REGENTS LIFESAVER
INTEGRATED ALGEBRA REGENTS EXAMINATION
June 20, 2014
FRIDAY – 8 AM
TEST FORMAT:
TEST TIPS:
Part I – 30 MC Questions (2 points each)
*show all work
Part II – 3 Qs. (2 points each)
*cancel out answers for MC questions
Part III – 3 Qs. (3 points each)
*label & # your -axis & -axis (arrows)
Part IV – 3 Qs. (4 points each)
*watch out for words in italics
*Last JUNE: 27 MC QUESTIONS = 80%
*underline important words in questions
TIME LIMIT: 3 hours (can leave after 2)
*don’t forget to label units (cm, in, yd)
*don’t forget arrows at the end of lines
TEST RULES:
*circle difficult questions & go back later
*no white-out ever
*draw pictures whenever you can
*may use a scientific or graphing calculator
*check all answers using a calculator
*Reference (formula) sheet provided in back of exam
*answer EVERY question
*cheating is forbidden
*write down formulas before using them
*REMEMBER:
Skills Review * indicates that you should memorize formula
*CHANGE CALC.TO DEGREE MODE
 Multiples & Least Common Multiples (LCM)
 Factors & Greatest Common Factors (GCF)
 Prime Numbers (2, 3, 5, 7, 11, 13, 17, 19, 23, . . .)
 Squares & Square Roots √
Perfect Squares:
 Rounding Numbers (tenths 1.0, hundredths 1.00, thousandths 1.000)
Modeling/Multiple Representations
 algebraic representations
 sample space and tree diagrams
 Classify Triangles (by sides and angles) – Equilateral, Isosceles, Scalene, Acute, Right, Obtuse
 parallel lines – same slope
 perpendicular lines – slopes are negative reciprocals of each other (ex. m = & m =
)
 inequalities ( < , > , ≠ , ≤ , ≥)
 systems of equations and inequalities (Solve for x and y)
 literal equations (formulas) ex. Solve for r. d = rt
Operations

rationals (including signed numbers and fractions)

irrationals
 simplifying irrationals
 simplifying and evaluating of algebraic expressions and formulas
 powers (exponents) ex.

polynomials COMBINE LIKE TERMS ex.
–
– –
 multiplying & dividing monomials
 multiplying binomials
–
FOIL
 Dividing polynomials by monomials
 factoring (“Can I factor out a GCF?”, Factor into 2 binomials, diff. of two perfect squares
 exponents (positive, zero and negative)
NO NEGATIVES EXPONENTS!
 Power raised to a power – MULTIPLY EXPONENTS!
 scientific notation (ex.
) ONLY 1 DIGIT LEFT OF THE DECIMAL!
 order of operations (PEMDAS)
)
Numbers and Numeration
 real numbers, including irrational roots and pi, undefined terms
 rational approximations of irrational numbers
 commutative property of addition & multiplication
 associative property of addition & multiplication
 distributive property
 identity property of addition & multiplication
 inverse property of addition & multiplication
(
or
or
)
Patterns/Functions
 solving simple linear equations algebraically
 equations with parentheses
 variables on both sides of equation
 fractional equations
 decimal equations
 translate among verbal descriptions, tables, equations, and graphs
 *graph linear relations: slope and intercept
 solving systems of linear equations and inequalities algebraically and graphically
 solving quadratic equations by factoring (We factor in the “AM”)
 *solving quadratic equations using the quadratic formula
 solving quadratic-linear pair algebraically and graphically (look for the point(s) of intersection)
 linear, quadratic, & absolute value graphs (lines, parabolas, & a graph that looks like a “V” or “”)
Measurement
 *lengths of sides and perimeters and circumference
 *areas (2-dimensional, so you’re only multiplying two values)
 *volumes (3-dimensional, so you’re multiplying three values)
 *Pythagorean theorem
 central tendencies (mean “average,” median “middle,” and mode “most”)
 sampling, tally, charts, frequency table (How “often” does something happen)
 bar graphs/histograms and cumulative frequency histograms, quartiles/percentiles
 broken line graphs, stem-and-leaf plots, box-and-whisker plots, scatter plots
 right triangle trigonometry (sine, cosine, and tangent)
 angle of elevation, angle of depression (SOH CAH TOA)
 ratios, proportions, percents
 direct variation ( ex.
)
( is the constant of variation)
 absolute value (the distance a # is away from zero on the # line)
 *distance between two points in the plane
 *midpoint ( )
 equation of a line, slope-intercept form (
)
 slope ( ) and intercepts of a line, slopes of parallel and perpendicular lines *formula
 relative error in measurement (always divide by the actual value, NOT the estimated value)
Uncertainty
 experimental and theoretical probability
 factorial notations! (ex.
)
 permutations
(order matters) and combinations nCr (order doesn’t matter)
 multiplication counting principle MULTIPLY THE # OF EACH OF THE CHOICES
 mutually exclusive and independent events
 probability of single and compound events, probability of the complement of an event
DON’T FORGET YOUR FORMULAS:
Distance formula:
Perimeter of a Figure: add all sides
d  (x1  x 2 )2  (y1  y 2 )2
Area of a square:
Midpoint Formula:
Area of a rectangle:
x  x y  y 
M (x,y)   1 2 , 1 2 
 2
2 
y 2  y1
x 2  x1

rise
run
m
y  mx  b
Equation of a Line:
= slope


2
2
2
Pythagorean Theorem: a  b  c
Circumference of a Circle: C   D
or C  2 r
Volume
of a Rectangular Solid:

V  lwh
Equation of a Circle
# of favorableoutcomes
# of possible outcomes
x2  y2  r2
Center (h, k): x  h  y  k  r
2
Equation of a Parabola:


2
2
y  ax 2  bx  c
b  b 2  4ac
Quadratic Formula: x 
2a

b
Axis of Symmetry: x 
(parabola)
2a

2
Discriminant: b  4ac

b 2  4ac
If b 2  4ac
If b 2  4ac
–

Complement: the probability of an event not
occurring.
–
Percent of Change =
Number Line:
(How many solutions will the quadratic equation have?)


Probability:
P(event) =
If
1
or A  bh
2
8, 15, 17
 Formulas: (SOH CAH TOA)
Trigonometric
Center (0, 0):
bh
 A  2

A   r2

Right Triangle Formulas:
5, 12, 13
Area of a triangle:
Area of a Circle:
= y-intercept
Pythagorean Triples: 3, 4, 5
A  bh
Area of a parallelogram:
Slope Formula: *use to find RATE OF CHANGE
m
A  bh or A  s 2
A  bh or A  lw
= POSITIVE #, then there are 2 solutions.
= ZERO, then there is only 1 solution.
= NEGATIVE #, then there are NO solutions.

amount of change
original amount
Integrated Algebra Formula Sheet
Guess what formula you’re given on the regents?!
The SLOPE FORMULA!