Assessment Task: Polynomials, Trigonometry Concepts and Questions

This assignment outlines two SAT assessment tasks focusing on Polynomials and Trigonometry. The Polynomials task involves deducing quadratic models, understanding graph features, and exploring cubic and quartic polynomials. It's divided into three parts with varying calculator usage. The Trigonometry task covers Pythagoras' theorem, trigonometric ratios, circular measure, radian measure, and trigonometric identities, also in three parts. Additionally, it includes mathematical investigations into the features of polynomials and trigonometry, requiring students to model situations using quadratic relationships and periodic functions within specific contexts like construction and navigation. Students can find more solved assignments and past papers on Desklib.

Assessment
Type and
Weighting
Details of assessment Assessment
Design Criteria
Assessment
conditions
( Time allotment,
supervision, use of
calculator)
C&T R&C
Skill and
application task
Weightage:
75%
SAT 1: Polynomials. Key questions and
concepts from Topic 2
The SAT is divided into three parts based on
the subtopics 2.1 and 2.2
Part 1: Regular questions related to deducing
quadratic models from zeroes or other points
based on subtopic 2.1. Ability to construct
quadratic relationships including areas of
rectangles with fixed perimeters (including
golden rectangles), business applications (profit
functions), elastic collisions, and projectile
paths.
Part 2: Complex questions on features of the
graphs of quadratic equations including the
parabolic nature, intercepts, turning points, and
axes of symmetry. Graphing technology needs
to be used to predict uniqueness of result.
Part 3: Questions based on subunit 2.2 cubic
and quartic polynomials. Deduce relationships
between volume and linear measure including
solubility of chemicals versus temperature, and
wind speed versus power output from a wind
generator. Student needs to used factorisation
or cubic technology to solve equations.
1, 2, 3, 4 1, 2, 3, 4
Supervised written
assignment.
Time allotted: 60 minutes
for each part.
Calculator prohibited for
part 1.
Calculator can be used for
part 3 and part 3.
Can be handwritten in one
or two A4 size paper.
SAT 2: Trigonometry. Key Concepts and
questions based on subunits 3.1, 3.2 and 3.3.
The SAT is divided into 3 parts.
Part 1: Routine questions based on subunit 3.1
using Pythagoras’ theorem and Trigonometric
ratios, including derivation of the cosine rule
using Pythagoras’ theorem.
Part 2: Based on subunit 3.2 circular measure
and radian measure. Students are required to
apply graphical representation for
trigonometric functions.
Part 3: Complex questions on trigonometric
functions of subunit 3.3. Students must deduce
the useful identities by looking at the unit
circle. Skill development by awareness of
construction and understanding of behaviour of
the identities.
1, 2, 3, 4 1, 2, 3, 4
Supervised written
assignment.
Time allotted: 60 minutes
for each part.
Calculator can be used.
Can be handwritten in one
or two A4 size paper.
Mathematical
investigation
Weightage:
Investigating features of Polynomials:
The investigation is mainly based on topic 2.
The students in order to model a given situation

25% must appropriately use quadratic relationships.
Investigation must be done beginning with a
simple case and then gradually move on to a
complex case using mathematical modelling.
Investigating features of Trigonometry:
Investigation mainly based on topic 3.
Investigation should be carried out by students
in application of mathematical modelling in
contexts such as such as construction, design,
navigation, and surveying by using periodic
functions. Investigation must be done to
understand the behaviour of tangent function
by graphical method, in similarity to the
sinusoidal functions.
One week time given for
each investigative
assignment.
Some class time given for
support verification.
A maximum of 8 pages
(A4 sheet) for each
assignment.