1. 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

2. 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

3. 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

4. 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
Which of the following expressions matches the pattern 3n+2 n+4 2n+3 2n+5
(calculator allowed)
Chapter 7

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

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

12. TRIANGLES The sum of the 3 angles in a triangle equal 180o
(non calculator)
Chapter 10

13. 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 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 x 108 becomes 450,980,000
(calculator allowed)
Chapter 2

14. 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 = x = 80 now divide both sides by /.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 • 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

15. 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 becomes 1745/10,000 – then reduce to lowest terms (simplest form) if possible
(calculator allowed)
Chapters 2 & 9

16. 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

17. 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

18. 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