Download Standards, Calculators and Graphics Calculators

Standards, Calculators and Graphics Calculators
GRADE 10
Grade 10 ADV
Std
Strand/Topic
Reasoning and Problem Solving
1
Use mathematical
reasoning to solve
problems
Number and Algebra
3
Use index notation and
solve numerical problems
Ref
4
4.3
5
Generate and manipulate
algebraic expressions
and formulae, and solve
algebraic equations
Generate and solve
problems with functions
and graphs
General application in Standards 1.1 to 1.14
3.1
5.4
5.14
5.19
Geometry and Measures
6
Develop geometrical
reasoning and proof, and
solve geometric problems
6.5
6.8
Probability and Statistics
8
Collect, process,
represent, analyse and
interpret data and
reach conclusions
10
Use of ICT
Specific Details
8.7
8.10
10.1
Understand exponents and nth roots, and apply the laws of
indices to simplify expressions involving exponents; use
the xy key on a calculator.
Identify and sum arithmetic sequences, including the first n
consecutive positive integers, and give a ‘geometric proof’
for the formulae for these
sums.
Use a graphics calculator or graph plotter and pencil and
paper methods to plot and interpret a range of functional
relationships, some continuous and others discontinuous,
arising in familiar contexts.
Interpret the solution set of the simultaneous equations E1
and E2, where E1 and E2 are the equations of two straight
lines.
Recognise a second-order polynomial in one variable, y =
ax2 + bx + c, as a quadratic function; plot graphs of such
functions (recognising that these are all parabolas) and
identify the intercepts with the coordinate axes, the axis of
symmetry and the coordinates of the maximum or
minimum point; understand when quadratic functions are
increasing, when they are decreasing and when they are
stationary.
Use a calculator to find sine and cosine values of a given
angle and to find the angle corresponding to a given value
of the sine or cosine of that angle, and know that these are
inverse functions defined on a restricted domain.
Use Pythagoras’ theorem to find the distance between two
points, to solve triangles, to find Pythagorean triples, and
to set up the Cartesian equation of a circle of radius r,
centred at the point (,).
Calculate measures of spread, including the variance and
standard deviation.
Draw stem-and-leaf diagrams and box-and-whisker plots
and use them in presentations of findings.
Use a calculator with statistical functions to aid the
analysis of large data sets, and ICT applications to present
statistical tables and graphs.
GRADE 11
Grade 11 FDN
Std
Strand
Reasoning and Problem Solving
1
Use mathematical
reasoning to solve
problems
Number and Algebra
Ref
Specific Details
General application in Standards 1.1 to 1.14
Specific reference to graphic calculators in Math Standards
Prepared by David Stubbs, updated 9 June 2009
Mosaica Education Inc.
Page 1
Std
5
Strand
Generate and solve
problems with functions
and graphs
Ref
5.1
5.10
5.13
5.14
5.16
Specific Details
Use a graphics calculator to plot and interpret a range of
simple functional relationships, some continuous and
others discontinuous, arising in familiar contexts.
Model a range of situations with appropriate quadratic
functions
Find approximate solutions of the quadratic equation ax2 +
bx + c = 0 by reading from the graph of y = ax2 + bx + c the
x-coordinate(s) of the intersection point(s) of the graph of
this function and the x-axis.
Find exactly by algebraic means, and approximately from
the points of intersection of a straight line with the graph of
a quadratic function, the solution set of two simultaneous
equations L1 and Q1, where L1 represents a linear relation
for y in terms of x, and Q1 a quadratic function of y in
terms of x.
Understand the statement y is inversely proportional to x
and set up the corresponding equation y = k/x; know some
characteristics, including that x ≠0 and that x = 0 is an
asymptote to the curve, as is y = 0; study examples of
inverse proportionality.
Geometry and Measures
6
Trigonometry
6.10
Use a calculator to find sine and cosine values of a given
angle and to find the angle corresponding to a given value
of the sine or cosine of that angle, and know that these are
inverse functions defined on a restricted domain.
Probability and Statistics
9
Use of ICT
9.1
Use a calculator with statistical functions to aid the
analysis of large data sets, and ICT applications to present
statistical tables and graphs.
Grade 11 ADV
Std
Strand/Topic
Ref
Reasoning and Problem Solving
1
Use mathematical
reasoning to solve
problems
Number and Algebra
5
Generate and solve
5.5
problems with functions
and graphs
5.6
5.7
5.8
5.10
Specific Details
General application in Standards 1.1 to 1.14
Find approximate solutions of the quadratic equation
ax2 + bx + c = 0 by reading from the graph of y = ax2
+ bx + c the x-coordinate(s) of the intersection
point(s) of the graph of this function and the x-axis.
