REGENTS LIFESAVER
INTEGRATED ALGEBRA REGENTS EXAMINATION
JANUARY 28, 2010
THURSDAY - 12 PM
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 x-axis & y-axis (arrows)
Part IV – 3 Qs. (4 points each)
*watch out for words in italics
*Last JUNE: 15 MC QUESTIONS = 65%
*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
*draw pictures whenever you can
*no white-out ever, no pencils (except for graphs)
*may use a scientific or graphing calculator
*check all answers using a calculator
*no formula sheet provided
*answer EVERY question
*cheating is forbidden
*write down formulas before using them
*REMEMBER: π ≠ 3.14
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 √
 Rounding Numbers (tenths, hundredths, thousandths, ten-thousandths, hundred-thousandths,…)
Modeling/Multiple Representations
 algebraic representations
 sample space, and tree diagrams
 Classifications of 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 = ¾ & m = -4/3)
 inequalities ( < , > , ≠ , ≤ , ≥)
 systems of equations and inequalities
 literal equations (formulas)
Operations
 + , - , •, ÷ rationals (including signed numbers and fractions)
 + , - , •, ÷ irrationals
 simplifying irrationals
 simplifying and evaluating of algebraic expressions and formulas
 powers – exponents ex. 48 = 4·4·4·4·4·4·4·4
 + , - polynomials COMBINE LIKE TERMS ex. (2xy + 3x – 4) + (4xy – x – 1)
 multiplying & dividing monomials
 multiplying binomials (2x + 3)(x – 4) FOIL
 Dividing polynomials by monomials
 factoring (common term, into binomials, difference of two squares)
 exponents of integers and expressions (including positive, zero and negative)
 scientific notation (ex. 3.567 x 106)
 order of operations (PEMDAS)
Numbers and Numeration
 real numbers, including irrational roots and pi, undefined terms
 rational approximations of irrational numbers
 closure property
 commutative property of addition & multiplication a + b = b + a or a • b = b • a
 associative property of addition & multiplication a + (b + c) = (a + b) + c or a • (b • c) = (a • b) • c
 distributive property a(b + c) = a(b) + a(c)
 identity property of addition & multiplication a + 0 = a
b•1=b
 inverse property of addition & multiplication a + -a = 0
b • (1/b) = 1
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
 *solving quadratic equations using the quadratic formula
 solving quadratic-linear pair algebraically and graphically
 linear and quadratic graphs (parabola and circle)
Measurement
 *lengths of sides and perimeters and circumference
 *areas
 *volumes
 *Pythagorean theorem a2 + b2 = c2
 central tendencies (mean “average,” median “middle,” and mode “most”)
 sampling, tally, charts, frequency table
 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
 ratios, proportions, percents
 direct variation ( ex. y = x, y = 3x, y = -5x) y = k x (k 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 (M)
 equation of a line, slope-intercept form (y = mx + b)
 slope (m) and intercepts of a line, slopes of parallel and perpendicular lines *formula
 error in measurement and consequence on subsequent calculations
 ratios of perimeters (a : b) and areas (a2 : b2) of similar figures, volumes (a3 : b3) of similar solids
Uncertainty
 experimental and theoretical probability
 factorial notations! (ex. 5! = 5 • 4 • 3 • 2 • 1)
 permutations nPr (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  x2 )2 (y1  y2 )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
m
m = slope
Area of a Circle:
b = y-intercept
Volume of a Rectangular Solid:
A
bh
2
1
or A  bh
2
A   r2
Circumference of a Circle: C   D
or C  2 r
V  lwh
Right Triangle Formulas:
Pythagorean Theorem: a 2
Area of a triangle:
rise
run
y  mx b
Equation of a Line:
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
Percent of Change =
 b2  c2
Pythagorean Triples: 3, 4, 5
8, 15, 17
5, 12, 13
amount of change
original amount
Probability: 0 < P(event) < 1
P(event) =
# of favorable outcomes
# of possible outcomes
P(A and B) = P(A) • P(B)
Equation of a Circle
Center (0, 0):
Center (h, k):
P(A or B) = P(A) + P(B) – P(A and B)
x 2 y 2  r 2
x  h  y  k
2
Equation of a Parabola:
Quadratic Formula:
Axis of Symmetry:
(parabola)
2
 r2
y  ax2  bx c
Complement: the probability of not having
and event P(~event) = 1 – P(event)
Trigonometric Formulas: (SOH CAH TOA)
b  b 2  4ac
x
2a
b
x
2a
Discriminant: b 2  4ac
(How many solutions will the quadratic equation have?)
2
If b  4ac = POSITIVE #, then there are 2 solutions.
If
b 2  4ac
= ZERO, then there is only 1 solution.
If
b 2  4ac
= NEGATIVE #, then there are NO solution s.
Number Line:
Integrated Algebra Formula Sheet