Download 7th Grade Math – Semester 2 Study Guide

7th Grade Math – Semester 2 Exam Study Guide
Chapter 6 -- Percents
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Percent  ratio that compares a # to 100
o percent is a relative value not an absolute value
 same % of different values gives different absolute #s
o % expresses parts per 100 or “/100”
Model  a representation that helps you visualize the “real thing”
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Converting % to decimal  move decimal point 2 places to left
Converting decimal to %  move decimal point 2 places to right
% to fraction  put % value over 100, then simplify.
o If % < 1, write it over 100, then X by how much it takes to make numerator a whole #
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2 ratios are proportional if their cross-products are equal
model  a representation that helps you visualize the real thing
o models help to identify how to write proportion (p311)
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formula: part / whole = n% / 100%
o hint  in a statement…e.g. “what is 39% of 120”…what comes after the “of” represents
the WHOLE
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to multiply by a %, turn it into a decimal first
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Sales tax = tax rate * purchase price
per cent  means per 100 or divide by 100…to do this, move decimal 2 places to left
Chapter 7 -- Geometry
Geometry Basic Concepts (7-1 to 7-2)
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Point  in spot or location. Has no size. Named with capital letter.
Line  series of points extending to ∞ in both directions. Named by two points on it.
Ray  one endpoint and extends to ∞ in other direction. Named by endpoint and another point.
Line segment  part of a line with 2 endpoints.
Plane  flat surface extending to ∞ in all directions
Intersecting lines  2 or more lines with exactly 1 point in common.
Parallel lines  lines on same plane that never intersect.
Perpendicular lines  lines that intersect and form right angle (90°).
Skew lines  lines on different planes…never intersect nor are ||
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Acute  between 0 and 90°.
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Right  90°.
Obtuse  between 90° and 180°
Straight angle  180°.
Complementary  ∑ of angles is 90°
Supplementary  ∑ of angles is 180°
Adjacent angles  2 angles next to each other, share vertex…supplementary.
Vertical angles  formed by 2 intersecting lines and are opposite each other…have = measures.
Congruent angles  angles with equal measures
Triangles
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Scalene  no congruent sides
Isosceles  at least 2 congruent sides
Equilateral  3 congruent sides
Right  1 right angle
Acute  3 acute angles
Obtuse  1 obtuse angle
∑ of all angles in a triangle = 180°
Polygons (7-5 to 7-7)
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Polygon  closed plane figure formed by 3 or more line segments
Regular polygon  all sides and angles congruent
Irregular polygon  all sides and angles not congruent
Quad  4
Lateral  lines
Penta  5
Hexa  6
Octa  8
Deca  10
Trapezoid  quadrilateralwith exactly 1 pair of || sides
Parallelogram  quadrilateral w/ 2 pairs of || sides
Rhombus  || gram with 4 congruent sides
Rectangle  || gram with 4 right angles
Square  || gram w/4 right angles and 4 congruent sides
congruent polygons have same size and shape…corresponding parts (angles and sides) are
congruent
# triangles in a polygon = # sides of polygon – 2
∑ of all angles in the polygon can be found by multiplying # of triangles that can be made in the
polygon by 180°
Circles (7-8)
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circle  set of points in a plane that are all the same distance from a given point (center).
Diameter  segment that passes through center and has both endpoints on circle
Radius  segment connecting center to the circle
o radius = ½ diameter
Central angle  angle with its vertex at the center of a circle
Chord  segment w/bot end points on circle
Arc  curve connecting 2 points on a circle
Semi-circle  arc that is ½ circle
7th Grade Math – Semester 2 Exam Study Guide
page 4 of 8
Chapter 8 -- Geometry and Measurement
Area of parallelograms and triangles
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area  there are 2 dimensions in measuring area…length and width or base and height
o area is always stated in units squared (units2) because of the two dimensions
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Area of parallelogram = bh … the base x height
Area of triangle = ½ bh … the area of a triangle is exactly one-half of a parallelogram
Area of trapezoid = ½ h (b1 + b2)
Circumference and Area of Circles (8-4)
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 …first understood by Archimedes as ratio of circumference and the radius of a circle
Circumference of a circle  C =  d
Diameter of a circle  d = 2r
Area of a circle  A =  r2
Square roots and irrational #s (8-5)
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area of a square = side x side (s2)
perfect square  product of the square of an integer
square root  inverse of squaring a #…
when we use the sq root symbol, we are referring to the non-neg sq root of a number (remember…
2 negatives multiplied together are positive)
sq root of fraction  take sq root of numerator and denominator
Irrational #s  non-terminating, non-repeating #s…cannot be written as ratio of two integers.
