The Grammar and Language of Algebra

Variables, Algebraic Thinking, and Algebraic Language

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QUESTION OF
Views #: 8
Questions #: 20
Time: 10 minutes
Pass Score: 80.0%
Style
Mode

How to represent the unknown?

1 pts

In algebra, a letter such as x usually represents a (1).

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variable
constant
fraction
prime
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Explanation

Translate Algebraic Statement

1 pts
volume_mute

The phrase 'five more than x' is written algebraically as:

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Algebraic Thinking

1 pts
volume_mute

Select all statements that correctly describe algebra.

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Expression Translation

1 pts
volume_mute

Translate 'twice a number y' into algebraic notation.

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Identify Algebraic Expression

1 pts
volume_mute

Which of the following is an algebraic expression?

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Sort Algebraic Forms

1 pts
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Arrange the following from simplest symbolic form to more complex symbolic form.

Equation
Variable
Expression
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Explanation

Match Words to Algebra

1 pts

Match the phrase with the correct algebraic form.

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  2. Click on the match in the second group

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Phrase

Seven less than x
Three times x

Algebric form

3x
x-7
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Explanation

Algebra as Shorthand

1 pts

Algebra acts as the (1) of mathematics.

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language
drawing
graph
table
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Classification of Statements

2 pts

Classify the following into expressions or equations.

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Meaning of Equality

1 pts
volume_mute

The symbol '=' means two quantities are:

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Definition of a Polynomial

1 pts
volume_mute

Which of the following expressions qualifies as a polynomial in \(x\)?

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Degree of a Polynomial

1 pts
volume_mute

What is the degree of the polynomial \(3x^5 + 2x^3 - x + 7\)?

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Remainder Theorem

1 pts
volume_mute

According to the Remainder Theorem, if a polynomial \(p(x)\) is divided by \((x - a)\), the remainder is:

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Factor Theorem

1 pts
volume_mute

According to the Factor Theorem, if \(x = a\) is a zero of polynomial \(p(x)\), then:

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Algebra as a Language for Thinking

1 pts
volume_mute

Consider the arithmetic pattern below:

\(3^2\) is 1 bigger than \(2 \times 4\)

\(4^2\) is 1 bigger than \(3 \times 5\)

\(5^2\) is 1 bigger than \(4 \times 6\)

Which algebraic identity correctly generalises this pattern for any natural number \(n\)?

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Explanation

Algebra Shorthand: Translate to Algebra

2 pts

Match each instruction in ordinary language to its equivalent algebraic expression.

To complete the line match

  1. Click on an item in the first group
  2. Click on the match in the second group

To delete a match, double click on a line

Ordinary Language

Think of a number, add 7 to it and double the result
Choose a number, multiply it by 5, add 2, square this expression, and divide the result by 8
Take a number, subtract 3 from it, then multiply by 4
Square a number and add twice the number

Algebraic Form

\(2(x + 7)\)
\(\frac{(5x+2)^2}{8}\)
\(x^2 + 2x\)
\(4(x - 3)\)
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Explanation

Induction vs. Deduction

1 pts
volume_mute

In mathematics, the process of reasoning from particular results to a general conclusion is called:

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Counter-Example to Fermat's Conjecture

1 pts
volume_mute

Pierre de Fermat conjectured that \(2^{2^n} + 1\) is prime for every natural number \(n\). Which mathematician disproved this conjecture, and for which value of \(n\)?

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Zeros of a Quadratic Polynomial

2 pts
volume_mute

Consider the polynomial \(q(x) = x^2 - x - 6\).

Which of the following are zeros of \(q(x)\)? (Select all that apply.)

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Explanation

Maximum Zeros of a Polynomial

2 pts
Please drag and drop the options to sort them

Sort the following polynomial types in ascending order based on the maximum number of zeros they can have.

Quartic (degree 4)
Linear (degree 1)
Cubic (degree 3)
Quadratic (degree 2)
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