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

Measurement and Geometry (MG) 17

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

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) 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
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 add the numbers divide by the number of numbers
Median	Middle order from smallest to biggest. find the middle number.
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	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.
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. (don’t 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 3-D 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^4bc)(7ab^3c)	42a^5b^4c^2
AF3.1
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
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 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)
AI10.0
AI15.0