assesses
designated California content standards from grades 6 and 7 and Algebra 1.
80
questions in a multiplechoice format are used to assess six strands:
Strand Number of Questions
Statistics, Data Analysis, and
Probability (P) 12
Mathematical Reasoning (MR)
8
Algebra 1 (AI) 12
About
a 55% is needed to pass the test.
However only about 45% of students pass the
first
time they take it. You can dramatically
improve your chances of passing by
considering
these test taking strategies and studying the important concepts in the table
below:
·
Watch
out for trick answers, ones from your calculations that do not answer the
question.
·
Estimate
to make calculations easier.
·
Plug
in the answers and see which one works.
·
If
you are not sure what to do, eliminate answers you know are incorrect then
guess.
·
Study
the table below. You can print it then
fold it down the middle and use it like
flashcards to review key
vocabulary and concepts.
·
Practice
sample problems and review more detailed information about each strand
at: http://www.cde.ca.gov/statetests/cahsee/resources/mathtg/section3.pdf
(Please
note that this table is a work in progress.
Some items are incomplete.)
Front 
Back 
Number Sense (NS) 

NS1.1 

Scientific Notation is used to

write very big or
small numbers. 
Numbers in Scientific Notation have the
form

x.xx * 10^{n} one
digit before the decimal, no extra zeros, 10 to nth power 
The exponent, n, tells you

how many places to
move the decimal point 
With Scientific Notation the exponent
n is __________ for large numbers
n is __________ for small numbers 
positive negative 
NS1.2 

To add numbers
with the same sign 
add the numbers
and keep the sign 
To add numbers
with different signs 
subtract the
numbers and keep the sign of the larger number. 
Subtraction Means 
Add The Opposite (SMATO) 
Rules for
Multiplication: For any real
number a a*1 = _____, a*0 = _____, a(1) = _____ If two numbers
have the same sign, their product is If two numbers
have different signs their product is 
a, 0,
a positive negative 
A negative times a
negative = 
a positive 
If you multiply an
even number of negatives the answer will be _________ 
positive 
If you multiply an
odd number of negatives the answer will be _________ 
negative 
The reciprocal of
3/4 is ________ 
4/3 
Any real number
divided by itself is _____ 
1 
Fill in the
blanks: a) 1 + ____ =
0 b) 2 + ____ = 0 c) 3/4 + ____ =
0 d) 1(____) = 1 e) 2(____) =
1 f) 3/4(____) = 1 
a) 1 b) 2 c) Ύ d) 1 e) ½ f) 4/3 
dividing by 2 is
the same as multiplying by _____ 
½ 
Rules for
division: If two numbers
have the same (different) sign, their quotient is __________ (___________) 
positive
(negative) 
The set of
corresponding positive and negative numbers and zero (Ex.
, 2, 1, 0,
1, 2,
) 
Integers 
The entire
collection of integers and positive and
negative fractions 
Rational numbers 
Numbers that
cannot be expressed as the ratio of two integers 
Irrational numbers 
The set of
rational and irrational numbers 
Real numbers 
FRACTIONS


To add or subtract
fractions we have to 
have common
denominators 
common
denominators means 
a number they can
both be. (lowest common
multiple) 
To make common
denominators 
multiply by
adjustment fractions (number / itself). 
Any number /
itself 
1 
Some subtraction
problems are more difficult than others because you have to 
borrow from the
whole number to make the fraction bigger. 
If you dont have
enough pieces of pizza to give away you must 
make a whole pizza
by borrowing. 
To multiply or
divide fractions we dont need ____ but we do
________________ 
common
denominators multiply them 
To divide
fractions 
multiply by the
reciprocal (copy dot flip) 
To multiply or
divide mixed numbers you must first 
change them to
improper fractions. 
To change a mixed
number to an improper fraction 
Whole number times
denominator then add to numerator. 
DECIMALS


