Download 7th Grade Assessment Review

SOLVING ALGEBRAIC EXPRESSIONS
• When solving – remember order of operations
PEMDAS – parentheses, exponents,
multiplication/division, addition/subtraction
• Grouping symbols include parentheses, division
bars, brackets
• Substitute the given values of the variables,
rewrite the problem, use order of operations to
solve
(calculator allowed)
Chapters 1 & 7
SOLVING ALGEBRAIC EXPRESSIONS
• Remember to enter fractions correctly into
calculator using the fraction key (a b/c) between
whole numbers and fractional parts
Example 5df + 3 when d= ¾ and f= 8
5 • 3 ab/c 4 • 8 = 30
Example 10e/4f when e=6 and f=8
10 • 6 divided by 4 • 8 = 60/32 = 1.875
(calculator allowed)
Chapters 1 & 7
NUMBER PATTERNS
• Number patterns represent something consistently
being done to a previous number
• First find the difference between the numbers; is it a
constant number or does it change?
• If it is constant, then the operations being used are
addition or subtraction
• If there is a varying difference, usually multiplication or
division are being used
• Remember to check and see if squares (a number
times itself 4 • 4) or cubes (a number times itself 3
times 5 • 5 • 5) are being used
(calculator allowed)
Chapters 1 & 7
NUMBER PATTERNS (MORE COMPLEX)
• Finding the nth term in a pattern
always let n first equal 1, then n equals 2, then n
equals 3, and so on.
substitute 1, 2, 3 into the expression and
determine which expression matches the given
numbers
Example: given the following numbers
5 7 9 11 14
Which of the following expressions matches the
pattern 3n+2 n+4 2n+3 2n+5
(calculator allowed)
Chapter 7
SCALE DRAWINGS
• Scale drawings are proportions (basically the same as
equivalent fractions with labels)
• Remember to keep like units in the same location in
the proportion
• Scale drawings are solved by multiplication or division
• Scale drawings refer to models, drawings, etc
• Scale drawings always include a key
• Check for accuracy by cross multiplying; both totals
must be equal
(calculator allowed)
Chapter 8
AREA
• Area of rectangles or squares =
length • width units squared
• When faced with irregular shaped figures, divide
the figure into known shapes (rectangles or
squares), find the area of each shape, and then
add to get the total
• Area of triangles =
½ b • h OR b • h ÷ 2 units squared
(calculator allowed)
Chapters 1 & 11
VOLUME AND SURFACE AREA
• Volume is length • width • height units cubed
• The formula for volume will be given to you; all
you have to do is multiply the 3 measurements
together.
• Surface area of a cube is 6 • side squared
• A cube is a 6 sided square; therefore find the area
of one side (length • width) and multiply that
answer by 6
(calculator allowed)
Chapter 11
CIRCLES
• PI is represented by this symbol π
• 3.14 or 22/7 is the numerical value of pi
• CIRCUMFERENCE – the distance around the
circle
• DIAMETER – the distance (a line) across a
circle passing through the center of the circle
• RADIUS – a line from the center of a circle to
one edge – twice a radius equals a diameter
(calculator allowed)
π Chapter 11
CIRCLE FORMULAS
• Circumference – to find circumference
πd (pi • diameter) or 2πr (2 • pi • radius)
• Area – to find area
πr2 (pi • radius • radius)
• If you are given the circumference or the area
and asked to find the radius or diameter, then use
division to solve.
Circumference is 998 inches; what are the diameter
and radius? 998= πd divide both sides by 3.14
(pi) and the diameter is 318 inches; divide the
diameter in half to get the radius – 159 inches
(calculator allowed)
Chapter 11
PARALLELOGRAMS & FORMULAS
• Parallelogram – a quadrilateral with 2 pairs of
parallel sides
• Area of parallelogram is b • h units squared
• Perimeter of parallelogram is 2 • top + 2 • side
or add all four sides (be sure to use a length
not the height as the side measurement
(calculator allowed)
Chapter 11
QUADRILATERALS
• Quadrilaterals all have 4 (quad) sides
• Quadrilaterals have 4 angles whose sum is 360o
• Rectangles – opposite sides are parallel and equal in length;
4 right (90o) angles
• Square – all 4 sides are of equal length; 4 right angles
• Trapezoid – 1 pair of parallel sides
• Parallelogram – opposite sides are parallel and of equal
length
• Rhombus – parallelogram with 4 equal (congruent) sides –
could be a square, but could be diamond shape
(non calculator)
Chapter 10
TRIANGLES
• The sum of the 3 angles in a triangle equal 180o
(non calculator)
Chapter 10
SCIENTIFIC NOTATION
• To change a number in standard form to scientific
notation, put the decimal to the right of the first digit,
count the number of remaining digits including the
zeros; rewrite the number with the decimal stopping
when the zeros begin. The total number of digits to
the right of the decimal is the exponent.
Example 1,287,000,000,000 in scientific notation form
becomes 1.287 x 1012
• To change a number in scientific notation to standard
form, move the decimal right the same number of
places as the exponent
Example 4.5098 x 108 becomes 450,980,000
(calculator allowed)
Chapter 2
PERCENTS
• Percents are per 100
• To find percent of an unknown number –
40% of x = 80
first turn the percent into a decimal {divide by 100 (move the decimal 2
places left)}, then solve algebraically
.40 • x = 80 .40x = 80 now divide both sides by .40 80/.40 = 200
• To find percent of a known number –
23% of 230 = x
first turn the percent into a decimal {divide by 100 (move the decimal 2
places left)}, then multiply
.25 • 230 = x .25 • 230 = 57.5
• When the percent is unknown –
What percent of 250 is 15? Divide the “is” number by the “of” number,
then multiply by 100
15/250 = 0.06 • 100 = 6%
this is the only time your answer will have a % sign in it
(calculator allowed)
Chapter 9
FRACTIONS AND DECIMALS
• To turn a fraction into a decimal; divide the
numerator by the denominator
• To turn a decimal into a fraction, write the
decimal number as the numerator over the
correct place value as the denominator –
example 0.1745 becomes 1745/10,000 – then
reduce to lowest terms (simplest form) if
possible
(calculator allowed)
Chapters 2 & 9
FRACTIONS & DECIMALS TO PERCENTS
• To turn a fraction into a percent –
first divide the numerator by the denominator, then
multiply the resulting decimal number by 100 (equates
to moving the decimal right 2 spaces)
• To turn a decimal into a percent, multiply the
decimal by 100 (see above 2 spaces right)
• To turn a percent into a decimal, divide by 100
(equates to moving the decimal 2 places left)
• To turn a percent into a fraction, put the percent over
100 and reduce to lowest terms
(calculator allowed)
Chapters 2 & 9
FORMING VARIABLE EXPRESIONS
• Addition – terms that indicate to add
plus, the sum of, increased by, total, more
than, added to
• Subtraction – terms that indicate to subtract
minus, the difference of, decreased by,
fewer than, less than, subtracted from
• Multiplication – terms that indicate to multiply
times, the product of, multiplied by, of
• Division – terms that indicate to divide
divided by, the quotient of
(calculator allowed)
Chapter 7
GRAPHS
•
•
•
•
•
•
•
•
•
•
Line graphs
Box and whisker plots
Frequency tables
Venn diagrams
Stem and Leaf plots
Data tables
Scatter plots
Bar graphs
Circle graphs
Misleading graphs and what makes them so
(non-calculator)
Chapter 3