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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.

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
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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
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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
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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