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Mathematics — Third Preparatory
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Unit 1
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Relations, Functions, Polynomials and Variation
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Mathematics — Third Preparatory
Unit 1
0/20
Numbers and Operations
1.1
1-1 The base, the exponent, and the product and quotient of powers
1.2
1-2 The zero exponent and the negative exponent
1.3
1-3 Power of a power, of a product and of a quotient
1.4
1-4 Sign of a power: even and odd exponents
1.5
1-5 Powers, square roots and fractional exponents
1.6
1-6 Simplifying expressions that combine several laws
1.7
1-7 Exponential equations by equalising the base
1.8
1-8 Equations with negative exponents and fractions
1.9
1-9 Equations solved by taking out a common factor
1.10
1-10 Equations in which the unknown is the base
1.11
1-11 Real-life applications
1.12
1-12 Summary of the laws of this unit
1.13
Exam traps and key takeaways
Relations, Functions, Polynomials and Variation
2.1
Ordered pairs and the Cartesian product
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2.2
Relations, domain, codomain and range
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2.3
Functions and the function test
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2.4
Graphing quadratic functions with a table
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2.5
Worked examples
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2.6
Common mistakes
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2.7
Lesson summary
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Unit 2
0/12
Algebra, Relations and Functions
1.1
2-1 The quadratic function: definition, values and points
1.2
2-2 The vertex form y = a(x − h)
2
+ k
1.3
2-3 The vertex from the general form
1.4
2-4 Sketching the parabola
1.5
2-5 Maximum and minimum applications
1.6
2-6 Polynomial functions and their degree
1.7
2-7 Zeros of a polynomial function
1.8
2-8 The rational algebraic function, its domain and simplifying
1.9
2-9 Common domain of two functions and equality of functions
1.10
2-10 Addition, subtraction, multiplication and division
1.11
2-11 Additive and multiplicative inverses, and properties
1.12
Exam traps and key takeaways
Unit 3
0/12
Geometry and Measurement
1.1
3-1 The two conditions of similarity and the ratio of perimeters and areas
1.2
3-2 Cases of similarity of triangles and the parallel line
1.3
3-3 Real-life applications of similarity
1.4
3-4 The dilation and its properties
1.5
3-5 Dilation on the coordinate plane
1.6
3-6 Sides relative to an angle, and the definitions of sin, cos and tan
1.7
3-7 Finding side lengths and complementary angles
1.8
3-8 Exact ratios of 30°, 45° and 60°
1.9
3-9 Using the calculator and applications of trigonometry
1.10
3-10 The slope of a line, parallel and perpendicular lines
1.11
3-11 Equations of a line and the intercepts
1.12
Exam traps and key takeaways
Unit 4
0/13
Statistics
1.1
4-1 Measures of central tendency: recap
1.2
4-2 Why do we need measures of dispersion?
1.3
4-3 The range
1.4
4-4 The median recap, quartiles and the interquartile range
1.5
4-5 The box plot (box-and-whisker)
1.6
4-6 Deviation, variance and standard deviation of a set of values
1.7
4-7 Standard deviation of a simple frequency distribution
1.8
4-8 Standard deviation of a grouped (class) distribution
1.9
4-9 Using the scientific calculator
1.10
4-10 Comparing two data sets
1.11
4-11 Effect of adding or multiplying every value
1.12
4-12 Outliers and choosing the right measure
1.13
Exam traps and key takeaways
Quiz
Lesson 1 – Cartesian Product, Relations, Functions and Quadratic Graphing — Lesson quiz
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Questions count:
6
Passing grade:
60%
Start Quiz
1.
If (a − 1, b
3
) = (5, 27), then:
a = 6 and b = 3
a = 4 and b = 9
a = 5 and b = 3
a = 6 and b = 9
2.
If X has 3 elements and Y has 4 elements, then n(X × Y) equals:
7
16
12
64
3.
Is R = {(1, 2), (1, 3), (2, 4)} a function from X = {1, 2} to Y = {2, 3, 4}?
Yes, because every element of Y is used
No, because the input 1 has two outputs
Yes, because the range has 3 elements
No, because the codomain is larger than the domain
4.
The range of the relation y = x + 2 on X = {1, 2, 3} is:
{1, 2, 3}
{0, 1, 2, …, 9}
{2, 3, 4}
{3, 4, 5}
5.
The vertex of the parabola f(x) = x
2
− 6x + 8 is:
(3, −1)
(−3, 35)
(6, 8)
(2, 0)
6.
The maximum value of f(x) = −2x
2
+ 8x − 3 is:
−3
2
5
8
1
2
3
4
5
6
Questions count:
6
Passing grade:
60%
Start Quiz
1.
If (a − 1, b
3
) = (5, 27), then:
a = 6 and b = 3
a = 4 and b = 9
a = 5 and b = 3
a = 6 and b = 9
2.
If X has 3 elements and Y has 4 elements, then n(X × Y) equals:
7
16
12
64
3.
Is R = {(1, 2), (1, 3), (2, 4)} a function from X = {1, 2} to Y = {2, 3, 4}?
Yes, because every element of Y is used
No, because the input 1 has two outputs
Yes, because the range has 3 elements
No, because the codomain is larger than the domain
4.
The range of the relation y = x + 2 on X = {1, 2, 3} is:
{1, 2, 3}
{0, 1, 2, …, 9}
{2, 3, 4}
{3, 4, 5}
5.
The vertex of the parabola f(x) = x
2
− 6x + 8 is:
(3, −1)
(−3, 35)
(6, 8)
(2, 0)
6.
The maximum value of f(x) = −2x
2
+ 8x − 3 is:
−3
2
5
8
1
2
3
4
5
6
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