Solve equations and inequalities using algebra or a
combination of algebra and graphical representation.
Use the graph of the function f(x) = ax2 + bx + c to
determine regions where ax2 + bx + c is greater than
or less than zero.
Find exactly by analytical methods and approximately
by graphical methods, the solution set of two
simultaneous equations L1 and Q1, where L1
represents a linear relation for y in terms of x, and Q1
a quadratic function of y in terms of x.
Understand the statement y is inversely proportional
to x and set up the corresponding equation y = k/x;
know some characteristics, including that x ≠0 and
that x = 0 is an asymptote to the curve, as is y = 0;
Specific reference to graphic calculators in Math Standards
Prepared by David Stubbs, updated 9 June 2009
Mosaica Education Inc.
Page 2
Std
Strand/Topic
Ref
5.11
5.18
Specific Details
study examples of inverse proportionality.
Use a graphics calculator, including use of the trace
function, to show approximate solutions to physical
problems requiring the location and physical
interpretation of the intersection points of two or more
graphs.
Understand the ideas of exponential growth and
decay and the forms of the associated graphs y = ax,
where a > 0; use a graphics calculator to plot the
graphs of the exponential function, ex, and the
natural logarithm function, ln x; know that one is the
inverse function of the other and use this to find
solutions to physical problems; solve for x the
equation y = ax and use this in problems; use the log
function (logarithm in base 10) on a calculator.
Probability and Statistics
14
Simulation
14.1
Use coins, dice or random numbers to generate
models of random data.
15
15.1
Use a calculator with statistical functions to aid the
analysis of large data sets, and ICT applications to
present statistical tables and graphs.
Use of ICT
GRADE 12
12 FDN
Std
Strand/Topic
Reasoning and Problem Solving
1
Use mathematical
reasoning to solve
problems
Number and Algebra
3
Use index notation and
solve numerical problems
5
Generate and solve
problems with functions
and graphs
Ref
5
5.8
Geometry and Measures
6
Trigonometry
6.10
Use a calculator to find sine and cosine values of a given
angle and to find the angle corresponding to a given value
of the sine or cosine of that angle, and know that these are
inverse functions defined on a restricted domain.
10.5
Calculate measures of spread, including the variance and
standard deviation.
13.1
Use coins, dice or random numbers to generate models of
Probability and Statistics
10
Collect, process,
represent, analyse and
interpret data and
reach conclusions
13
Specific Details
General application in Standards 1.1 to 1.14
3.1
5.1
Develop further confidence in all the calculation skills
established in Grades 10 and 11.
Use a graphics calculator, including the trace function, to
show approximate solutions to physical problems requiring
the location and physical interpretation of the intersection
points of two or more graphs.
Understand the ideas of exponential growth and decay and
the forms of the associated graphs y = ax, where a > 0;
use a graphics calculator to plot the graphs of the
exponential function, ex, and the natural logarithm function,
ln x; know that one is the inverse function of the other and
use this to find solutions to physical problems; solve for x
the equation y = ax and use this in problems; use the log
function (logarithm in base 10) on a calculator.
Specific reference to graphic calculators in Math Standards
Prepared by David Stubbs, updated 9 June 2009
Mosaica Education Inc.
Page 3
Std
Strand/Topic
Ref
14
Use of ICT
14.1
Specific Details
random data.
Use a calculator with statistical functions to aid the
analysis of large data sets, and ICT applications to present
statistical tables and graphs.
12 ADV
Std
Strand/Topic
Ref
Reasoning and Problem Solving
1
Use mathematical
reasoning to solve
problems
Number and Algebra
5
Work with functions
5.1
and their graphs
5.3
6
7
Solve equations
associated with
functions
Calculate the derivative
of a function
6.1
to
6.4
7.1
to
7.15
Probability and Statistics
14
Simulation
14.1
15
15.1
Use of ICT
Specific Details
General application in Standards 1.1 to 1.16 and
specifically 1.5, 1.15 and 1.16
Use a graphics calculator to plot exponential
functions of the form y = ekx; describe these
functions, distinguishing between cases when k is
positive or negative, and the special case when k is
zero.
Understand the modulus function y = | x | and sketch
its graph.
General application
General application
Use coins, dice or random numbers to generate
models of random data.
Use a calculator with statistical functions to aid the
analysis of large data sets, and ICT applications to
present statistical tables and graphs.
Specific reference to graphic calculators in Math Standards
Prepared by David Stubbs, updated 9 June 2009
Mosaica Education Inc.
Page 4