maths notes

Angle RelationshipsNaming and measuring angles, types of angles, vertically opposite angles, complementary and supplementary angles, angles and parallel lines. Solving geometrical problems using reasoning.Revolution - 360 degreesAcute - Less than 90 degreesObtuse - Between 90 and 1980 degreesReflex - Between 180 and 360 degreesRight - Exactly 90 degreesStraight - Exactly 80Complementary - 90-degree anglesSupplementary - 180-degree anglesAngles are measured with a protractor in degrees.The point of the angle is called a vertex.Name the angle from one end of the arm to the vertex and to the end of the other arm.Preferably try to name the angle in alphabetical order with an acute angle symbol in front.When writing 'therefore' make a little triangle with 3 dots in front.Interval - a straight line which has a starting point and an ending point.Ray - has a starting point and then just continues on.Line - A line continues on in both directions.Angles which are equal are indicated by using the same symbol.Vertically opposite angles are formed when 2 straight lines intersect.Adjacent angles have the same vertex and share a common arm.Parallel lines never meet and do not touch each other at any point. Are at the exact same angle.A line which crosses a set of parallel lines is called a transversal.If we know 1 angle, we know all of them.When a transversal line crosses at set of parallel lines, it creates -Corresponding angles.Alternate angles. - Are always equal.Co interior angles. - In parallel lines always add up to 180 degrees.The sum of a triangle always equal to 180 degrees.The exterior angle of a triangle is equal to the sum of the 2 interior opposite angles.The angle sum of a quadrilateral always equal to 360 degrees.Basic NumberPlace value, expanded notation, the four operations, order of operations, word problems, squares and square roots, cubes and cube roots, factors and multiples, HCF and LCM, factor trees, prime numbers, divisibility tests.The value of the digit depends on its place of value.Each set of numbers is set into groups of 3 separated by commas.Each group is called a period.Millions, Hundredths thousands Ten thousands Thousandths, Hundredths Tens UnitsExpanded notation is a helpful way to to rewrite numbers in order to show case the place value of each digit.E.g. 15,098 ----> 10,000, 50,000BODMASCalculations in brackets firstWork from left to rightDo division and multiplicationThen addition and subtractionPrime and composite numbersPrime number - is only divisible by itself and 1Composite number - Has other factorsThe only even prime number is 2IndicesAn index or power simplifies an expression when a number is by itself a number of times.The little number means how many times you have timesed the number. The big number is called the 'base' numberPrime FactorsEvery composite number can be expressed as a product of its prime factors. - Factor tree. ( The prime numbers that you multiply by to give that particular number.)HCFComplete a factor tree for each numberCircle the common factorsMultiply the circled numbers together to give the HCF.the HCF of 2 numbers is the largest number that goes into both of them.LCM The LCM is the smallest number which is a multiple for both numbers.Square and Cube RootsTo cube a number, just use it in a multiplication 3 times.The cube root of a number is a special value that when cubed gives the original number.IntegersNumbers bigger than 0 is a positive number.Numbers smaller than 0 are negative numbers.Negatives are the opposite of positives. - On a number lineShows the position and order of numbers.As we move to the right, the numbers become larger.As we move to the left, the numbers become smaller.Positive and negative numbers have size and direction.If they are a whole number, they are called an integer.Fractions and decimals are not integers.- Ordering IntegersAscending is from smallest to largest.Descending is from largest to smallest.- Adding and subtracting IntegersAdding a positive integer means moving to the right.Adding a negative integer is the same as subtracting the number, so we move to the left.(Don't forget the negative symbol)+ - = -+ + = +- - = +- Multiplying and Dividing+ * + = +- * - = ++ * - = -- * + = -+ / + = +- / - = ++ / - = -- / + = -Try to always simply any Order of operations question given from left to right.Convex and Concave QuadrilateralsThe diagonals of a convex quadrilateral are completely inside the quadrilateral.The diagonals of a convex quadrilateral are partly outside the quadrilateral.Fractions Numerator -----------------> Vinculum DenominatorImproper fraction - when the numerator is bigger than the denominator.Mixed numeral - a whole number and a proper fraction combined.Proper fraction - when the numerator is less in value than the denominator.Equivalent fraction - multiply or divide the numerator and denominator by the same number.Simply fractions - to make the fraction as simple as possible - in its simplest form.- Adding fractions Need a common denominator.Need to find a LCM.Whatever you do to the bottom, do to the top.Simplify.- Subtracting fractionsNeed a common denominator - LCM. Whatever you do to the bottom, do to the top.Subtract from each other.Simplify.- Finding a fraction of an amountDivide the whole number by the denominator of the fraction.Multiply the quotient (answer) by the numerator of the fraction.Simplify.- Multiplying fractionsMultiply the numeratorsMultiply the denominatorsSimplify.- Dividing fractions Turn the second fraction upside down.Multiply the numerator Multiply the denominator You can flip the 2nd fraction back around but it doesn’t really matterSimplify.Percentages, Fractions, and DecimalsDecimals, Fractions, and Percentages are just different ways of showing the same value. A Half can be written... As a fraction:1/2As a decimal:0.5As a percentage:50% - Conversions From percent to a decimal, divide by 100, move to decimal places to the left and remove the % sign.From decimal to a percent, multiply by 100, move the decimal point 2 places to the right and add a "%" sign. From fraction to a decimal, divide the top number by the bottom number (divide the numerator by the denominator).From decimal to a fraction, write down the decimal over the number 1. Multiply the top and bottom 10 for every number after the decimal point. Simplify.From fraction to a percentage, divide the top number by the bottom number then multiply the result by 100, and add the "%" sign.From percentage to a fraction, first convert to a decimal (divide by 100), write down the decimal over the number 1. Multiply the top and bottom 10 for every number after the decimal point. Simplify.