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Mostly Used Calculator Models for VCE Mathematics

Recommended CAS’s by VN (based on the above information and not in any particular order)
• Casio ClassPad 330*
• TI-89
• TI-89 (Titanium)
• TI-nspire CAS
• TI-nspire CAS with Touchpad
• TI-nspire CX CAS
*Known to crash during VCAA exams

Approved Calculators for VCE Mathematics (CAS)

CAS calculators
In 2012, the following CAS calculators are approved by the VCAA for use in Further Mathematics Examination 1 and Further Mathematics Examination 2, Mathematical Methods (CAS) Examination 2 and Specialist Mathematics Examination 2. The full functions of approved CAS calculators may be used (that is, the memories of these calculators do not require clearing prior to entry to the examination).

Casio
Algebra FX2.0, Algebra FX2.0 PLUS, ClassPad 300, ClassPad 300 PLUS, ClassPad 330

Hewlett Packard
HP 40G, HP 40GS, HP 48G, HP 48G II, HP 49G, HP 49G PLUS, HP 50G

Texas Instruments
TI-89, TI-89 (Titanium), TI-92/TI-92 PLUS/Voyage 200, TI-nspire CAS, TI-nspire CAS with Touchpad, TI-nspire CX CAS

What you should know for VCE Mathematical Methods Units 3&4

AREAS OF STUDY For Mathematical methods Unit 3 &4

1. Functions and graphs
This area of study covers the behaviour of functions of a single real variable, including key featuresof their graphs such as axis intercepts, stationary points and points of inflection, domain (including maximal domain) and range, asymptotic behaviour and symmetry. The behaviour of these functions is to be linked to applications in practical situations.

This area of study will include:
• graphs and identification of key features of graphs of the following functions:
– power functions, y = xn;
– exponential functions, y = ax;
– logarithmic functions, y = loge(x) and y = log10(x), the relationship a = ek where k = loge(a);
– circular functions, y = sin(x), y = cos(x) and y = tan(x);
– modulus function, y = |x| where |x| = x when x ≥ 0 and |x| = -x when x < 0;

• transformation from y = ƒ(x) to y = Aƒ(n(x + b)) + c, where, A, n, b and c ∈ R, and ƒ is one of the functions specified above and the relation between the graph of the original function and the graph
of the transformed function (including families of transformed functions for a single transformation parameter) such as:
y = 0.4/(x+3)2 , y = –10sin(n(x – c)) –5, c ∈ R, y= A(x +7)5 – 2, A ∈ R;

• graphs of polynomial functions;

• graphs of sum, difference, product and composite functions of ƒ and g where ƒ and g are functions
of the types specified above such as:
y = sin (x) + 2x y = |cos (2x)| y = x2ekx, k ∈ R
y = a /(x2 +1) a∈ R y = (x2 – 2)n, n ∈ N;
• graphical and numerical solution of equations;

• graphs of inverse functions;

• recognition of the general form of possible models for data presented in graphical or tabular form, using polynomial, power, circular, exponential and logarithmic functions;

• applications of simple combinations of the above functions (including simple hybrid functions),and interpretation of features of the graphs of these functions in modelling practical situations;
for example, y = ax + b + msin(nx) as a possible pattern for economic growth cycles or y = axne-kx + b as a model for the amount of medication remaining in the blood stream after a dose
of the medication.

2. Algebra
This area of study covers the algebra of functions, including composition of functions, simple functional equations, inverse functions and the solution of equations. This area of study includes the identification of appropriate solution processes for solving equations, and systems of simultaneous equations, presented in various forms. It covers recognition of equations and systems of equations that are solvable using inverse operations or factorisation, and the use of graphical and numerical
approaches for problems involving equations where exact value solutions are not required or which are not solvable by other methods. This should support work in the other areas of study.

This area of study will include:
• review of algebra of polynomials, equating coefficients and solution of polynomial equations with real coefficients of degree n having up to and including n real solutions;

• the relationship of ƒ(x ± y), ƒ(xy) and ƒ to values of ƒ(x) and ƒ(y) for different functions ƒ;

• logarithm laws and exponent laws, recognition of equivalent forms using compound and double angle formulas for sine, cosine and tangent;

• solution of systems of simultaneous linear equations, including consideration of cases where no solution or an infinite number of possible solutions exist; for example, to find a cubic polynomial
function ƒ that satisfies the conditions ƒ′(3) = 0, ƒ(3) = 4 and ƒ(10) = –1 (familiarity with matrix representation of systems of simultaneous linear equations with up to five equations in five unknowns will be assumed);

