mikeyawet

• Indices


  A shorthand way of representing the repeated multiplication of a number by itself
• Indices


  • 22 = 2 x 2
  • 32 = 2 x 2 x 2
• Indices are used to perform operations on large numbers easily without the use of a calculator
• Laws of indices


  1. am x an = am+n (when expressions with the same base are multiplied, the indices are added)

  2. am / an = am-n (when expressions with the same base are divided, the indices are subtracted)

  3. (am)n = amn (note that m and n have been multiplied to yield the next index mn)

  4. a1/n = n√a

  5. an/m = (a1/m)n

  6. a0 = 1

  7. a-n = 1/an
• Indices


  Rules used to manipulate expressions involving indices
• Laws of indices


  1. When expressions with the same base are multiplied, the indices are added

  2. When expressions with the same base are divided, the indices are subtracted

  3. Raising an expression to a power, the indices are multiplied

  4. The reciprocal of an expression, the index becomes negative

  5. Raising an expression to a fractional power

  6. a^0 = 1

  7. a^(-n) = 1/a^n
• Surd


  A number written using the square root sign (√)
• Surds


  • Rational surds (e.g. √4, √9, √16) can be written as exact values
  • Irrational surds (e.g. √2, √3, √5) cannot be written as exact values
• Operations with surds


  1. Adding and subtracting surds

  2. Multiplying and dividing surds

  3. Rationalising the denominator
• Foreign exchange rate


  The value of one currency compared to another
• Simple interest


  Interest calculated on the principal amount only
• Simple interest formula


  I = Prt, where I is the interest, P is the principal, r is the annual interest rate, and t is the time period in years
• Gross income


  The total amount of money earned before taxes and deductions
• Taxable income


  The amount of income on which tax is levied, equal to gross income less any tax-exempt benefits
• Income tax


  Tax paid to the government on earned income
• Compound interest


  Interest calculated on the principal and the accumulated interest from previous periods
• Compound interest


  Interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan
• Compound interest formula


  Compound Interest = Total amount of Principal and Interest in future (or Future Value) less Principal amount at present (or Present Value)

  = [P (1 + i)^n] - P

  = P [(1 + i)^n - 1]

  (Where P = Principal, i = nominal annual interest rate in percentage terms, and n = number of compounding periods)
• Compound interest is interest that is charged on principal and interest added over regular intervals of time
• Appreciation


  The increase in value of an item
• Depreciation


  The decrease in value of an item
• Hire purchase


  A way of buying goods on credit and paying small amounts over a period of time. The goods bought do not belong to the buyer until they have paid the full agreed price
• If a solid is composed of flat surfaces, the surface area is the sum of the areas of the flat surfaces (called faces)
• Coordinate geometry


  Using the two-dimensional number plane (Cartesian plane or x-y axis) to specify the exact position of points, lines and shapes

  
• The Cartesian plane has a point of reference called the origin, with a horizontal x-axis and a vertical y-axis. Points on this plane are represented by an ordered pair (x, y)

  
• Cartesian plane


  Coordinate plane with x and y axes

  
• Points on Cartesian plane

  • A(-2,-4)
  • B(-1,-2)
  • C(1,2)
  • D(2,4)

  
• Plotting points on Cartesian plane

  1. Mark the points

  2. Join the points using a ruler

  
• Equation y = x


  Relationship between variables x and y where for any given x, y = x
• Values for y = x

  • (2,2)
  • (3,3)
• Plotting y = x on Cartesian plane


  1. Fill in table of values

  2. Write values in coordinate form

  3. Draw line on Cartesian plane

  
• Equation y = x + 1


  Relationship between variables x and y where for any given x, y = x + 1
• Plotting y = x + 1 on Cartesian plane

  1. Fill in table of values

  2. Plot points and join with line

  
• Plotting line 2 + 2/y = x


  1. Fill in table of values

  2. Plot points and join with line
• Equation of a line


  Equation connecting x and y coordinates of all points on a line

  
• 1. intercept


  Point where a line cuts the y-axis
• Gradient


  Measure of how steep a line is, calculated as vertical step/horizontal step
• Finding gradient using coordinates

  Use formula gradient = (y2 - y1)/(x2 - x1)
• Positive gradient


  Indicates an increasing line
• Negative gradient


  Indicates a decreasing line