All SAT II Math I Resources
Example Questions
Example Question #1 : Single Variable Algebra
Which of the following phrases can be represented by the algebraic expression
?
The square root of the difference of eighteen and a number
The square root of the difference of a number and eighteen
The square root of the product of a number and negative eighteen
Eighteen less than the square root of a number
The square root of a number multiplied by negative eighteen
The square root of the difference of a number and eighteen
is the square root of
,which is the difference of a number and eighteen; therefore,
is "the square root of the difference of a number and eighteen".
Example Question #2 : Single Variable Algebra
Which of the following phrases can be represented by the algebraic expression ?
The product of negative nine and the reciprocal of a number
Nine less than the reciprocal of a number
The reciprocal of the difference of a number and nine
Nine decreased by the reciprocal of a number
The reciprocal of the product of negative nine and a number
Nine less than the reciprocal of a number
is nine less than
, which is the reciprocal of a number. Therefore,
is "nine less than the reciprocal of a number. "
Example Question #1 : Equations Based On Word Problems
Which of the following phrases can be written as the algebraic expression ?
The difference of eight and the square of a number
The square of the difference of a number and eight
Twice the difference of eight and a number
The square of the difference of eight and a number
The difference of eight and twice a number
The square of the difference of eight and a number
is the square of the expression
;
is the difference of eight and a number.
Subsequently, is "the square of the difference of eight and a number".
Example Question #5 : Equations Based On Word Problems
Jim sells apples for per pound and oranges for
per pound. What is a formula to find the
revenue for
pounds of apples and
pounds of oranges?
Since you are solving for , that goes on one side of the equation.
and
's revenues are based on how much they sell for per pound.
So for every pound of apples they make dollars or
.
For every pound of oranges they make dollars or
.
To put it all together, you get
.
Example Question #3 : Single Variable Algebra
Sam currently has five ducks. He will receive 3 new ducks every two months. How many individual ducks must he have after 7 months?
Sam starts out with five ducks. He receives 3 ducks after every two months.
where .
After the first 2 months, he will have 8 ducks.
After the next 2 months, he will have 11 ducks.
After the next 2 months, he will then have 14 ducks.
However, Sam will not receive 3 ducks until the 8th month. This means that he will only have 14 ducks in possession by the 7th month.
The answer is:
Example Question #1 : Solving Equations
Solve for .
Add 9 to each side of the equation.
Multiply each side of the equation by 4.
Example Question #2 : Single Variable Algebra
Solve for .
To isolate , we must first eliminate the fraction on the left hand side by multiplying each side by 3.
Next, 5 must be subtracted fromm both sides.
Finally, 2 must be divided out of each side.
Thus, this is our answer.
Example Question #2 : Solving Equations
Solve for in terms of
:
To solve this equation in terms of y, we must isolate it. We start by moving those terms, that do not involve y, to the right hand side. Thus, we add 6 to both sides.
Next, since there are no other terms on the left hand side that do not include y, we must factor a y out of them.
Now, we can divide to isolate y.
Example Question #3 : Solving Equations
Solve for the unknown variable:
To solve , group like terms on one side of the equal sign.
Example Question #11 : Single Variable Algebra
Solve for .
To isolate the variable in the equation, perform the opposite operation to move all constants on one side of the equation and leaving the variable on the other side of the equation.
Subtract on both sides. Since
is greater than
and is negative, our answer is negative. We treat as a normal subtraction.
Divide on both sides. When dividing with a negative number, our answer is negative.
All SAT II Math I Resources
