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Chapter I
Sets and logic
1
Sets and operations on them
Lessons 1
2
Statements and logical operations
Lessons 2–3
3
Implication, predicates and quantifiers
Lessons 4–5
4
Correct reasoning and problem solving
Lessons 6–7
Chapter II
Percentages, equations and inequalities
5
Simple and compound interest
Lessons 8
6
Percentage problems
Lessons 9
7
Rational equations
Lessons 10
8
Irrational equations
Lessons 11
9
Exponential equations
Lessons 12
10
Approximate solving and rational inequalities
Lessons 13–14
11
Irrational inequalities
Lessons 15
Geometry
Planimetry review and introduction to stereometry
12
The logic of planimetry and problem-solving methods
Lessons 16–17
13
Planimetry review
Lessons 18
14
Polyhedra and solids of revolution
Lessons 19–20
15
Surface area problems
Lessons 21
16
Lines, planes and sections in space
Lessons 22–23
17
Practice with lines and planes in space
Lessons 24
Chapter III
Elementary functions and equations
18
Function, monotonicity and extrema
Lessons 25–26
19
Linear and quadratic models
Lessons 27
20
Periodic processes, sine and cosine
Lessons 28–29
21
The simplest trigonometric equations
Lessons 30
22
Trigonometric inequalities and graph transformations
Lessons 31–32
23
Parametric graphs and the exponential function
Lessons 33–34
24
Exponential inequalities and the logarithm
Lessons 35–36
25
Exponential and logarithmic models
Lessons 37
Chapter IV
Complex numbers
26
Complex numbers and operations on them
Lessons 38
27
The trigonometric form of a complex number
Lessons 39–40
28
Roots of complex numbers
Lessons 41
Geometry
Parallelism and perpendicularity in space
29
Mutual position of lines in space
Lessons 42
30
Parallelism of a line and a plane, and of two planes
Lessons 43–44
31
Parallel projection and parallelism problems
Lessons 45–46
32
Perpendicular lines and planes, obliques, distance
Lessons 47–48
33
Three perpendiculars and perpendicular planes
Lessons 49–50
34
Orthogonal projection and perpendicularity in practice
Lessons 51–52
☰ Contents · Mathematics
Grade 10
›
Mathematics
›
Week 24
Exponential inequalities and the logarithm
Lessons 35–36 · 2 lessons · M. A. Mirzaahmedov, Sh. N. Ismailov, A. Q. Amanov (algebra and analysis), B. Q. Haydarov (geometry). Mathematics Grade 10, Parts 1 and 2, 1st edition. EXTREMUM PRESS, Tashkent, 2017
Lesson 35
Lesson 36
Quiz
8
Homework
5
Answers are for parents and teachers.
Show all answers
1
Solve 5^(x + 1) ≥ 25.
Answer
[1, +∞)
2
Solve (1/3)^(2x − 1) > 1/9.
Answer
(−∞, 3/2)
3
Solve log₃(2x + 1) = 2.
Answer
4
4
Solve log₂(x − 1) < 3.
Answer
(1, 9)
5
Compute log₄ 8 and explain your result.
Answer
3/2, because 4^(3/2) = (2²)^(3/2) = 2³ = 8.
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Week 24 · Quiz
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Week 25 · Lesson 37: Modelling with exponential and logarithmic functions
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