Contents
Review 1 Signed numbers, Algebraic
expressions ··········································· 4
Review 2 Equations ············································· 26
Review 3 Proportion and inverse
proportion ··········································· 52
Review 4 Figures ··················································· 86
Review 5 Organizing and making use ofdata ························································ 160

3 Using simultaneous equations (2) ·········· 42Problems relating to speed / Complementar yproblems relating to speed / Problems relating to salt
water / Problems relating to increases and decreases
in number / Complementary problems relating tosalt water and relating to ratios
Study seminar
Simultaneous linear equations
with three unknowns

Comprehension test for Chapter 2,End-of-chapter problems ···································· 50Chapter

1Calculating withexpressions

1 Calculating with expressions ······················· 7
Monomials and polynomials, and like terms / Adding
polynomials / Subtracting polynomials / Multiplying
and dividing polynomials by numbers / Using theDistributive Law / Calculations on expressions that
contain fractions / Multiplying monomials / Dividing
with monomials / Multiplying and dividing monomials
2 Using expressions ············································ 17
Evaluating expressions / Transforming equalities /Explanations using expressions / Using algebraic
expressions to calculate area and volume / Propertiesof proportional expressions

Comprehension test for Chapter 1,
End-of-chapter problems ···································· 24Chapter

2

Simultaneous equations

1 Solving simultaneous equations ··············· 29
Simultaneous equations and their solutions / Using
the addition/subtraction method / Using thesubstitution method / Solving equations with decimalor fractional coefficients / Various simultaneousequations / Properties of proportion and simultaneousequations / Simultaneous equations in the form of
A＝B＝C
2 Using simultaneous equations (1) ·········· 37
Problems about the values for variables / Problems
relating to numbers / Problems relating to prices /Problems relating to the number of articles or people

Chapter3

Linear functions

1 Linear functions ················································· 55
Linear functions / Rates of change / Graphs ofproportion and graphs of linear functions / Slopes
and intercepts / Domains
2 Finding expressions for linear functions····················································································· 62
Using the rate of change and a set of x, y values /Using two sets of x, y values / Finding expressions
for parallel lines
3 Linear functions and equations ················ 66
Graphing equations / Solutions to simultaneous
equations and the intersection of graphs / Graphs oflinear functions and areas of triangles
4 Graphs and figures ··········································· 72
Bisecting the area of triangles / Length of segments
and equations
5 Using linear functions ···································· 77
Using linear functions

Comprehension test for Chapter 3,
End-of-chapter problems ···································· 84

8th grade

Chapter

4Parallel and congruent

1 Parallel lines and angles ······························· 91
Vertical angles, Corresponding angles, Alternate
interior angles / Parallel lines and angles / Interior
and exterior angles in triangles / Using the propertiesof triangles / Classifying triangles
2 Polygons and angles ········································ 96
Interior angles in polygons / Exterior angles inpolygons / Finding the measurement of various angles
3 Congruent figures ··········································· 101
Congruent figures / Conditions for congruent
triangles
4 Proof setup ························································· 105
Hypothesis and conclusion / Proofs for thecongruence of two triangles / Proofs that use theproperties of parallel lines / Proofs regarding figure
construction

Comprehension test for Chapter 4,
End-of-chapter problems ·································· 116

Chapter

5

Triangles andquadrilaterals

1 Isosceles triangles ·········································· 119
Definitions, Converse of theorems / Properties ofisosceles triangles / Proofs with isosceles triangles
2 Right triangles ·················································· 127Conditions for congruent right triangles / Proofs
with right triangles
3 Parallelograms ·················································· 133
Proper ties of parallelograms / Proofs withparallelograms / Conditions for parallelograms /Proving that a figure is a parallelogram
4 Special kinds of parallelograms, Parallellines and area ···················································· 142
Rectangles, Rhombuses, Squares / Conditions forbecoming special kinds of parallelograms / Parallellines and area / Changing shapes without changing
area
Study seminar Midpoint theorem

Chapter6

Probability

1 Number of ways for an event to happen··················································································· 163
Number of ways for an event to happen
Study seminar Calculating to find the numberof ways for an event to happen
2 Probability ·························································· 167
Meaning of probability / Basics of probability / Diceand probability / Complementary problems about
dice and probability / Balls and probability / Cards
and probability / Coins and probability
Study seminar
Probability that an event will
not happen

Comprehension test for Chapter 6,
End-of-chapter problems ·································· 178

Chapter

7

Data Analysis

1 Quartile points and Box and Whisker Plot··················································································· 180
Quartile points (1) / Quartile points (2) / Box andWhisker Plot / Relationship between Histogramand Box and Whisker Plot○Let’s review·························································· 186

Key points learned during the second yearof junior high school ············································ 192

Comprehension test for Chapter 5,
End-of-chapter problems ·································· 150
Complements
Complements

Functions and figures ················· 152
Properties of circles ···················· 156

Note: “Final test (placed from page 186 to page 191 in the original book)” is omitted in this book.