EmSAT Math Achieve 2018, Lecture notes of Algebra

EmSAT Math Achieve is a computer-based test and has 3 major sections - Algebra, ... problems. • Rewrite rational functions. • Create equations that describe.

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Ministry of Education Academic Year 2017-2018
National and International Tests
EmSAT Math Achieve 2018
Total Time for Test: 60 questions: 2 hours
EmSAT Math Achieve is a computer-based test and has 3 major sections - Algebra, Geometry, and
Statistics. Test sections, questions, and options are randomized. Sections and subsections of the test are
timed by the computer. Test takers can see how much time they have throughout the test.
Section 1: Algebra
Interpret the structure of expressions
Write expressions in equivalent forms
to solve problems
Perform arithmetic operations on
polynomials
Understand the relationship between
zeros and factors of polynomials
Use polynomial identities to solve
problems
Rewrite rational functions
Create equations that describe
numbers or relationships
Understand solving equations as a
process of reasoning and explain the
reasoning
Solve equations and inequalities in
one variable
Solve systems of equations
Represent and solve equations and
inequalities graphically
Understand the concept of a function
and use function notation
Interpret functions that arise in
applications in terms of the context
Analyze functions using different
representations
Build a function that models a
relationship between two quantities
Build new functions from existing
functions
Construct and compare linear and
exponential models and solve
problems
Interpret expressions for
functions in terms of the situation
they model
Extend the domain of
trigonometric functions using the
unit circle
Model periodic phenomena with
trigonometric functions
Prove and apply trigonometric
identities
Extend the properties of
exponents to rational exponents
Use properties of rational and
irrational numbers.
Reason quantitatively and use
units to solve problems
Perform operations with complex
numbers
Represent and model with vector
quantities.
Perform operations on vectors.
Perform operations on matrices
and use matrices in applications
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Page 1 of 17 Ministry of Education Academic Year 2017-

EmSAT Math Achieve 2018

Total Time for Test: 60 questions : 2 hours

EmSAT Math Achieve is a computer-based test and has 3 major sections - Algebra, Geometry, and

Statistics. Test sections, questions, and options are randomized. Sections and subsections of the test are

timed by the computer. Test takers can see how much time they have throughout the test.

Section 1: Algebra

 Interpret the structure of expressions

 Write expressions in equivalent forms

to solve problems

 Perform arithmetic operations on

polynomials

 Understand the relationship between

zeros and factors of polynomials

 Use polynomial identities to solve

problems

 Rewrite rational functions

 Create equations that describe

numbers or relationships

 Understand solving equations as a

process of reasoning and explain the

reasoning

 Solve equations and inequalities in

one variable

 Solve systems of equations

 Represent and solve equations and

inequalities graphically

 Understand the concept of a function

and use function notation

 Interpret functions that arise in

applications in terms of the context

 Analyze functions using different

representations

 Build a function that models a

relationship between two quantities

 Build new functions from existing

functions

 Construct and compare linear and

exponential models and solve

problems

 Interpret expressions for

functions in terms of the situation

they model

 Extend the domain of

trigonometric functions using the

unit circle

 Model periodic phenomena with

trigonometric functions

 Prove and apply trigonometric

identities

 Extend the properties of

exponents to rational exponents

 Use properties of rational and

irrational numbers.

 Reason quantitatively and use

units to solve problems

 Perform operations with complex

numbers

 Represent and model with vector

quantities.

 Perform operations on vectors.

 Perform operations on matrices

and use matrices in applications

Page 2 of 17 Ministry of Education Academic Year 2017-

Sample Question 1

Answer: C

Sample Question 2

Answer: C

Page 4 of 17 Ministry of Education Academic Year 2017-

Sample Question 3

Answer: C

Sample Question 4

Answer: B

Page 7 of 17 Ministry of Education Academic Year 2017-

Section 2: Geometry

 Experiment with transformations in the plane

 Understand congruence in terms of rigid

motions

 Prove geometric theorems

 Understand similarity in terms of similarity

transformations

 Prove theorems involving similarity

 Define trigonometric ratios and solve problems

involving right triangles

 Apply trigonometry to general triangles

 Understand and apply theorems about circles

 Translate between the geometric description and

the equation for a conic section

 Use coordinates to prove simple geometric

theorems algebraically

 Explain volume formulas and use them to solve

problems

 Visualize relationships between two- dimensional and three-dimensional objects

Sample Question 1

Answer: B

Answer: C

Answer: A

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