Download Yr_12_2CD_MAT_Program_Assessment_Schedule_2011_2

Year 12 2 CD 2015
Semester 1
Week
Unit
Topic/syllabus entry
Resources
A.J.Sadler
Term 1
1-2
2CMAT
3.1
3.1.1
3.1.4
Quantify chance
use Venn diagrams to represent sample spaces for two events and to illustrate set concepts (subset, intersection,
union, complement)
use two-way tables to represent sample spaces for two events
use Venn diagrams and two-way tables to calculate simple probabilities for compound events (event A or B, event A
and B, event A given event B, complement of A)
use fractions, decimals and percentages to describe probability and move freely between them
3.1.5
use set and probability notation n(U), n(A), n(A') or n( A ), n(A  B), n(A  B), n(A|B) and P(A), P(A) , P(A  B), …
3.1.2
3.1.3
3
2CMAT
3.2
3.2.1
3.2.2
4-5
5
2CMAT
2CMAT
6-7
2CMAT
8-9
2CMAT
2.2
2.2.1
2.2.2
2.2.3
2.2.4
Interpret chance
use probabilities to predict proportions and number of outcomes that are likely to satisfy provided criteria in
n trials
use chance terminology when describing events (‘probability of’, ‘complement of’).
Networks
interpret information represented in network diagrams (basic networks only, project networks not included)
develop systematic methods to determine the shortest path between two vertices of a network
determine minimal spanning trees for networks using network diagrams and Prim’s algorithm
determine the maximal flow for networks with one source and one sink.
1.1
Estimation and calculation
1.1.1 use calculators and written methods efficiently
1.1.2 round numbers to a given number of significant figures
1.1.3 round, truncate and decide on appropriate accuracy as part of calculation and estimation
1.1.4 recognise the effects of errors due to truncating and rounding
1.1.5 convert numbers to and from scientific notation.
2.1
2.1.1
2.1.2
1.2.1
Coordinate geometry
determine the gradient and equations of parallel and perpendicular lines
apply distance and gradient relations to solve problems in the Cartesian plane.
sketch quadratic functions in the following forms:
y  a( x  b )( x  c )
y  a( x  b )2  c
Chapter 1
Preliminary
Chapter 2
EPW 1
Preliminary
Chapter 3
TEST 1
(chapter 1-3)
Preliminary
Chapter 4
Chapter 5
Chapter 6
TEST 2
Chapter (4-6)
y  ax 2  bx  c , where, a, b and c are integers
1.2.2
1.2.3
1.2.4
1.2.6
Week
Unit
identify families of quadratic functions from their equations
identify features of parabolas:
–
intercepts– lines of symmetry
–
– turning points
–
– concavity.
interpret parabolas:
– relationships between variables
– turning points and optimisation.
use function notation.
Topic/syllabus entry
Resources
A.J.Sadler
Term 2
1
2CMAT
1.3
Equivalence, equations and inequalities
1.3.1 without a calculator, factorise differences of two squares such as
a 2  b2 , a 2 x 2  b 2 and readily-factorised quadratic expressions of the form x2  bx  c
1.3.2 solve quadratic equations:
–
algebraically, if in factored form
–
graphically.
2
3
2CMAT
2CMAT
1.4
1.4.1
1.4.2
1.4.3
1.4.4
1.4.5
1.4.6
3.4
3.4.1
3.4.2
3.4.3
3.4.4
Finance
calculate compound interest recursively with technology
calculate repayments and amount owing for loans
interpret and compare loans with simple and compound interest
make decisions about loans
calculate inflation and depreciation.
interpret financial information including tax tables, commercial advertisements, and credit card rates,
charges and credit limits.
Represent data
construct frequency histograms for ungrouped and grouped data
 fx
x
calculate mean using x   and x 
notation, and median and mode for ungrouped frequency
f
n
data
calculate weighted mean, mean for grouped data, and modal and median classes
describe spread between data displayed in frequency tables and graphs using terms such as gaps, clusters,
Preliminary
Chapter 7
Chapter 8
EPW 2
Chapter 9
more dense/less dense regions, outliers
calculate range for ungrouped and grouped data
calculate relative frequency and proportions of data in fractional, decimal and percentage forms and use
them to describe spread
3.4.7 plot time-series and bivariate data, fit trend lines by eye and calculate their equations.
3.5.1
identify independent and dependent variables for experimental and time-series data
3.5.2
predict using interpolation and extrapolation and trend line graphs and equations, recognising the risks
of extrapolation
3.5.3
explain why predicted and actual results are likely to differ.
3.4.5
3.4.6
4
2CMAT
Revision and Exams
5-6
Chapter 10
TEST 3
(Chapter 7-9)
EXAM
Semester 2
7
2DMAT
8
2DMAT
1.1
1.1.1
3.2
3.2.1
3.2.2
3.2.3
3.2.4
1.
9-10
2DMAT
Estimation and calculation
use index laws to multiply and divide numbers with integer powers.
Quantify chance
use long-run relative frequency to estimate probabilities
use lists, tables and tree diagrams to determine sample spaces for one-, two- and three-stage events
use sample spaces to calculate simple probabilities and probabilities for compound events
use the relationship P(A) + P(A΄) = 1 to calculate probabilities for complementary events
use the facts that probabilities sum to 1 and range from 0 to 1 to check probabilities.
