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Grade 7 Midyear Exam. Memory Aid 2014. Prime and Composite Numbers. Prime number has only 2 divisors: E.g. 17 has 1 and 17. Composite number has more than 2 divisors: E.g. 24 has 1,2,3,4,6,8,12,24
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Grade 7 Midyear Exam Memory Aid 2014
Prime and Composite Numbers • Prime number has only 2 divisors: E.g. 17 has 1 and 17. • Composite number has more than 2 divisors: • E.g. 24 has 1,2,3,4,6,8,12,24 • Factorization: the number written as a product of factors. E.g. 24 written as 2 x 12 or 3 x 8 • Prime factorization: the number written as a product of its prime factors. E.g. 24 = 2 x 2 x 2 x 3 or 23 x 3
Order of Operations (bedmas) • 1. brackets • 2. exponents • 3. multiplication • 4. division • 5. addition • 6. subtraction • 3 and 4 can switch, 5 and 6 can switch
rounding • Example: 875.2763 • Round to the nearest hundred: 900 • Round to the nearest ten: 880 • Round to the nearest one: 875 • Round to the nearest tenth: 875.3 • Round to the nearest hundredth: 875.28 • Round to the nearest thousandth 875.276 • Look at the number to its right, if 5 or more add one and everything becomes zero after it, if 4 or less don’t change the number.
Exponents, square root • 45 = 4 x 4 x 4 x 4 x 4 • 40 = 1 • 41 = 4 • (-3)2 = -3 x -3 = +9 • (-3)3 = -3 x -3 x -3 = -27 • √16 = 4 because 4 x 4 = 16 (opposite of exponent 2)
Point, line, segment, ray • Angle bisector
Factor Trees for gcfanf lcm GCF = 2 x 3 = 6 LCM = 2 x 2 x 2 x 2 x 3 x 7 = 336
Graphs • 2 types of variables: qualitative (flavor or color) and quantitative (height, age) • Range = highest number – lowest number • Mean = average (add all the numbers and divide by the number of items) • Median = middle number in a list when the numbers are in order • Mode = the number that occurs most often • E.g. = 1,3,6,2,5,8 • range = 8-1 = 7 • mean = (1+3+6+2+5+8)/6 = 25/6 • median = 1,2,3,5,6,8 = (3+5)/2 = 4 • mode = none
Average • Sum of all the values divided by the total number of values.
Integers IF YOU ARE NOT SURE = USE YOUR CALCULATOR • Sum of 2 positive integers is positive • Sum of 2 negative integers is negative Subtracting Integers • -12 -5 = -12 + -5 = -17 • 26 - -14 = 26 + 14 = 40 Multiplication and Division • + x + or + ÷ + positive - x + or -÷ + negative • - x – or -÷ - positive + x – or +÷ - negative
Angle types and measures Zero angle
Opposite and adjacent angles • Opposite (1 = 3 or 2 = 4) Adjacent Same vertex, common side, not overlapping
Complementary and supplementary angles • Complementary: add up to 90 degrees and form a right angle. • Supplementary: add up to 180 degrees and form a straight line.
Alternate interior, exterior and corresponding angles • Alt int, alt ext and corresponding angles are congruent or equal when 2 parallel lines intersect a transversal line.
Parallel, perpendicular, intersecting and perpendicular bisector
Translation and reflection • Reflect by doing perpendicular lines with a triangular ruler on the reflection line. • Translate by doing parallel lines to the vector (prolong vector first) with a triangle on the vector and a ruler against the triangle.
Algebra • Rule for a series of numbers: • Term = common difference x rank + number • Term and rank = 2 different letters • Common difference = link between numbers • Number = first term of series – common difference • Example: y = 4x -3 • If x = 7, solve for y y = 4 x 7 – 3 = 28 – 3 = 25 • When x = 7, y = 25
Polygons • Polygon = plane figure with closed broken line • Regular polygon = all sides and angles are congruent • Convex polygon = all interior angles are less than 180o • Perimeter = add all sides (be careful with units)
Quadrilateral page 177 important • Four sided polygon • Sum of interior angles = 360 degrees • Pentagon =5 • Hexagon = 6 • Heptagon = 7 • Octagon = 8 • Nonagon = 9 • Decagon = 10 • Hendecagon = 11 • Dodecagon = 12
Angles of polygons • n = number of sides of polygon • Measure one 1 of the interior angles of a regular polygon: • (n – 2) x 180 ÷ n • Sum of the measures of the interior angles of a polygon: • S = (n-2) x 180
triangles • Sum of interior angles = 180 degrees
Probabilities • Dice: 1,2,3,4,5,6 • Cards: 4 suits (hearts, clubs, spades, diamonds) • 13 cards per suit (1-10 + jack, queen, king) • And = multiply • Or = add • Sample space: all outcomes of an event
Scientific notation • 235 = 2.35 x 102 • 0.0256 = 2.56 x 10-2 • 4.76 x 103= 476 • 100.02 x 10-4= 0.010002 • Scientific to real: if positive exponent move decimal point to the right, if negative exponent move decimal point to the left. • Real to scientific: if number is smaller than 1, exponent will be negative, if number is larger than 1, exponent will be positive.
conversions • King Henry Doesn’t Usually Drink Chocolate Milk • Kilo-, Hecto-, Deca-, unit (meter, gram, liter), Deci-, Centi-, Milli- • 2 options • Moving right = multiply by 10 • Moving left = divide by 10 • Move decimal point left or right depending on what your initial unit is and where you want to end up.
Decimal, percent and fraction conversions • A) fraction to decimal: divide numerator by denominator • B) fraction to percent: divide numerator by denominator, multiply answer by 100 and add % sign • C) percent to decimal: remove % sign, divide by 100 • D) percent to fraction: remove % sign, put over denominator of 100 and reduce if possible • E) decimal to fraction: multiply by 100 and put over denominator of 100, reduce if possible • F) decimal to percent: multiply by 100 and add % sign
fractions • Finding a common denominator: what is the least common multiple between both denominators, change both to the new number and adjust your numerator (what you do to the bottom, you also do to the top)
