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INSTRUCTION
Kumon vs. High School Math Curriculum Chart
Kumon is pleased to announce a comparison chart
between the Kumon Math Curriculum and the National
Math Curriculum (for math subjects: Algebra I, Algebra II,
Geometry, Trigonometry, Math Analysis, Linear Algebra, and
Calculus). As each state creates its own curriculum, we have
compiled the curriculum of eight states (California, Florida,
Hawaii, Illinois, Michigan, New York, New Jersey, and Texas)
to create our view of the National Math Curriculum.
This chart may be used to motivate the students in your
Center in a variety of ways, including:
1. Showing to students and parents how the Kumon
Math Worksheets compare to what they are currently
learning, and what they will learn, in school.
2. Increasing your knowledge and understanding of
the general topics that are taught in the general high
school math courses. One point to remember is that,
as each state sets its own curriculum (and there are
even differences between districts and schools), there
may be some differences between exactly what your
students are learning in school and what is displayed
on this chart.
Some points to remember about the Kumon Curriculum are:
•
24
It is a Global Curriculum that is based on the
performances of all countries.
VOICES: A QUARTERLY MAGAZINE FOR INSTRUCTORS
•
It is also structurally different from the “spiral
curriculum” implemented in American schools.
•
It thoroughly prepares students to be successful in
life, not just in school.
•
It will assist students in their school math studies.
Following are some examples of standards from each of the
High School Math Curriculum subjects along with Kumon
problems related to that standard.
School Topic – Algebra I
1. Solve linear equations and inequalities.
o Kumon Examples: 
8x + 3y =
• H 41a (1) 
30
5x + 3y = 21
•
H 132a (1)
3x + 4 < 5x + 8

4x − 8 < x + 1
2. Solve quadratic equations by factoring, completing the
square, or using the quadratic formula.
o Kumon Examples:
2
• I 112a (2) x + 5x + 6 = 0 (factor)
•
I 125a (3) x
the square)
2
− 6x − 5 = 0
(complete
INST R U C T I O N
•
I 132a (2) 2x − 7x + 1 =
(Quadratic Formula)
2
0
School Topic – Algebra II
1. Perform basic four operations on complex numbers.
o Kumon Examples:
• J 112b (13) −9 × −16 =
•
J 113a (4)
•
J 113b (9)
•
J 114a (2)
9 ÷ −25 =
(2 + 2i )(3 + 2i ) =
(2 − 5 2i )(3 + 4 2i ) =
2. Determine a quadratic function from its roots or graph.
o Kumon Example:
• K 36b (4) Find the equation of the
parabola which intersects the x-axis at
2 points (1, 0), (3, 0) and passes through
point (4, – 6).
3. Solve problems dealing with absolute value.
o Kumon Examples:
• L 32b (2) x x + 3 =
(
)
•
L 33b (3) Graph the function
•
L 38b (1) Find the point of
intersection of the two functions
y = 2x − 3
School Topic – Geometry
1. Know and use angle and side relationships in special
triangles (30-60-90, 45-45-90)
o Kumon Examples:
• I 180a Find the value of x and y in each
figure using the following theorems:
• (1) In a right triangle with 30°
and 60° angles, the ratio of the
length of each side to each other
is
•
1: 3 : 2 .
(2) In a right triangle with 45°
angles, the ratio of the length
of each side to each other is
1:1: 2 .
2. Find equations of parallel and perpendicular lines.
o Kumon Examples:
• M 165a (1) Given point P(1,1) and the line
l: 3x + 4 y = 12 , obtain the equation of
a line m which passes through point P
and is perpendicular to l.
• M 180b (3) Obtain the equation of the
line that passes through the point of
intersection of lines 4x − y = −1 and
x + 6 y = −3 , and is parallel to line
6x − 3y = 2 .
y = x 2 − 2x − 3 , y = x + 3
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25
INSTRUCTION
School Topic – Trigonometry
School Topic – Calculus 1. Know the sine and cosine graph.
o Kumon Examples:
• M 72a 1. Draw the graph of
from 0 to 2π.
• M 78a 1. Draw the graph of
1. Find the derivative of a function.
o Kumon Examples:
• Differentiate the following functions:
2
• L 48a (8) y = ax
• L 50a (2)
from
π
−
2
y = sin x ,
y = cos x ,
to 3π.
2. Use addition formulas for sines and cosines to prove or
simplify trigonometric identities.
o Kumon Example:
• M 114a (1) Prove the following equality
using the Addition Theorem:
sin 2α = 2sinα cosα
School Topic – Mathematical Analysis 1. Derive equations using locus of points.
o Kumon Example:
• N 2b 4. Obtain the equation of the locus
of point P x, y such that the distance
( )
from P to A (5,4 ) is 2.
2. Find the maximum and minimum of a function
o Kumon Example:
• K 70a 1. Given the
quadratic function
2
() (
)
f x = x−a +2
(0 ≤ x ≤ 1)
find the maximum and minimum
values.
School Topic – Linear Algebra
1. Add and multiply matrices.
o Kumon Example:
• *XM 7b 2.(3) Perform the following
calculations of matrices.
  1 2   −4 2   4 −4 
+
 − 
=

  2 −3  1 4   −3 1 
2. Compute the dot product of 2 vectors.
o Kumon Example:
r
• *XV 7a 1. Given that a
( ),
r
r
b = ( 2,3) , and c = ( 3,4 ) , evaluate the
= 1,2
following expressions, and determine
whether each result is a vector or a
scalar.
r r
• (1) a g b =
26
VOICES: A QUARTERLY MAGAZINE FOR INSTRUCTORS
(
)(
y = x 2 3x 2 + 1 3x + 2
)
2. Solve definite and indefinite integrals.
o Kumon Examples:
• Evaluate the following integrals:
• L 120b (1)
∫
2
1
•
( 4x
3
)
− 6x 2 dx =
L 113b (9)
∫ ( x + 1)
2
(
)
2
dx − ∫ x − 1 dx =
We hope that you find this comparison chart useful in
motivating your students.
*XM and XV are sections of Level X, to be released later this
year, which contains Elective Course material including:
Triangles, Vectors, Matrices, Probability, and Statistics.