Download Junior Year Math Studies Standards Foundations – Chapter One

Junior Year Math Studies Standards
Foundations – Chapter One
A.
Recognize, use, and manipulate numbers as well as distinguish between N, Z, Q, and R as
different sets of numbers. Perform operations with fractions. Use algebra to rearrange
(including factoring and expanding) and evaluate expressions. Rearrange literal formulas
through the use of the order of operations.
B.
Use algebra to rewrite, solve, and graph linear equations and inequalities.
C.
Use basic geometry concepts to determine area and perimeter (including on the coordinate
plane) of circles, triangles, quadrilaterals, and compound shapes. Apply the Pythagorean
Theorem to solve problems. Use right triangle trigonometry and the ratios of the six
trigonometric functions as well as their inverses to solve simple problems including those
with missing side lengths and missing angle measures.
D.
Convert between units of world currencies. Use basic statistics concepts to collect data,
make bar/pie charts, and interpret pictograms.
Numbers and Algebra – Chapter Two
E.
Recognize, use, and manipulate numbers. Make approximations using rounding and
significant digits, and calculate error and percent error. Understand factors and multiples.
Perform calculations using scientific notation and express values in standard form. Be able to
use a GDC in scientific notation mode. Use different systems of measurement including
System International/SI/Metric. Be able to link various SI units of measure together using
scientific notation.
F.
Solve linear systems of equations/simultaneous equations as well as inequalities using
substitution, elimination, and a GDC to form and interpret graphs. Determine when there
are no solutions and when there are infinitely many solutions.
G.
Use algebra to rewrite, solve, and graph quadratic equations as well as inequalities by
factoring, completing the square, and using the quadratic formula or through the use of the
graphing capabilities of a GDC.
Functions – Chapter Three
H.
Understand the definitions of functions as well as relations/ordered pairs and be able to
construct and interpret mapping diagrams. Determine the domain and range algebraically
and graphically. Determine the independent and dependent variables. Use function
notation to communicate symbolically. Use the relationships within a linear function to find x
and y intercepts and the gradient/slope/rate of change. Determine the gradient and
equation of a line from a wide variety of given circumstances. Write linear equations in
general/slope-intercept and standard forms.
I.
Use the relationships within a quadratic function to find x and y intercepts, the vertex, and
the axis of symmetry. Use the relationships within an exponential function to find x and y
intercepts as well as horizontal and vertical asymptotes.
J.
Evaluate exponential expressions and use logarithms to solve simple exponential equations.
K.
Use linear, quadratic, cubic, and exponential algebraic functions as models to solve
application problems.
L.
Sketch and graph linear, quadratic, exponential, and piecewise algebraic functions manually.
Graph linear, quadratic, exponential, and piecewise algebraic functions through the use of a
GDC.
M.
Use graph transformation concepts to graph horizontal and vertical translations, reflections,
and stretches from primary/parent/family graphs of linear, quadratic, and exponential
functions.
Trigonometric Functions – Chapter Four (Sections One through Four)
N.
Evaluate all six trigonometric functions as well as their inverses through the use of the Unit
Circle and a GDC.
O.
Graph the sine and cosine functions. Determine amplitude, period, vertical shift, maxima,
minima, zeros, intervals of increasing and decreasing, domain, range, as well as points of
transition/points of inflection from equations and graphs of sine and cosine functions.
P.
Graph transformed sine and cosine functions from equations. Extract equations from graphs
of transformed sine and cosine functions.
Polynomial Functions – Chapter Four (Sections Five through Eight)
Q.
Use graph transformation concepts to graph horizontal and vertical translations, reflections,
and stretches from primary/parent/family graphs of cubic, and quartic functions. Use a GDC
to graph linear, quadratic, cubic, and quartic functions. Determine maxima, minima, x and y
intercepts, zeros, intervals of increasing and decreasing, intervals of concave up and concave
down, stationary points of transition/points of inflection, domain, range, and end behavior
from equations and graphs of polynomial functions.
R.
Use degree of polynomials to determine the maximum number of terms, the highest power
of the variable possible, and the maximum number of zeros. Determine the numbers of real
and complex zeros.
S.
Graph hyperbolic functions manually and by using a GDC. Determine x and y intercepts,
zeros, intervals of increasing and decreasing, intervals of concave up and concave down,
domain, range, asymptotes, and end behavior from equations and graphs of hyperbolic
functions.
T.
Analyze (including determining vertical and horizontal asymptotes) unfamiliar functions
through the use of a GDC.
U.
Solve equations involving unfamiliar functions using a variety of methods.
Coordinate Geometry – Chapter Five
V.
Determine the midpoint of a segment and the distance between two points. Determine the
gradients/slopes for lines that are parallel and perpendicular. Write linear equations in
general/slope-intercept and standard forms.
W.
Determine x and y intercepts and the coordinates for all points of intersection when given
two function equations. Be able to calculate them manually and through the use of a GDC.
X.
Determine if polygons meet the requirements of special triangles and quadrilaterals.
Right Triangle Trigonometry, Analytic Trigonometry, and Spatial Geometry – Chapter Six
Y.
Use right triangle trigonometry and the ratios of the six trigonometric functions as well as
their inverses to solve complex problems including those with missing side lengths and
missing angle measures. Sketch and interpret drawings of application problems including
those with angles of depression and angles of elevation.
Z.
Use the Sine Rule/Law of Sines and Cosine Rule/Law of Cosines to solve problems.
