CHSPE PRACTISE EXAM WITH
ACCURATE SOLUTIONS
Scientific Notation Rules - ANS-If the number is positive the decimal moves to the
RIGHT.
If the number is negative the decimal moves to the LEFT
mean - ANS-the arithmetic average of a distribution, obtained by adding the scores and
then dividing by the number of scores
Median - ANS-the middle score in a distribution; half the scores are above it and half
are below it
Mode - ANS-The value that occurs most frequently in a given data set.
GCF (Greatest Common Factor) - ANS-The largest number that can divide each
number from a set of numbers without a remainder.
Ex. The G.C.F. of 8 and 12 is 4.
KCF - ANS-Keep, Change Flip. This is used for dividing fractions
How to factor trinomials with a leading coefficient that is not 1? - ANS-1) Multiply the
leading coefficient by the constant
2) Find 2 numbers that multiply to the product of that but add to the middle number
3) Rewrite and replace the middle term with the 2 numbers (REM: put xs next to the
numbers u replace with)
4) Factor by grouping (factor gcf from the first 2 terms separately from the last 2)
5) The 2 binomials should have the same value in the parenthesis with 2 diff numbers
outside [ex. 2x(x-3) 1(x-3)]
6) Bring the number in parenthesis down and put the outside numbers in their own
parenthesis [ex. (x-3)(2x+1)]
How do you multiply fractions? - ANS-Cancel or reduce if possible, then multiply straight
across. Some people like to multiply straight across and then reduce. Either way, if you
can reduce, you MUST REDUCE.
How do you divide fractions? - ANS-Keep, Change, Flip!
1) Keep the first fraction
2) Change the sign
3) Flip the second fraction (reciprocal)
, How do you multiply exponents? - ANS-Multiply the constant terms and add the
exponents; ex. 4w² × 8w³ = (4×8)w²+³ = 32w⁵
- ex. x^4 • x^5 = x^9
exponent raised to another exponent - ANS-multiply the exponents
(ex. (x^3)^4 = x^12
How do you 'square root' a number? e.g. √36 - ANS-Find what number multiplies by
itself to give the number you are square rooting.
e.g. √36 is 6
If not a perfect square #, split it into two numbers, one of which is a perfect square.
Solve. The perfect square will go on the outside, and the remainder will stay inside.
Zero Rule - ANS-Anything to the zero power equals 1
negative exponent - ANS-take the reciprocal and change the exponent to positive
(REM. Invisible 1)
Negative coefficient and positive exponent - ANS-ex. -3^2
The - sign doesn't apply to the ^2, so think of the equation as -(3)(3) = -9
If the equation was (-3)^2, then the - would apply, and it would mean (-3)(-3) = +9
What should you do if you have a negative exponent? - ANS-Make it positive
Do the reciprocal to make the exponent positive
ex x^-5 = 1/x^+5
What should you do if you have an equation like this: (#x^2)^3 - ANS-(#x^2)^3
First, remember that the exponent connected to the coefficient (#) is 1. We need to
distribute the outside exponent (3) To both of the inside exponents. (1 and 2). Then,
simplify the coefficient (1^2 = 1) and rewrite.
How do you divide variables raised to exponents with a common base (ex y^5/y^-3) -
ANS-When dividing by a common base, you need to subtract the exponents.
Think of the division line as a huge minus sign.
After I DIVIDE variables, the variable goes: __________
ex. 18a^3b^-4c^-a^7b^5c^-9 - ANS-On top, no exceptions
standard form of a linear equation - ANS-Ax + By = C
ACCURATE SOLUTIONS
Scientific Notation Rules - ANS-If the number is positive the decimal moves to the
RIGHT.
If the number is negative the decimal moves to the LEFT
mean - ANS-the arithmetic average of a distribution, obtained by adding the scores and
then dividing by the number of scores
Median - ANS-the middle score in a distribution; half the scores are above it and half
are below it
Mode - ANS-The value that occurs most frequently in a given data set.
GCF (Greatest Common Factor) - ANS-The largest number that can divide each
number from a set of numbers without a remainder.
Ex. The G.C.F. of 8 and 12 is 4.
KCF - ANS-Keep, Change Flip. This is used for dividing fractions
How to factor trinomials with a leading coefficient that is not 1? - ANS-1) Multiply the
leading coefficient by the constant
2) Find 2 numbers that multiply to the product of that but add to the middle number
3) Rewrite and replace the middle term with the 2 numbers (REM: put xs next to the
numbers u replace with)
4) Factor by grouping (factor gcf from the first 2 terms separately from the last 2)
5) The 2 binomials should have the same value in the parenthesis with 2 diff numbers
outside [ex. 2x(x-3) 1(x-3)]
6) Bring the number in parenthesis down and put the outside numbers in their own
parenthesis [ex. (x-3)(2x+1)]
How do you multiply fractions? - ANS-Cancel or reduce if possible, then multiply straight
across. Some people like to multiply straight across and then reduce. Either way, if you
can reduce, you MUST REDUCE.
How do you divide fractions? - ANS-Keep, Change, Flip!
1) Keep the first fraction
2) Change the sign
3) Flip the second fraction (reciprocal)
, How do you multiply exponents? - ANS-Multiply the constant terms and add the
exponents; ex. 4w² × 8w³ = (4×8)w²+³ = 32w⁵
- ex. x^4 • x^5 = x^9
exponent raised to another exponent - ANS-multiply the exponents
(ex. (x^3)^4 = x^12
How do you 'square root' a number? e.g. √36 - ANS-Find what number multiplies by
itself to give the number you are square rooting.
e.g. √36 is 6
If not a perfect square #, split it into two numbers, one of which is a perfect square.
Solve. The perfect square will go on the outside, and the remainder will stay inside.
Zero Rule - ANS-Anything to the zero power equals 1
negative exponent - ANS-take the reciprocal and change the exponent to positive
(REM. Invisible 1)
Negative coefficient and positive exponent - ANS-ex. -3^2
The - sign doesn't apply to the ^2, so think of the equation as -(3)(3) = -9
If the equation was (-3)^2, then the - would apply, and it would mean (-3)(-3) = +9
What should you do if you have a negative exponent? - ANS-Make it positive
Do the reciprocal to make the exponent positive
ex x^-5 = 1/x^+5
What should you do if you have an equation like this: (#x^2)^3 - ANS-(#x^2)^3
First, remember that the exponent connected to the coefficient (#) is 1. We need to
distribute the outside exponent (3) To both of the inside exponents. (1 and 2). Then,
simplify the coefficient (1^2 = 1) and rewrite.
How do you divide variables raised to exponents with a common base (ex y^5/y^-3) -
ANS-When dividing by a common base, you need to subtract the exponents.
Think of the division line as a huge minus sign.
After I DIVIDE variables, the variable goes: __________
ex. 18a^3b^-4c^-a^7b^5c^-9 - ANS-On top, no exceptions
standard form of a linear equation - ANS-Ax + By = C
