x^{2} + 6x - 11 y = x^{2} + 2x(6/2) + (6/2)^{2} - 11 - (6/2)^{2} y = (x + 3)^{2} - 20 Sketching Graphs of Quadratic EquationsA. eg. y= +/-(x - h)^{2} + kSteps 1. Identify shape of curve
Steps 1. Identify shape of curve
InequalitiesWays to solve equalities:1. Add or subtract numbers from each side of the inequality eg 10 - 3 < x - 3 2. Multiply or divide numbers from each side of the inequality by a constant eg 10/3 < x/3 3. Multiply or divide by a negative number AND REVERSE THE INEQUALITY SIGNS eg. 10 < x becomes 10/-3 > x/-3 Example Geometrical terms and relationshipsParallel LinesPerpendicular Lines Right Angle Acute Angles: angles less than 90^{o} Obtuse Angles: angles between 90^{o} and 190^{o}Obtuse Angles: angles between 180^{o} and 360^{o} ^{Polygons}Polygon: a closed figure made by joining line segments, where each line segment intersects exactly 2 othersIrregular polygon: all its sides and all its angles are not the same Regular Polygon: all its sides and all its angles are the same The sum of angles in a polygon with n sides, where n is 3 or more, is Name of Polygons
Triangles
Quadrilaterals
Similar Plane FiguresFigures are similar only if
Similar Solid FiguresSolids are similar if their corresponding linear dimensions are proportional.Congruent FiguresCongruent figures are exactly the same size and shape.2 triangles are congruent if they satisfy any of the following: a. SSS property: All 3 sides of one triangle are equal to the corresponding sides of the other triangle. b. SAS property: 2 given sides and a given angle of one triangle are equal to the corresponding sides and angle of the other triangle. c. AAS property: 2 given angles and a given side of one triangle are equal to the corresponding angles and side of the other triangle. d. RHS property: The hypothenuse and a given side of a right-angled triangle are equal to the hypothenuse and the corresponding side of the other right-angled triangle. BearingsA bearing is an angle, measured clockwise from the north direction.Symmetry
Angle properties
Angle Properties of CirclesMensurationAll the mensuration formulas you'll ever need can by found here...http://oscience.info/math-formulas/mensuration-formulas/ But here's a quick reference for the important ones... Area of Figures
Radian Measure
Volume of Figures
TrigonometryPythagora's theoremTrigonometrical RatioSINE RULETo find an angle, can write as follows: COSINE RULEArea of TriangleMeanModeThe mode is the most frequent value.MedianThe median of a group of numbers is the number in the middle, when the numbers are in order of magnitude (in increasing order).If you have n numbers in a group, the median in: Types of Chart1. Bar chart: the heights of the bars represent the frequency. The data is discrete.2. Pie chart: the angles formed by each part adds up to 360^{o} 3. Histogram: it is a vertical bar graph with no gaps between the bars. The area of each bar is proportional to the frequency it represents. 4. Stem-and-leaf diagram: a diagram that summarises while maintaining the individual data point. The stem is a column of the unique elements of data after removing the last digit. The final digits (leaves) of each column are then placed in a row next to the appropriate column and sorted in numerical order. 5. Simple frequency distribution and frequency polygons: a plot of the cumulative frequency against the upper class boundary with the points joined by line segments. 6. Quartiles Probability is the likelihood of an event happening
2 events are independent if the outcome of one of the events does not affect the outcome of another 2 events are dependent if the outcome of one of the events depends on the outcome of another
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