To add or subtract
fractions 
1. write the problem
vertically by lining up the decimal points and put the decimal point
in the answer. 2. add or subtract
as normal. (remember for subtraction you may have to add zeros
and borrow). 
To multiply
decimals 
1. multiply as
whole numbers (disregard the decimal point) 2. count the decimal places used in the original numbers. 3. put the decimal
point in your answer that many places to the left. 
To divide decimals 
1. set up the
problem as long division. move the decimal point in the divisor to
make it a whole number. 2. move the
decimal point in the dividend the same number of spaces to the right and put
the decimal point at the same place in the
answer. 3. divide as
normal. 
To estimate
division (a quotient) 
Choose numbers
close to the dividend and divisor that are easy to divide. 
To multiply
(divide) a number by 10, 100, or 1,000 
move the decimal
place to the right (left) for each zero in 10, 100, or 1,000. 
NS1.3 

To convert:
fraction to decimal 
1. just do long
division or 1. multiply by an
adjustment fraction to get the denominator to be a power of 10. 2. write as a
decimal with the correct place value. 
To convert:
decimal to fraction 
1. write the
decimal portion over its smallest place value (10, 100, 1000, etc.) 2. simplify (by
canceling common factors). 
To convert:
percent to decimal 
move the decimal 2
places to the left. 
To convert:
decimal to percent 
move the decimal 2
places to the right 
To convert:
percent to fraction 
eliminate the % and
write over 100 
To convert:
fraction to percent 
fraction ΰ decimal ΰ percent 
NS1.6 

% increase (decrease) =

1. amount of
increase (decrease) original amount 2. covert the
decimal to a percent. 
NS1.7 

discount (markup/sales tax) =
new price = 
original price *
rate of discount (markup/sales tax) original price
discount (or + markup/sales tax) 
commission earned =

sales * commission
rate 
profit =

revenues 
expenses 
I =
Simple Interest

p*r*t principal*rate*time 
Compound Interest

Interest on the
interest. (more than simple interest) p*r for each time period, increasing the
principal each time. I^{1st} =
p*r, I^{2nd} = (p+I^{1st})*r, I^{3rd} = (p^{2nd}+I^{2nd})*r 
If you forget how to do compound
interest, do simple interest and _____________________

choose the answer
that is a little bigger. 
NS2.1 

Negative exponents indicate ____________
erase the negative and move it to the ___________ 
reciprocals numerator (top) or
denominator (bottom) 
Exponent rules, NS2.3, (do, do not) work
for negative exponents.

do 
NS2.2 

To find prime factorization make a
____________

factor tree 
NS2.3 

b^{n} = The b is called
the ____________ The n is called
the ____________ 
b*b*b*b
(b times
itself n times) (if b is any real
number and n is any + integer) base exponent 
To multiply powers
of the same base: keep the base and
_____________________ 
add the exponents 
To divide powers
of the same base: keep the base and
_____________________ 
subtract the
exponents 
To find a power of
a power of a base: keep the base and
_____________________ 
multiply the
exponents 
NS2.4 

To square an number

multiply it by
itself 
Square root, √ , means

what number times
itself is . . . 
√94 is between what two integers? 
9 and 10 
NS2.5 

The distance
between a number and zero on the number line is called _____________________
and is always ______________ 
absolute value positive 
Symbol used to
represent the absolute value of a number, n 
n 


Statistics, Data Analysis, and Probability (P) 

6P1.1 

Mean

Average

Median

Middle

Mode

The number that
occurs most often. 
Extreme values, very big or small, have
the most effect on the (mean, median, mode)?

Mean 
6P2.5 

6P3.1


If there are n ways to do one
thing and r ways to do another thing, how many ways are there to do
both things together?

n*r 
6P3.3


Probabilities, the chance something will
happen, are always between ____ and ____.
They can be expressed as _____, _____, or _____. 
0 and 1 fractions,
decimals, or percents 
To calculate probability A will
happen, P(A)

number of
favorable outcomes number of possible
outcomes 
Probability = _____ it definitely will
not happen.
Probability = _____ it definitely will not happen. 
0 1 
To calculate probability x will
not happen

1 P(x) 
6P3.5


If events are independent

Then the outcome
of one event does not influence the outcomes of others. 
If events are dependent

Then the outcome
of one event does influence the outcome of others. 
The probability more than one thing will
happen:
P(A and B) =
P(A or B) = 
P(A) * P(B) P(A) + P(B) 