• composition of functions, where ƒ composition g is defined by ƒ(g(x)), given rg ⊆ dƒ, such as loge(x2+ 1), e2x– 4ex– 5, |sin(x)|;

• functions and their inverses, including conditions for the existence of an inverse function, and use of inverse functions to solve equations involving exponential, logarithmic, circular and power functions;

• solution of equations of the form aƒ(n(x + b)) + c = k and recognition of the inverse function for ƒ (over a suitable principal value domain where necessary) where a, b, c, n and k ∈ R;

• graphical and numerical approaches to solving equations where exact methods may not apply or be required, such as equations of the form aƒ(n(x + b)) + c = g(x) , where f and g are power, exponential, logarithmic or circular functions; for example, finding approximate values for the coordinates of the points of intersection of the graphs of y = 3sin(2x) and y = e-x + 1, with specification of values to a required accuracy;

• solution of literal equations such as ax3+ b = c or emx + n = k;

• general solutions of equations such as cos(x) + cos(3x) = 1/2 , x ∈ R and the specification of exact solutions or numerical solutions, as appropriate, within a restricted domain;

• solution of general equations which arise from finding the points of intersection of graphs of functions, such as a straight line with a given parabola, or y =1/x with ƒ(x) = ax2 + bx + c.

3. Calculus
This area of study covers graphical treatment of limits, continuity and differentiability (including local linearity) of functions of a single real variable and differentiation, anti-differentiation and integration of these functions. This material is to be linked to applications in practical situations.

This area of study will include:
• deducing the graph of the derivative function from the graph of a function and the relation between the graph of an anti-derivative function and the graph of the original function;

• derivatives of xn, for n ∈ Q, ex, loge(x), sin(x) and cos(x) and tan(x) (formal derivation is not required);

• properties of derivatives, (aƒ(x) ± bg(x))′ = aƒ′(x) ± bg′(x) where a, b ∈ R;
• derivatives of ƒ(x) ± g(x), ƒ(x) × g(x), and ƒ(g(x)) where ƒ and g are polynomial functions, exponential, circular, logarithmic or power functions (or combinations of these functions) such
as:
x5+ (1-x2)1/2 x sin(2x) ecos(x)

• application of differentiation to curve sketching and identification of key features of curves, identification of intervals over which a function is constant, stationary, strictly increasing or strictly
decreasing, identification of the maximum rate of increase or decrease in a given application context (consideration of the second derivative is not required) and tangents and normals to curves;

• identification of local maximum/minimum values over an interval and application to solving problems, identification of interval endpoint maximum and minimum values;

• average and instantaneous rates of change, including formulation of expressions for rates of change and related rates of change and solution and interpretation of problems involving rates of change and simple cases of related rates of change;

• the relationship ƒ(x + h) ≈ ƒ(x) + hƒ′(x) for a small value of h and its geometric interpretation;

• anti-derivatives of polynomial functions and of ƒ(ax + b) where ƒ is xn for n ∈ Q, ex, sin(x), or cos(x) and linear combinations of these;

• definition of the definite integral as the limiting value of a sum where the interval [a, b] is partitioned into n subintervals, with the i th subinterval of length δxi and containing xi*, and δx =max{δxi: i = 1, 2, … n} and evaluation of numerical approximations based on this definition;

• examples of the definite integral as a limiting value of a sum involving quantities such as area under a curve, distance travelled in a straight line and cumulative effects of growth such as inflation;

• anti-differentiation by recognition that F´ (x) = ƒ(x) implies ;

• informal treatment of the fundamental theorem of calculus, ;

• properties of anti-derivatives and definite integrals:

• application of integration to problems involving calculation of the area of a region under a curve and simple cases of areas between curves, such as distance travelled in a straight line; average value of a function; other situations modelled by the use of the definite integral as a limiting value of a sum over an interval; and finding a function from a known rate of change.

4. Probability
This area of study includes the study of discrete and continuous random variables, their representation using tables, probability functions or probability density functions (specified by rule and defining parameters as appropriate); and the calculation and interpretation of central measures and measures of spread. The focus is on understanding the notion of a random variable, related parameters, properties and application and interpretation in context for a given probability distribution.

