## The Mathematics part of the California High School Exit Examination (CAHSEE)

assesses designated California content standards from grades 6 and 7 and Algebra 1.

80 questions in a multiple-choice format are used to assess six strands:

Strand                                                Number of Questions

## Number Sense (NS)14

Statistics, Data Analysis, and Probability (P)           12

## Algebra and Functions (AF)                                   17

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

(Please note that this table is a work in progress.  Some items are incomplete.)

Front

Back

# Scientific Notation is used to

write very big or small numbers.

# Numbers in Scientific Notation have the form

x.xx * 10n

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

# 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) ¾                              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 don’t have enough pieces of pizza to give away you must

make a whole pizza by borrowing.

To multiply or divide fractions we don’t 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 à decimal à percent

# % increase (decrease) =

1. amount of increase (decrease)

original amount

2. covert the decimal to a percent.

# 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

# 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.

I1st = p*r, I2nd = (p+I1st)*r, I3rd = (p2nd+I2nd)*r

# If you forget how to do compound interest, do simple interest and _____________________

choose the answer that is a little bigger.

# Negative exponents indicate ____________

erase the negative and move it to the ___________

reciprocals

numerator (top) or denominator (bottom)

do

factor tree

# NS2.3

bn =

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

# To square an number

multiply it by itself

# Square root, √ , means

what number times itself is . . .

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|

# Mean

Average

1. add the numbers
2. divide by the number of numbers

# Median

Middle

1. order from smallest to biggest.
2. find the middle number.

# Mode

The number that occurs most often.

Mean

n*r

# 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

1 – P(x)

# 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.

P(A or B) =

P(A) * P(B)

P(A) + P(B)

# 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)

# Stem and leaf plots

Tens|Ones

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.

# 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. (don’t affect each other)

# 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.

# 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

# 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

# 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 3-D object) =

area of all the surfaces added together.

# Volume is the _______________

Volume of a prism =

space inside.

lwh        (length*width*height)

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

break it up into several basic shapes.

slide

flip

hypotenuse

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

a2 + b2 = c2

(side)2 + (side)2 = (hypotenuse)2

# Congruent figures have ______________________

the same size and shape.

# 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

# AF2.1

am*an = __________

am+n

b2*b*2b6 = ______

2b9

(am)n = __________

amn

(k4)4*k-3

k13

42a5b4c2

# AF3.3

The steepness of a line

slope

slope =

rise  =  vertical change       =  y2 – y1

run       horizontal change       x2 – x1

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

# 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.

# 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 y-intercept, 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 =  y2 – y1

x2 – x1

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 y-intercept, 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 Addition-or-Subtraction 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)