Download Grade 7 Midyear Exam memory aide

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
Cartesian plane
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 gcf anf lcm
7
2 2
2
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
Measures
zero
degrees
an angle an angle
that is
that is 90°
less than exactly
90°
an angle
that is
greater
than 90°
but
less than
180°
an angle
that is
180°
exactly
an angle
that is
greater
than 180°
Measure
s 360
degrees
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
Triangle and quadrilateral
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
 Octagon = 8
 Hexagon = 6
 Nonagon = 9
 Heptagon = 7
 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
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)
ADD, SUBTRACT fractions
MULTIPLY AND DIVIDE FRACTIONS
Negative exponents