Grade 11 Math

CONTENTS

The second last year of school life, Grade 11 is also an extremely competitive year where students tend to feel the pressure of college applications and extra credits for admissions. Mathematics at this point becomes even more critical as a mandatory subject, making its understanding imperative.

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Measurement

Measurement is the process of assigning a number to a physical property, like length, area, mass, etc.
Unit rates
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Scale drawings: word problems

Equations

An equation says that two things are equal. It will have an equal sign “=”. In other words, an equation is like a statement “This equals that”. Equation is a mathematical sentence built from expressions using one or more equal signs.
Solve linear equations
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Solve linear equations: word problems
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Absolute value and opposites
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Solve absolute value equations
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Graph solutions to absolute value equations

Inequalities

An equality compares two values, showing if one is less than, greater than, or simply not equal to another value. Inequality is a mathematical sentence built from expressions using one ore more of the symbols <, >, ≥, or ≤.
Graph a linear inequality in one variable
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Graph a linear inequality in the coordinate plane
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Write inequalities from graphs
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Write a linear inequality: word problems
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Solve linear inequalities
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Graph solutions to linear inequalities
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Solve absolute value inequalities
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Graph solutions to absolute value inequalities
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Graph solutions to quadratic inequalities
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Solve quadratic inequalities

Functions

A function related an input to an output. It works like a machine that takes something in (input) and at the end gives us something back (output). F(x) is the traditional way of expressing functions. Each function has three parts the Input, the Relationship and the Output. Understanding functions is very important for future math works.

Domain and range

Identify functions

Evaluate functions

Find values using function graphs

Complete a table for a function graph

Find the slope of a linear function

Graph a linear function

Write the equation of a linear function

Linear functions over unit intervals

Complete a function table: absolute value functions

Graph an absolute value function

Systems of equations

Two or more equations containing common variables is called the system of equations. In solving a system of equations, we try to find values for each of the variables that will satisfy every equation in the system. The equations in the system can be linear or non-linear.

Is (x, y) a solution to the system of equations?

Solve a system of equations by graphing

Solve a system of equations by graphing: word problems

Find the number of solutions to a system of equations

Classify a system of equations

Solve a system of equations using substitution

Solve a system of equations using substitution: word problems

Solve a system of equations using elimination

Solve a system of equations using elimination: word problems

Solve a system of equations using any method

Solve a system of equations using any method: word problems

Solve a non-linear system of equations

Systems of inequalities

Two or more inequalities containing common variables is called the system of inequalities. System of inequalities sometimes include equations as well as inequalities. System of inequalities are used when a problem requires a range of solutions, and there is more than one constraint on those solutions.

Is (x, y) a solution to the system of inequalities?

Solve systems of inequalities by graphing

Find the vertices of a solution set

Linear programming

Factoring

Finding what to multiply to get an expression is called factoring or factorizing. Factoring is like splitting an expression into a multiplication of simpler expressions. Factoring is important because it helps us to simplify expressions.

Factor monomials

Factor quadratics

Factor quadratics using algebra tiles

Factor using a quadratic pattern

Factor by grouping

Factor sums and differences of cubes

Factor polynomials

Quadratic relations

Quadratic relation is a type of relationship, where the second differences within Y coordinates are equal. Quadratic relation is represented by a parabola on a graph.

Characteristics of quadratic functions

Complete a function table: quadratic functions

Find a quadratic function

Graph a quadratic function

Match quadratic functions and graphs

Solve a quadratic equation using square roots

Solve a quadratic equation using the zero product property

Solve a quadratic equation by factoring

Complete the square

Solve a quadratic equation using the quadratic formula

Using the discriminant

Parabolas

Parabola is a special curve, shaped like an arch. Any point of a parabola is at an equal distance from a fixed point (the focus), and a fixed straight line (the directrix). For formal definition we say: for a given point, called focus, and a given line not through the focus, called directrix, a parabola is the locus of points such that the distance of the focus equals the distance to the directrix. Not all U-shaped curves are parabola, a parabola should satisfy the conditions listed above. Parabola has many important applications in real life, such as designing automobiles headlights to calculating the path of a ballistic missile.