This area of study will include:
• random variables, including:
– the concept of discrete and continuous random variables;
– calculation and interpretation of the expected value, variance and standard deviation of a random variable (for discrete and continuous random variables, including consideration of the
connection between these);
– calculation and interpretation of central measures (mode, median, mean);
– property that, for many random variables, approximately 95 per cent of their probability distribution is within two standard deviations of the mean;
– bernoulli trials and two state markov chains, including the length of run in a sequence, steady values for a markov chain (familiarity with the use of transition matrices to compute values of
a markov chain will be assumed);

• discrete random variables:
– specification of probability distributions for discrete random variables using graphs, tables and
probability functions;
– interpretation of mean (μ) median, mode, variance (σ2
) and standard deviation of a discrete
random variable and their use;
– the binomial distribution, Bi(n, p), as an example of a probability distribution for a discrete
random variable (students are expected to be familiar with the binomial theorem and related
binomial expansions);
– the effect of variation in the value(s) of defining parameters on the graph of a given probability
function for a discrete random variable;
– probabilities for specific values of a random variable and intervals defined in terms of a random
variable, including conditional probability;

• continuous random variables:
– construction of probability density functions from non-negative continuous functions of a real
variable;
– specification of probability distributions for continuous random variables using probability
density functions;

– calculation using technology and interpretation of mean (μ) median, mode, variance (σ2) and
standard deviation of a continuous random variable and their use;

– standard normal distribution, N(0, 1), and transformed normal distributions, N(μ, σ2), as examples of a probability distribution for a continuous random variable (use as an approximation to the
binomial distribution is not required);

– the effect of variation in the value(s) of defining parameters on the graph of a given probability density function for a continuous random variable;

– probabilities for intervals defined in terms of a random variable, including conditional probability (students should be familiar with the use of definite integrals, evaluated by hand or using
technology, for a probability density function to calculate probabilities; while not required,
teachers may also choose to relate this to the notion of a cumulative distribution function).

What you should know for VCE Mathematical Methods Unit 2

AREAS OF STUDY For Mathematical methods Unit 2
1. Functions and graphs
This area of study covers graphical representation of functions of a single real variable and the studyof key features of graphs of functions such as axis intercepts, domain (including maximal domain)and range of a function, asymptotic behaviour, periodicity and symmetry.

This area of study will include:
• revision of trigonometric ratios and their applications to right-angled triangles, including exact
values for sine, cosine and tangent of 30°, 45° and 60°;

• radians: unit circle definition, conversion between radians and degrees;

• the unit circle and definition of the sine, cosine and tangent functions as functions of a real variable,
including exact values for nπ/6 and nπ/, n ∈ Z;

• the relationships sin2 (x) + cos2(x) = 1 and tan(x) = ;sin(x)/cos(x)

• symmetry properties, complementary relations and periodicity properties for the sine, cosine and
tangent functions;

• graphs of circular functions of the form y = aƒ(bx) + c, where ƒ is the sine, cosine or tangent
function, and a, b and c ∈ R;

• simple applications of circular functions of the above form to model tidal heights, sound waves,bio-rhythms, ovulation cycles, temperature fluctuations during a day and the interpretation of
period, amplitude and mean value in these contexts and their relationship to the parameters a, band c;

• graphs of y = Aakx + C, where a ∈ R+, for simple cases of a, A, k and C ∈ R;

• the graph of y = loga(x) as the graph of the inverse function of y = ax, including the relationships aloga(x) = x and loga(ax) = x;

• simple applications of exponential functions of the above form to model growth and decay in populations and the physical world, appreciation and depreciation of value in finance; the interpretation of initial value, rate of growth or decay and long run value in these contexts and their relationship to the parameters A, k and C.

2. Algebra
This area of study provides an opportunity for the revision and further development of content prescribed in Unit 1, as well as the study of related algebra material introduced in the other areas of study in Unit2 including circular functions, exponential functions and logarithmic functions. The content as described in the ‘Algebra’ area of study in Unit 1 is to be distributed across Units 1 and 2.

3. Rates of change and calculus

This area of study covers first principles approach to differentiation, formal differentiation and anti-differentiation of polynomial functions and power functions and related applications, including graph sketching.

This area of study will include:
• the derivative as the gradient of the graph of a function at a point and its representation by a gradient
function;

• notation for derivatives: Dx(ƒ),dy/dx , ƒ´(x) ,d(ƒ(x))/dx;

• graphical and numerical approaches to approximating the value of the gradient function for simple polynomial functions and power functions at a given point in the domain of the function;

• first principles approach to finding the gradient function for ƒ(x) = xn, n ∈ Z and simple polynomial functions;

• derivatives of simple power functions and polynomial functions;

• applications of differentiation:
– finding rates of change;
– determining maximum or minimum values of functions, including interval endpoint maximum
and minimum values and their application to simple maximum/minimum problems;
– use of the gradient function, to assist in sketching graphs of simple polynomials, in particular,
the identification of stationary points;

• anti-differentiation as the reverse process of differentiation and identification of families of curves with the same gradient function;

• application of anti-differentiation to problems involving straight-line motion, including calculation of distance travelled.

