Algebra – Things to Remember! Scientific Notation: 3.2 x 1013 The first number must be 1 < n < 10

Factorial: 5! = 5•4•3•2•1 0! = 1

Absolute Value: | -5 | = 5 |5|=5

Exponents: (−3) 2 ≠ −32 20 = 1

4−3 =

1 43

m+ n

x •x = x ( x n ) m = x n• m m

n

xm = x m−n n x ( xy ) n = x n • y n

Undefined: 6 is undefined when x = 7 since 7−x the denominator = 0. Multiply: (distribute or FOIL) ( x + 3)( x + 2) = x • x + x • 2 + 3• x + 3• 2 = x2 + 5x + 6 (a + b) 2 = a 2 + 2ab + b 2 (a − b) 2 = a 2 − 2ab + b 2

Polygons and sides: triangle – 3 quadrilateral – 4 pentagon – 5 hexagon – 6 septagon – 7 octagon – 8 nonagon – 9 decagon – 10 dodecagon - 12

Add Fractions: Get the common denominator: 5 x 3x 5 x 9 x 14 x 7 x + = + = = 6 2 6 6 6 3

Factor: Look for a GCF (greatest common factor) Factor binomial or trinomial. a 2 − b 2 = (a + b)(a − b)

Inequalities: 5 − 3x ≤ 13 + x −3 x ≤ 8 + x

Circles: Equation of circle center at origin: x 2 + y 2 = r 2 where r is the radius Equation of circle not at origin: ( x − h) 2 + ( y − k ) 2 = r 2 where (h,k) is the center and r is the radius Equations of Lines: y = mx + b slope-intercept y − y1 = m( x − x1 ) point-slope

−4 x ≤ 8 x ≥ −2

Remember to change direction

of inequality when mult/div by a negative.

x = abscissa, y = ordinate Slope: vertical change rise y2 − y1 m= = = . horizontal change run x2 − x1

Properties of Real Numbers: Commutative Property: a + b = b + a Associative Property: a+(b+c) = (a+b)+c Distributive Property: a(b+c) = ab + ac Identity: a+0=a Inverse: a + (-a) = 0 Zero Property:

ab = ba a(bc) = (ab)c a•1=a a • (1/a) = 1 a•0=0

Degree: Degree of monomial = sum of exponents 4x3 is of degree 3 x2y3 is of degree 5 Solving Equations: 1. Deal with any parentheses in the problem. 2. Combine similar terms on same side of = sign. 3. Get the needed variables on the same side of = sign. 4. Isolate the needed variable by add or subtract. 5. Find the needed variable by divide or multiply. Quadratic Equation: Interval Notation: 2 (1,5) ↔ 1 < x < 5 x − 5x + 6 = 0 Set = 0.

( x − 3)( x − 2) = 0 Factor. x = 3; x = 2 Find roots Function: Passes the vertical line test. A set of ordered pairs in which each x element has only one y element associated with it. Parallel and Perpendicular: Parallel: slopes are equal. Perpendicular: slopes are negative reciprocals (flip over and negate)

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[1,5] ↔ 1 ≤ x ≤ 5 Parabola: y = ax 2 + bx + c Axis of symmetry: −b x= 2a Roots: where the graph crosses the x-axis.

Perimeter: add the distances around the outside.

Trig: Right triangles only Pythagorean Theorem: 2 2 2 o a o Right Triangles only. c = a + b sin A = ; cos A = ; tan A = Triples: 3, 4, 5 h h a Circumference: C = 2π r = π d 5, 12, 13 Angle of elevation: from horizontal line of sight up. 8, 15, 17 Angle of depression: from horizontal line of sight down. 7, 24, 25 Area: Volume and Surface Area: Data: 5 Statistical Summary: minimum, maximum, median, 1st quartile, 1 Vrectangular solid = l i wih Atriangle = bh 3rd quartile 2 SArectangular solid = 2lh + 2hw + 2lw Quartiles divide data into 4 equal parts. s2 3 Vcylinder = π r 2 h Percentiles divide data into 100 equal parts. Aequilateral triangle = 4 2 number of scores below x SAclosed cylinder = 2π rh + 2π r Percentile rank of score x = i100 , where n is Arectangle = bh n Permutations: Asquare = bh = s 2 the number of scores. Arrangement in specific order. Mean = average. Aparallelogram = bh n! Mode = most often (may be more than one answer). d1 id 2 n Pr = Median = middle. (n − r )! Arhombus = bh = 2 Outliers = values that are far away from the rest of the data. 1 Median best describes data if outliers exist. 0! = 1 Atrapezoid = h(b1 + b2 ) Range = difference between the maximum and minimum values. 2

Acircle = π r 2 n π r2 Asector of circle = 360 1 2 Asemicircle = π r 2 1 Aquarter circle = π r 2 4 Conditional probability: P(B/A) means probability of B given A has occurred.

Box and Whisker Plot: The first and third quartiles are at the ends of the box, the median is indicated with a vertical line in the interior of the box, and the maximum and minimum are at the ends of the whiskers. Box-and-whisker plots are helpful in interpreting the distribution of data.

Sets: A ∪ B Union - all elements in both sets. A ∩ B Intersection - elements where sets overlap.

Exponential Growth and Decay: Decay: y = ab x where a > 0 and 0 < b < 1

A ' Complement - elements not in the set. { } or ∅ means null set.

Growth: y = ab x where a > 0 and b > 1

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