Identify the direction a parabola opens

Find the vertex of a parabola

Find the axis of symmetry of a parabola

Write equations of parabolas in vertex form from graphs

Write equations of parabolas in vertex form using properties

Graph parabolas

Polynomials

The sum or difference of terms which have variables raised to positive integer powers and which have coefficients. A polynomial can have constants, variables and exponents, but never division by variable. Even though the poly- means many the polynomials terms should be finite.

Polynomial vocabulary

Add and subtract polynomials

Multiply a polynomial by a monomial

Multiply two binomials

Multiply two binomials: special cases

Multiply polynomials

Radical functions and expressions

A radical function contains a radical expression with the independent variable in the radicand. For example, y= √x is a radical function which is also called a square root function in this case.

Roots of integers

Roots of rational numbers

Find roots using a calculator

Nth roots

Simplify radical expressions with variables I

Simplify radical expressions with variables II

Multiply radical expressions

Divide radical expressions

Add and subtract radical expressions

Simplify radical expressions using the distributive property

Simplify radical expressions using conjugates

Domain and range of radical functions

Solve radical equations

Rational exponents

Using rational numbers as exponents. A rational exponent represents both an integer exponent and an nth root. The root is found in the denominator and the integer exponent is found in the numerator. In other words, a rational exponent is an exponent that is a fraction

Evaluate rational exponents

Multiplication with rational exponents

Division with rational exponents

Power rule

Simplify expressions involving rational exponents I

Simplify expressions involving rational exponents II

Rational functions and expressions

A function that be written as a polynomial divided by a polynomial is a rational function. It is rational because one is divided by the other, like a ratio. Note that every polynomial function is a rational function with denominator of 1. A function that cannot be written in the form of a polynomial such as f(x)=Sin(x), is not a rational function.

Rational functions: asymptotes and excluded values

Evaluate rational expressions I

Evaluate rational expressions II

Simplify rational expressions

Multiply and divide rational expressions

Add and subtract rational expressions

Solve rational equations

Exponential functions

In exponential functions the variable is the power rather than the base. .

Evaluate exponential functions

Match exponential functions and graphs

Solve exponential equations

Identify linear and exponential functions

Exponential functions over unit intervals

Describe linear and exponential growth and decay

Exponential growth and decay: word problems

Compound interest: word problems

Continuously compounded interest: word problems

Angle measures

In geometry, an angle measure can be defined as the measure of the angle formed by the two rays or arms at a common vertex. Angles are measure in degrees by using a protractor.

Quadrants

Graphs of angles I

Graphs of angles II

Coterminal angles

Reference angles

Right triangles

A triangle that has a right angle (90^0). Right triangles are important in geometry due to their properties and the use of Pythagoras theorem.

Pythagorean Theorem

Converse of the Pythagorean theorem

Pythagorean Inequality Theorems

Special right triangles

Trigonometry

Trigonometry is the study of triangles with emphasis on calculations involving the lengths of sides and the angles. Trigonometry is based on six functions, namely Sine, Cosine, Tangent, Cotangent, Secant, and Cosecant. Trigonometry also includes study of the properties of these functions and their graphs. Trigonometry is an important field in mathematics with a lot of applications in real life problems, like calculating the waves and tides in oceans, creating maps, satellite systems and a lot more.

Trigonometric ratios: sin, cos and tan

Trigonometric ratios: csc, sec and cot

Trigonometric ratios in similar right triangles

Find trigonometric ratios using the unit circle

Sin, cos and tan of special angles

Csc, sec and cot of special angles

Find trigonometric functions using a calculator

Inverses of sin, cos and tan

Inverses of csc, sec and cot

Solve trigonometric equations I

Solve trigonometric equations II

Trigonometric ratios: find a side length

Trigonometric ratios: find an angle measure

Solve a right triangle

Law of Sines

Law of Cosines

Solve a triangle

Area of a triangle: sine formula

Area of a triangle: Law of Sines

Two-dimensional figures

Two-dimensional geometry or plane geometry is about flat shapes like triangles and circles. Two-dimensional figures have only two dimensions such as width and height but no thickness. It also known as “2D”.

Polygon vocabulary

Interior angles of polygons

Perimeter

Area of triangles and quadrilaterals

Area and perimeter in the coordinate plane I

Area and perimeter in the coordinate plane II

Area and circumference of circles

Area of compound figures

Area between two shapes

Area and perimeter of similar figures

Classify quadrilaterals

Properties of parallelograms

Three-dimensional figures

Having three dimensions such as Height, Width and Depth, like any real-world object is a three-dimensional figure. Three-dimensional geometry is about solid shapes like spheres or cubes. It is also known as “3D”.