Determine the area of any triangle.
AA.
Use formulas to determine the surface area and volume of three-dimensional shapes/solids
including cuboids, prisms, pyramids, cylinders, spheres, hemispheres, and cones.
BB.
Calculate diagonal distances in solids. Use trigonometry and geometry together to solve
complex spatial problems.
Sets - Chapter Nine
CC.
Use and interpret international set notation to communicate information symbolically.
Determine subsets, intersections, unions, and complements.
DD.
Use Venn Diagrams of two and three circles to display/model scenarios and evaluate
elements of sets.
Logic – Chapter Ten
EE.
Translate between verbal and symbolic statements involving logic connectives/operators
including implication, equivalence, negation, conjunction, disjunction, and exclusive
disjunction. Determine the truth value of statements including compound statements. Make
connections between set notation and logic notation. Verbally and symbolically state the
converse, inverse, and contrapositive of an implication and determine their truth values.
FF.
Construct truth tables for statements and compound statements including those with three
propositions. Use truth tables to classify statements as logically equivalent, tautologies, and
contradictions.
Probability – Chapter Eleven
GG.
Translate between verbal and symbolic statements involving probability scenarios. Interpret
lists, tables, and tree diagrams that depict sample space, events, and outcomes. Use Venn
Diagrams to model probability scenarios and calculate probabilities.
HH.
Compute probabilities of events, complement events, mutually exclusive events, combined
events, independent events, dependent events, and conditional events. Be able to account
for replacement or the lack of replacement.
Senior Year Math Studies Standards
Descriptive Statistics – Chapter Twelve
II.
Classify data by category descriptions. Make and interpret tables of data as well as data
displayed in bar charts, pie charts, and pictograms.
JJ.
Use measures of position including percentiles and quartiles to understand data. Use
measures of central tendency including mean, median, and mode to understand data. Use
mid-interval values to estimate the mean of group data. Link the median to 50th percentile.
Understand how the population standard deviation and mean relate to the same standard
deviation and mean.
KK.
Use measures of dispersion/variability including range, interquartile range, variance, and
standard deviation (using IBO notation) to understand data. Use and interpret statistical
notation to communicate information symbolically. Make and interpret box and whisker
plots. Understand outliers by forming and interpreting stem and leaf plots.
LL.
Construct and interpret frequency distribution tables for data sets. Calculate class widths,
class boundaries, midpoints, cumulative frequencies, relative frequencies, and cumulative
relative frequencies.
MM.
Construct and interpret histograms, frequency polygons, relative frequency polygons,
cumulative frequency graphs, and relative cumulative frequency (percentile) graphs.
Inferential Statistics – Chapter Thirteen
NN.
Form and interpret the line of regression/best fit through calculations and eyeapproximations. Use a GDC’s list functions to enter data, produce scatter plots, and
determine regression lines. Use the regression line to interpolate and extrapolate including
understanding the reliability of results. Understand how to use Pearson’s product-moment
coefficient/correlation coefficient/r-value to describe data relationships. Use the IB formula
to calculate the r-value.
OO.
Understand the usage and vocabulary of hypothesis testing including null and alternative
hypotheses, significance levels, contingency tables, expected frequencies, degrees of
freedom, as well as p values. Perform and interpret a Chi-square hypothesis test using a GDC
or the use of formulas. Use the critical values of the x2 distribution to provide information.
Use p values to for upper and lower one-tailed tests.
Calculus – Chapter Fourteen
PP.
Understand how derivatives are formed and what information they can provide. Understand
the concept of a limit using tables and graphs.
QQ.
Calculate derivatives from the limit definition. (Note: Limits must be understood only for the
narrow purposes described in standards PP and QQ.) Use the power rule to calculate first
and second derivatives for functions including polynomials as well as those where variables
have negative integer exponents.
RR.
Use the derivative to determine the equation of the tangent line at a given point on a
function. Use the derivative to determine intervals of increasing and decreasing using
interval notation. Use the derivative to locate maxima and minima (extrema) as well as
stationary points of transition/points of inflection/points of inflexion. Determine the
coordinates of absolute and local extrema over given intervals.
SS.
Use derivatives for optimization applications.
Sequences and Series – Chapter Seven
TT.
UU.
VV.
WW.
Recognize arithmetic sequences and series. Generate terms from given arithmetic
sequences. Write recursive definitions for arithmetic sequences.
Recognize geometric sequences and series. Generate terms from given geometric sequence.
Write recursive definitions for geometric sequences.
Determine arithmetic and geometric series partial sums. Determine geometric series infinite
sums. Use and interpret sigma notation to communicate arithmetic and geometric series
information symbolically.
Model scenarios and solve application problems using arithmetic and geometric sequences.
Financial Maths – Chapter Eight
XX.
YY.
ZZ.
Calculate currency conversions including commissions. Calculate and solve problems
involving simple interest. Link with arithmetic sequences.
Calculate and solve problems involving compound interest including those that compound
yearly, half-yearly, quarterly, monthly, and daily. Link with geometric sequences and
exponential functions. Determine n, the number of time periods, through the use of iterative
methods, successive approximation methods, and a GDC.
Calculate depreciation, appreciation and complete indexing for inflation. Calculate loan
repayment schemes as well as investment and savings schemes by constructing and
interpreting tables. Use GDC to calculate and solve problems involving investments, savings,
and loans.