Pythagorean Theorem (8-6)
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Right triangle  sides that form right angle are called legs. Side opposite right angle is
hypotenuse.
Pythagorean Theorem – sum of the squares of the lengths of the legs is = to the square of the
length of the hypotenuse.
o Formula  a2 + b2 = c2
o a and b are the legs of the right triangle, c is the hypotenuse
Three-dimensional figures (8-7)
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3-dimensional figure  a solid figure with length, width, height that does not lie on a plane
height  measured as perpendicular length from one base to another
face  flat surface on 3D figure
prism  3D figure w/2 parallel and congruent faces, called bases… prism is named based on its
bases
cylinder  3D w/2 || bases that are circles
pyramid  3D w/triangular faces that meet at a point (vertex) and a base that is a polygon
7th Grade Math – Semester 2 Exam Study Guide
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cone  circular base and one vertex
sphere  set of all points in space equidistant from a center.
page 5 of 8
7th Grade Math – Semester 2 Exam Study Guide
page 6 of 8
Volume of Rectangular Prisms and Cylinders (volume = area of base x height)
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volume  number of cubic units (units3) needed to fill the space inside a 3-dimensional figure
volume of rectangular prism  lwh … or area of base (lw) x height
volume of cylinder   r2 h … or area of base ( r2) x height
Chapter 9
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graphs used to visually represent relationship between 2 or more sets of numbers / data
scale  ratio
usually label the dimensions of a graph (axes) as X and Y
interval  pattern between values on a scale
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sequence  set of numbers that follow a pattern
term  each # in a sequence
arithmetic sequence  sequence created by adding a fixed # to the previous one
geometric sequence  sequence created by multiplying a fixed # to the previous one
Functions (9-4 to 9-6)
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function  a relationship that assigns exactly 1 output value for each input
Graphing functions (9-5)
graphs typically use Y as vertical and X as horizontal axes
points on graph labeled as (x,y)
origin pt is (0,0)
to graph, create X-Y table and calculate at least 2 points
linear function (variable X is power of 1) – graphs a straight line
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parabolic function (X2)
7th Grade Math – Semester 2 Exam Study Guide
page 7 of 8
Chapter 10 – Graphing in the Coordinate Plane
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points on graph labeled as (x,y)…this is called an ordered pair
4 quadrants in coordinate plane labeled I, II, III, IV
Y is vertical axis and X is horizontal axis
Linear equations
o y = mx + b
 b  where the line crosses the y axis
 m  slope (steepness of the line)
 rise over run (rise / run)  ∆y / ∆x
o you can calculate slope from 2 points by: (y2 – y1) / (x2 – x1)
 if m is positive  line is ascending
 if m is negative  line is descending
you can graph a line 2 ways:
1. make an x y table and plot points
2. use y = mx + b
non-linear equations
o some form of y = x2  graph is a parabola
o some form of y = | x |  graph is a “V”
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translation  “slide”…moves every point the same distance and direction
reflection  “flip”…flips a figure over a line of reflection…creates a mirror image of the original…
you can fold a figure on itself
symmetry  a figure has line symmetry if a line can be drawn through the figure so that one side
is a mirror image of the other
rotation  transformation that turns a figure about a fixed point
rotational symmetry  figure can be rotated < 180° to get the figure look as it did before
7th Grade Math – Semester 2 Exam Study Guide
page 8 of 8
Chapter 12 – Probability
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Probability
o Theoretical and experimental probability
Counting Principle
o m ways of making a first choice and n ways of making a second choice, then there are
m x n ways of making a first choice followed by a specific second choice
Compound Events
o Independent events  the occurrence of one event does not affect the probability of
the occurrence of the other event
o Dependent events  the occurrence of one event affects the probability of the
occurrence of the other event
Permutations
o Factorial  5! = 5 x 4 x 3 x 2 x 1
o Arrangement of objects in a particular order…e.g., there are 16 teams competing in
Olympic Hockey. What are the number of ways that gold, silver, and bronze medals can
be given out
 the number of ways k objects can be taken out of a set of n total objects in
order
Combinations
o Grouping of objects in which the order does not matter
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 the number of ways k objects can be taken out of a set of n total objects