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