Three-dimensional figure vocabulary

Parts of three-dimensional figures

Nets and drawings of three-dimensional figures

Introduction to surface area and volume

Surface area of prisms and cylinders

Surface area of pyramids and cones

Volume of prisms and cylinders

Volume of pyramids and cones

Surface area and volume of spheres

Introduction to similar solids

Surface area and volume of similar solids

Surface area and volume review

Cross-sections of three-dimensional figures

Solids of revolution

Congruent figures

When we change a shape by using Turn, flip, slide or resize it is called transformation. If one shape can become another using Turn, Flip or Slide then shapes are congruent. Congruence keeps the size, area, angles and line lengths of the shape.

Congruence statements and corresponding parts

Solve problems involving corresponding parts

Identify congruent figures

Proofs involving angles

Proofs involving parallel lines I

Proofs involving parallel lines II

SSS and SAS Theorems

ASA and AAS Theorems

SSS, SAS, ASA and AAS Theorems

SSS Theorem in the coordinate plane

Congruency in isosceles and equilateral triangles

Hypotenuse-Leg Theorem

Proofs involving triangles I

Proofs involving triangles II

Triangle

Triangle is a polygon with 3 sides.

Classify triangles

Triangle Angle-Sum Theorem

Midsegments of triangles

Triangles and bisectors

Identify medians, altitudes, angle bisectors and perpendicular bisectors

Angle-side relationships in triangles

Triangle Inequality Theorem

Similarity

When we change a shape by using Turn, flip, slide or resize it is called transformation. Two shapes are similar when one can become the other after a resize, flip, slide or turn. When two shapes are similar then the corresponding angles are equal, and the lines are in proportion. This can make life a lot easier when solving geometry problems.

Identify similar figures

Similarity ratios

Similarity statements

Side lengths and angle measures in similar figures

Similar triangles and indirect measurement

Perimeters of similar figures

Similarity rules for triangles

Similar triangles and similarity transformations

Similarity of circles

Triangle Proportionality Theorem

Areas of similar figures

Logic

One area of mathematics that has its roots deep in philosophy is the study of logic. Mathematical log helps to detect whether a statement is valid or invalid.

Identify hypotheses and conclusions

Counterexamples

Truth tables

Truth values

Conditionals

Negations

Converses, inverses and contrapositives

Biconditionals

Sequences and series

A pattern is a series or sequence that repeats. Mathematics patterns are sequences that repeat according to a rule or rules. Numbers can have interesting patterns, like Arithmetic sequences Geometric sequences and so on. Number sequence is a list of numbers in a special order. The sum of infinite terms that follow a rule is called a Series. Sequences and series are important mathematic subject for future and more advanced math problems.

Classify formulas and sequences

Find terms of an arithmetic sequence

Find terms of a geometric sequence

Find terms of a recursive sequence

Evaluate formulas for sequences

Write a formula for an arithmetic sequence

Write a formula for a geometric sequence

Write a formula for a recursive sequence

Sequences: mixed review

Introduction to sigma notation

Identify arithmetic and geometric series

Find the sum of a finite arithmetic or geometric series

Introduction to partial sums

Partial sums of arithmetic series

Partial sums of geometric series

Partial sums: mixed review

Convergent and divergent geometric series

Find the value of an infinite geometric series

Write a repeating decimal as a fraction

Probability

Probability is the chance of something happening or how likely it is that some event will happen. Probability is a number between 0 (not happening) to 1 (certainly happening). Easiest way to understand probability is to toss a coin. There are two outcomes of tossing a coin namely Heads or Tails. So, the probability of the coin landing Heads is 1⁄2 same as the probability of the coin landing tails 1⁄2

Introduction to probability

Calculate probabilities of events

Permutations

Counting principle

Permutation and combination notation

Find probabilities using permutations and combinations

Find probabilities using two-way frequency tables

Identify independent events

Probability of independent and dependent events

Find conditional probabilities

Independence and conditional probability

Find conditional probabilities using two-way frequency tables

Find probabilities using the addition rule

Find probabilities using the normal distribution

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