Leaving Cert Algebra 2 Set B Questions - L.C. Maths

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Course Content

Algebra 1

0/14

Algebraic Fractions

Binomial Expansions

Algebraic Identities

Linear Equations

Simultaneous Linear Equations

Algebra 2

0/16

Quadratic Equations

Quadratic Roots

Simultaneous Linear & Quadratic Equations

Forming Quadratic Equations

Maxima and Minima

Polynomial Graphs

Trigonometry 1

0/18

Sine, Cosine & Tangent

The Unit Circle

Trigonometric Graphs

Related Trigonometric Graphs

Solving Trigonometric Equations

Coordinate Geometry of the Line

0/14

Area of a Triangle

Equation of a Line

Dividing a Line Segment

Triangle Concurrencies

Distance from Point to Line

Angle between Lines

Real World Problems

Probability 1

0/14

Elementary Probability

Relative Frequencies

Mutually Exclusive Events

Independent Events

Conditional Probability

Geometry 1

0/6

Triangle & Parallelogram Theorems

Circle Theorems

Differential Calculus

0/10

Derivatives from First Principles

Derivatives by Rule

Product, Quotient & Chain Rules

Second Derivatives

Trigonometry 2

0/10

Trigonometric Identities

Compound Angles

Double-Angle Formulae

Sum, Difference & Product Formulae

Inverse Trigonometric Functions

Sequences & Series

0/12

Arithmetic Sequences

Arithmetic Series

Geometric Sequences

Geometric Series

Limits of Sequences

Other Sequences

Statistics 1

0/9

Population Sampling

Location & Variability

Stem & Leaf Diagrams

Distribution Shapes

Coordinate Geometry of the Circle

0/14

Circles centred at Origin

Circle centred Elsewhere

Finding Equations of Circles

Touching Circles

Circles Tangent to Axes

Algebra 3

0/16

Quadratic & Rational Inequalities

Mathematical Proofs

Exponential Functions

Logarithmic Functions

Proofs by Induction

Complex Numbers

0/12

Introduction to Complex Numbers

Manipulating Complex Numbers

Conjugate Roots Theorem

Polar Coordinates

Argand Diagrams

De Moivre’s Theorem

Geometry 2

0/4

Integration

0/8

Indefinite Integrals

Definite Integrals

Integration & Areas

Average Values of a Function

Differential Calculus Applications

0/8

Stationary Points

Graphs of Derivatives

Maxima and Minima Problems

Rates of Change

Financial Maths

0/8

Compound Interest

Loans & Mortgages

Length, Area & Volume

0/6

Sectors of Circles

Trapezoidal Rule

Probability 2

0/9

Expected Values

Bernoulli Trials

The Independence of Events

Functions

0/15

Set Representation of Relations

Graphical Representation of Relations

Graphing Similar Relations

Introduction to Functions

Inverses & Compositions

Types of Functions

Exponential Functions

Logarithmic Functions

Functions & Graphs

Statistics 2

0/4

Scatter Diagrams

Lines of Best Fit

Normal Distributions

Inferential Statistics

0/6

Population Proportions

Central Limit Theorem

Population Means

Digital Lessons

About Lesson

Start with the quiz…

Knowledge Check Quiz

EXAMS.IE

Quadratic Roots

Hint

This is a quadratic equation.

1 / 5

How many solutions are there to the equation \(x^2=9\)?

\(0\)

\(1\)

\(2\)

\(3\)

This is a quadratic equation.

That's right!

This is a quadratic equation.

Hint

The function has two coordinate pairs in which \(y=0\)\.

2 / 5

If a quadratic equation has two distinct real roots, what is true about the graph of the corresponding function?

It touches the \(x\) axis in one place.

It crosses the \(x\) axis in two places.

It touches the \(y\) axis in one place.

It crosses the \(y\) axis in two places.

The function has two coordinate pairs in which \(y=0\)\.

That's right!

The function has two coordinate pairs in which \(y=0\)\.

Hint

The function has one coordinate pair in which \(y=0\)\.

3 / 5

If a quadratic equation has one distinct real root, what is true about the graph of the corresponding function?

It does not cross the \(x\) axis.

It does not cross the \(y\) axis.

It touches the \(x\) axis in one place.

It touches the \(y\) axis in one place.

The function has one coordinate pair in which \(y=0\)\.

That's right!

The function has one coordinate pair in which \(y=0\)\.

Hint

The function has no coordinate pairs in which \(y=0\)\.

4 / 5

If a quadratic equation has only complex roots, what is true about the graph of the corresponding function?

It does not cross the \(x\) axis.

It does not cross the \(y\) axis.

It touches the \(x\) axis in one place.

It touches the \(y\) axis in one place.

The function has no coordinate pairs in which \(y=0\)\.

That's right!

The function has no coordinate pairs in which \(y=0\)\.

Hint

The square root of the discriminant will be a complex number.

5 / 5

If a quadratic equation has only complex roots, what is true about the discriminant for that equation?

It is greater than zero.

It is equal to zero.

It is less than zero.

It is a complex number.

The square root of the discriminant will be a complex number.

That's right!

The square root of the discriminant will be a complex number.

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