4. Probability
This area of study covers introductory counting principles and techniques and their application to probability, the law of total probability in the case of two events, and the application of transition matrices to conditional probabilities.

This area of study will include:
• addition and multiplication principles for counting;

• combinations: concept of a selection and computation of nCr and for pascal's triangle;

• applications of counting techniques to probability;

• the law of total probability for two events Pr(A) = Pr(A|B)Pr(B) + Pr(A|B´)Pr(B´);

• use of 2 × 2 transition matrices to calculate probabilities of two state markov chains (consideration of steady state not required).

What you should know for VCE Mathematical Methods Unit 1

AREAS OF STUDY For Mathematical methods Unit 1

1. Functions and graphs
This area of study covers the graphical representation of functions of a single real variable and the study of key features of graphs of functions such as axis intercepts, domain (including maximal domain) and range of a function, asymptotic behaviour and symmetry.

This area of study will include:
• Distance between two points in the Cartesian plane, coordinates of the midpoint of a line segment,and gradients of parallel and perpendicular lines;

• use of the notation y = ƒ(x) for describing the rule of a function and evaluation of ƒ(a), where a is
a real number or a symbolic expression

• graphs of power functions y = Xn for n ∈ N and n = –1, –2, 1/2 and transformations of these to the form y = a (x + b)n + c where a, b and c ∈ R;
• graphs of polynomial functions to degree 4;

• qualitative interpretation of features of graphs, and families of graphs, including an informal
consideration of rates of change, including:
– graphs of functions that have been obtained empirically, such as heart rate data during an exercise sequence, economic trend data;
– relations as models for data, such as the weight-height index I = w/h2 kg/m2;

• ‘the vertical line test’ and its use to determine whether a relation is a function;

• graphs of relations including those specified by conditions or constraints, such as arcs of circles or a region defined by an inequality, for example ‘the set of all points whose distance from a fixed point (a, b) is less than a given value’;

• graphs of inverse relations.

2. Algebra
This area of study supports material in the ‘Functions and graphs’, ‘Rates of change and calculus’ and ‘Probability’ areas of study and this material is to be distributed between Units 1 and 2. In Unit 1 the focus is on the algebra of polynomial functions to degree 4. Content introduced in Unit 1 may be revised and further developed in Unit 2.

This area of study will include:
• use of symbolic notation to develop algebraic expressions and represent functions, relations and equations;

• substitution into, manipulation, expansion and factorisation of algebraic expressions, including the remainder and factor theorems;

• recognition of equivalent expressions and simplification of algebraic expressions involving functions and relations, including use of exponent laws and logarithm laws;

• determination of rules of simple functions and relations from given information, including polynomial functions to degree 4 and of transformations (dilation, reflection and translation) of the square root and circle relations;

• solution of polynomial equations to degree 4, analytically, numerically and graphically;

• use of inverse functions to solve equations;

• solution of equations of the form Aƒ(bx) + c = k, where A, b, c and k ∈ R, and ƒ is sine, cosine, tangent or ax using exact or approximate values on a given domain, and interpretation of these equations;

• the connection between factors of ƒ(x), solutions of the equation ƒ(x) = 0 and the horizontal axis intercepts of the graph of the function ƒ;

• solution and interpretation of simultaneous equations involving two functions by numerical, graphical and analytical methods;

• use of parameters to represent a family of functions and general solutions of equations involving these functions;

• development of polynomial models, for example by the use of finite difference tables or solution of a system of simultaneous linear equations obtained from values of a function, or a simple
combination of values of a function;

• index laws and logarithm laws, including their application to the solution of simple exponential equations;

• application of matrices to transformations of points in the plane (dilation from the coordinate axes; reflection in the coordinate axes and the line y = x, and translation from the coordinate axes), and the solution of systems of simultaneous linear equations in up to four unknowns.

3. Rates of change and calculus
This area of study covers constant and average rates of change and an informal treatment of instantaneous rate of change of a function in familiar contexts, including graphical and numerical approaches to the measurement of constant, average and instantaneous rates of change.