7P1.1


Bar graphs

use vertical or
horizontal bars to compare the number of items in each category. 
Line graphs are often use to show
____________

changes over time.
(time is on the horizontal) 
Pictograms


Stem and leaf plots

TensOnes 0
 3,3,3,5,8,9 1
 2,3,4,4,8,8,9 2
 0,2,2,4 3
 1,3 
Box and wisker plots show
_______________

the median,
quartiles, and extremes. 
Circle graphs show data as a
______________

percentage of a
total. 
7P1.2


Correlation is _______________________

a measure of the
relationship between 2 variables. 
Draw a line of best fit through a
scatterplot:
If it goes up, ____________ If it goes down, ____________ If it is difficult to draw a line, ______________ 
positive
correlation. (one
increases the other increases) negative
correlation. (one
increases the other decreases) no correlation. (dont affect each other) 
7P1.3


The minimum and maximum are the
__________

highest and lowest
values in a set of data. 
The upper (lower) quartile is the
____________

median of the
upper (lower) half. 


Measurement and Geometry (MG) 

MG1.1 

To convert between two units of measure

position the
conversion fraction so the old units cancel out, then multiply or divide. Ex. original
units * new units . = new units 1 original units 
MG1.2 

To use a scale model set up a
_______________.
Then ___________ to solve for the unknown. 
proportion Ex. model
length = model width actual length actual width cross multiply 
MG1.3 



MG2.1 

Perimeter is ___________________________
Found by _____________________________ 
the distance
around a polygon. adding up the
sides. 
Circumference is _______________________
Given by the formula: 
the distance
around a circle. C =πd or C = 2πr 
Area of a parallelogram =

bh
(base*height) 
A triangle is _________ of a
parallelogram.
So the area of a triangle = 
½ ½ bh 
Surface Area (of a 3D object) =

area of all the
surfaces added together. 
Volume is the _______________
Volume of a prism = 
space inside. lwh
(length*width*height) 
MG2.2 

To calculate the area or surface area of
a complex object _______________________________

break it up into
several basic shapes. 
MG2.3 



MG2.4 



MG3.2 

When you translate an object you
_________ it.

slide 
When you reflect an object you _________
it.

flip 
MG3.3 

The _____________ is the side of a
triangle across from the right angle.

hypotenuse 
The Pythagorean Theorem says that if a
triangle is a right triangle, then:

a^{2} + b^{2} = c^{2} (side)^{2}
+ (side)^{2} = (hypotenuse)^{2} 
MG3.4 

Congruent figures have
______________________

the same size and
shape. 


Algebra and Functions (AF) 

AF1.1 

a letter used to
represent an unknown number 
variable 
words that mean
addition 
sum, plus, and,
increased, more than 
words that mean
subtraction 
difference, minus,
decreased, less than, remainder 
words that mean
multiplication 
product, times,
of, by 
words that mean
division 
quotient, divided,
ratio, parts of 
When translating
less than 
reverse the order 
translate: a number is six
less than twice another number 
x = 2y 6 
In a word problem
the verb (usually is) represents _______ 
= 
AF1.2 

The order of
operations used to simplify an expression is _______________ 
G grouping (),
[], 1+2/3 E exponents M multiplication D division A addition S subtraction 
Commutative
Property 
the order in which
you add or multiply real numbers does not affect the result. a + b = b + a ab = ba (for all real numbers a,b) 
Associative
Property 
if you are only
adding or multiplying real numbers the grouping of the numbers does not
affect the result (a + b) + c = a +
(b + c) and (ab)c = a(bc) (for all real numbers a,b,c) 
Distributive
Property 
a(b + c) = ab +
ac (for all real numbers a,b,c) 
We use the
distributive property to 
destroy ( )s when
we get stuck with GEMDAS. 
Four ways to represent multiplication 
8 X n 8*n 8(n) 8n 
AF1.5 



AF2.1


a^{m}*a^{n}
= __________ 
a^{m+n} 
b^{2}*b*2b^{6}
= ______ 
2b^{9} 
(a^{m})^{n}
= __________ 
a^{mn} 
(k^{4})^{4}*k^{3} 
k^{13} 
AF2.2 