Functions and graphs
1.2.1 sketch graphs of:
y  bx , b  0
1.2
Chapter 1
Chapter 2
Preliminary
EPW3
y  x n , for n = 2, 3, -1
1.2.2
recognise functions of the forms y  b x , b  0 and
y  x n for n = 2, 3, -1 from tables and graphs
1.2.3
describe the effects of varying a, b and c on the graph of y  af ( x  b )  c where f ( x )  x2 ,
Chapter 3
f ( x )  x3 or f ( x )  k x (Vary up to two parameters in any one example.)
11
2DMAT
1.2.4
1.2.5
distinguish linear, quadratic, cubic, exponential and reciprocal functions from equations and graphs
sketch the cubic functions:
y  a( x  b )( x  c )( x  d ) y  a( x  b )( x  c )2
Preliminary
Chapter 3
TEST 4
(chapter 1-3)
y  a( x  b )3
1.2.6
use technology to graph y  ax3  bx2  cx  d
Term 3
1
2DMAT
1.4
Patterns
1.4.1 link arithmetic sequences to linear functions, and geometric sequences to exponential functions
1.4.2 determine recursive rules for
terms of arithmetic, geometric
and Fibonacci sequences and
Tn1  Tn  3 , T1  4
test generalisations by systematically checking cases and searching for counter-examples
investigate real-world applications of arithmetic, geometric and Fibonacci sequences.
write the rules with recursive
1.4.3
1.4.4
2
2DMAT
1.3
1.3.1
1.3.2
1.3.3
1.3.4
3
2DMAT
4
2DMAT
3.5
3.5.1
3.5.2
3.6
3.6.1
3.6.2
3.6.3
3.6.4
3.6.5
3.6.6
5
2DMAT
6
2DMAT
Chapter 4
notation such as
Equivalence, equations and inequalities
rearrange and simplify algebraic expressions into forms useful for computation
estimate the solutions for ab x  c using substitution, where a, b and c are constants
solve quadratic, cubic and exponential equations graphically
solve simultaneous equations graphically.
Represent data
produce tables and graphs and summary statistics to support analysis
determine the standard deviation, n, for grouped and ungrouped data using the inbuilt facility on a
calculator.
Interpret data
discern viability of range and standard deviation for ranking datasets in order of spread
interpret spread summaries in terms of their mathematical definitions
compare datasets using mean and standard deviation, and noting features of tabulated or graphed data
use words that acknowledge uncertainty when comparing data sets such as ‘scores for … tend to be
more spread than scores for …’
infer results for populations from samples, recognising possible chance variation between them
report on collected data to include commenting on external factors i.e. hidden variables that might have
affected data and recognising possible chance variation in sample.
3.1
Conduct chance experiments
3.1.1 plan and conduct simulations using technology-based random number generators.
3.3
Interpret chance
3.3.1 predict the results for repetition of simulations with different numbers of trials
3.3.2 recognise that a first-stage result in a two-stage experiment may or may not affect a second stage result
Chapter 5
EPW 4
Preliminary
Chapter 6
Chapter 6 contd.
Test 5
(Chapter 4-6)
Chapter 7
EPW 5
Chapter 8
3.3.3
7
2DMAT
estimate population size using the capture-recapture technique.
2.1
2.1.1
Measurement
use sine, cosine and tangent ratios to determine sides and angles of right triangles, degree measure
only
2.1.2
use the formula area ΔABC =
1
absin C
2
2.1.3
use sine and cosine rules to determine sides and angles of acute
contexts only)
8
2DMAT
3.5
3.5.4
3.5.5
3.5.6
8-9
TEST 6
(Chapter 7-9)
triangles (two-dimensional
Interpret data
read information from frequency tables, nested and layered tables, frequency graphs and time-series
graphs and scatterplots
discern the suitability of mean, median and mode for indicating central location
calculate numbers of data in categories from relative frequencies and proportions
Mock exams
Preliminary ( Pythag)
Chapter 9
Preliminary
Assessment outline: Unit 2C MAT/2DMAT
ASSESSMENT
WEIGHTINGS
TIME
T1 W 5
RESPONSE
27%
T1W 9
T2 W 4
T2 W 6
UNIT 2C
TEST 1
Chapter 1 – 3 2 C
TEST 2
Chapter 4 – 6 2 C
TEST 3
Chapter 7 – 10 2 C
SEMESTER 1 Exam
Semester 1
TASK
WEIGHTING
NUMBER
AND
ALGEBRA
T1 W 3
T2 W 2
CHANCE AND
DATA
3%
√
√
4%
√
√
5%
√
15%
√
INVESTIGATION
8%
SPACE AND
MEASUREMENT
Investigation1 Take home
part with in-class validation
3%
Investigation 2 Take home
part with in-class validation
5%
TOTAL
35%
√
√
√
√
√
Assessment outline: Unit 2C MAT/2DMAT
ASSESSMENT
WEIGHTINGS
TIME
T2 W11
RESPONSE
48%
T3W4
T3 W7
T3 W10
UNIT 2D
TEST 4
Chapter 1 – 3 2 D
TEST 5
Chapter 4 – 6
2D
TEST 6
Chapter 7-9
2D
SEMESTER 2 exam (mock)
Semester 2
TASK
WEIGHTING
NUMBER
AND
ALGEBRA
CHANCE AND
DATA
5%
√
√
√
6%
√
√
7%
√
30%
√
INVESTIGATION T2 W9
17%
Investigation 3 Take home
part with in-class validation
5%
T3 W2
Investigation 4 Take home
part with in-class validation
6%
Investigation 5 Take home
part with in-class validation
6%
TOTAL
65%
T3 W5
SPACE AND
MEASUREMENT
√
√
√
√
√