This area of study will include:
• average and instantaneous rates of change:
– rate of change of a linear function, use of gradient as a measure of rate of change;
– average rate of change, use of the gradient of a chord of a graph to describe average rate of change of y = ƒ(x) with respect to x, over a given interval, practical examples of average rates
of change such as average speed on a bush walk and average slope of a hill from bottom to top;
– the measurement of rates of change of polynomials functions; achieved by finding successive numerical approximations to the gradient of a polynomial function at a point by taking another
point very close to it on either side of the graph of the function, and finding the gradient of the line joining the two points, and then repeating this procedure, leading to an informal treatment
of the gradient of the tangent as a limiting value of the gradient of a chord;

• tangents to curves and local linearity of differentiable curves, use of gradient of a tangent at a point on the curve to describe instantaneous rate of change of y = ƒ(x) with respect to x, practical examples of instantaneous rates of change, such as speedometer readings and revolution counters and other applications of rates of change:
– graphs of functions and interpretation of the rate of change of a function, where the rate of change is positive, negative, or zero, relationship of the gradient function to features of the original function;
– motion graphs, construction and interpretation of displacement–time and velocity–time graphs and informal treatment of the relationship between displacement–time and velocity–time
graphs;
– use of rates of change and corresponding graphs in other contexts, such as describing the rate of change of heartbeat during an exercise sequence or the rate of change of the height of water in a container that is being filled at a constant rate.

4. Probability
This area of study covers introductory probability theory, including the concept of events, probability and representation of event spaces using various forms such as lists, grids, venn diagrams, karnaugh maps, tables and tree diagrams. Impossible, certain, complementary, mutually exclusive, conditional and independent events involving one, two or three events (as applicable), including rules for computation of probabilities for compound events.

This area of study will include:
• random experiments, events and event spaces;

• probability as an expression of long run proportion;

• simulation using simple generators such as coins, dice, spinners, random number tables and
technology;

• display and interpretation of results of simulations;

• probability of simple and compound events;

• lists, grids, venn diagrams, karnaugh maps and tree diagrams;

• the addition rule for probabilities;

• conditional probability, Pr(A|B) = Pr(A ∩ B)/ Pr(B ) ;

• independence, and the multiplication rule for independent events, Pr(A ∩ B) = Pr(A).Pr(B) when
A and B are independent events

This is how VCE (Mathematics) is evaluated...
(Please share this with Parents who have VCE level Children or with fellow students...Will be very useful for them since the schools are about to start for the new year..)

LEVELS OF ACHIEVEMENT

Units 1 and 2

Procedures for the assessment of levels of achievement in Units 1 and 2 are a matter for school decision. Assessment of levels of achievement for these units will not be reported to the Victorian Curriculum and Assessment Authority. Schools may choose to report levels of achievement using grades, descriptive statements or other indicators.

Units 3 and 4

The Victorian Curriculum and Assessment Authority will supervise the assessment of all students undertaking Units 3 and 4.
In the study of Mathematics the student’s level of achievement will be determined by school-assessed coursework and two end-of-year examinations. The Victorian Curriculum and Assessment Authority will report the student’s level of performance on each assessment component as a grade from A+ to E or UG (ungraded). To receive a study score, students must achieve two or more graded assessments and receive S for both Units 3 and 4. The study score is reported on a scale of 0–50. It is a measure of how well the student performed in relation to all others who took the study. Teachers should refer to the current year’s VCE and VCAL Administrative Handbook for details on graded assessment and calculation of the study score. Percentage contributions to the study score in Mathematics are as follows:

Further Mathematics
• Unit 3 school-assessed coursework: 20 per cent
• Unit 4 school-assessed coursework: 14 per cent
• Units 3 and 4 examination 1 : 33 per cent
• Units 3 and 4 examination 2 : 33 per cent

Mathematical Methods (CAS)
• Unit 3 school-assessed coursework: 20 per cent
• Unit 4 school-assessed coursework: 14 per cent
• Units 3 and 4 examination 1 : 22 per cent
• Units 3 and 4 examination 2 : 44 per cent

Specialist Mathematics
• Unit 3 school-assessed coursework: 14 per cent
• Unit 4 school-assessed coursework: 20 per cent
• Units 3 and 4 examination 1 : 22 per cent
• Units 3 and 4 examination 2 : 44 per cent

Examination 1 for Mathematical Methods (CAS) Units 3 and 4 and Examination 1 for Specialist Mathematics Units 3 and 4 are technology free examinations. Details of the assessment program are described in the sections on Units 3 and 4 in this study design.

Sourcehttp://www.vcaa.vic.edu.au/Documents/vce/mathematics/mathsstd.pdf

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Dear Parents and Students.... Do pay an extended attention on the assessment structure of VCE (Mathematics) to get the best out of it ...If not followed carefully you may loose the opportunities of scoring well... We intend to publish it in future posts ... if you like this idea please like this post and share it with your friends...Tnx...