(6a^{4}bc)(7ab^{3}c)

42a^{5}b^{4}c^{2} 
AF3.1 



AF3.3


The steepness of a
line 
slope 
slope = 
rise
= vertical change = y_{2} y_{1} run horizontal change x_{2} x_{1} 
When reading from
left to right: lines that go up
have ___________ slope lines that go down
have ___________ slope 
positive negative 
The steeper the
line 
The greater the
absolute value of the slope 
The slope of a
horizontal line 
zero 
The slope of a
vertical line 
no slope 
AF3.4


The slope of a best fit line equals the
___________
of the quantities. 
ratio 
AF4.1


equation 
a mathematical way
to represent a balanced system. 
operations that
undo each other 
inverse operations 
To solve a linear
equation for a specific variable we need to _______________________________ 
get the variable
alone on one side of the equal sign. 
Steps for solving
linear equations 
1) Rewrite the
equation and simplify each side. 2) Write the
inverse operation needed on both sides to get the variable alone and draw a
line underneath. 3) Perform the
inverse operation for each side of the equation always keeping things lined
up. 4) Go back to step
2) as needed(reverse GEMDAS) 5) Check 
AF4.2


A ratio is
comparison of ____________________ just a
________________ 
Comparison of two
quantities Fraction 
An equation saying
two ratios are equal. (= Fractions) 
Proportion 
To solve a
proportion we __________________ 
Cross multiply. 


Mathematical Reasoning (MR) 

MR1.1 

MR1.2 

MR2.1 

MR2.3 

MR2.4 

MR3.1 

MR3.3 



Algebra 1 (AI) 

AI2.0 



AI3.0 



AI4.0 



AI5.0 



AI6.0 

a set of
coordinates that serve to locate a point on a coordinate system 
ordered pair 
Special points at
which a line cuts the axes. 
intercepts 
How do you find
the x intercept 
set y = 0 and solve
the resulting equation for x 
How do you find
the y intercept 
set x = 0 and
solve the resulting equation for y 
Slope Intercept
Form of a linear equation 
y = mx + b m = slope, b = y intercept (for all
real numbers m and b) 
The steps to graph
a line 
1. Solve for y to
get y = mx +b form. 2. Find b, the
yintercept, on the graph. 3. Use m, the
slope, to graph the line. 
AI7.0 

If an ordered pair
is a solution to an equation it will produce 
an identity 
Linear equations
in standard form 
ax + by = c a, b, and c are integers. 
The three steps to
write the equation of a line in slope intercept form are: 
1. find slope
(m) m = y_{2} y_{1} x_{2} x_{1} 2. find y
intercept (b) substitute x, y, and
m
into y = mx + b and
solve for b 3. write the
equation substitute m and b
into y = mx + b 
AI8.0 

If the lines have
the same slope 
Then they are
parallel. 
AI9.0 

Two or more
equations in the same variable form 
a system of linear
equations 
To solve a system
of two equations with two variables, you must 
find all ordered
pairs (x, y) that make both equations true. 
We have learned
three methods for solving a system of linear equations, they are 
the graphing
method, the substitution method, and the addition or subtraction method. 
The steps of the
Graphing Method are 
1. Solve each
equation for y to get y = mx +b
form. 2. Find b, the
yintercept, on the graph. 3. Use m, the
slope, to graph the line. 4. Write the
solution 5. Check 
The steps of the
Substitution Method 
1. Solve one
equation for one of the variables. 2. Substitute this
expression into the other equation and solve for the other variable. 3. Substitute this
value into the equation in Step 1 to find the value of the first variable. 4. Check 
The steps of the
AdditionorSubtraction Method 
1. Multiply one or
both equations to get the same or opposite coefficients for one of the
variables. 2. Add or Subtract
the equations to eliminate one variable. 3. Solve the
resulting equation for the remaining variable. 4. Substitute this
value into either original equation to find the value of the first variable. 5. Check. 
The three possible
solutions to a system of linear equations. 
1. point or
ordered pair  the lines cross 2. no solution
the lines are parallel 3. infinite
solutions the same line (equation) 
AI10.0 



AI15.0 


