All SAT II Math II Resources
Example Questions
Example Question #1 : Single Variable Algebra
Which of the following phrases can be written as the algebraic expression ?
Eight subtracted from the absolute value of a number
The absolute value of the difference of eight and a number
The absolute value of the difference of a number and eight
The absolute value of the product of negative eight and a number
Eight decreased by the absolute value of a number
The absolute value of the difference of eight and a number
is the absolute value of , which is the difference of eight and a number. Therefore, is "the absolute value of the difference of eight and a number."
Example Question #2 : Single Variable Algebra
Which of the following phrases can be written as the algebraic expression ?
Seven decreased by the opposite of a number
Seven decreased by the absolute value of a number
The opposite of a number decreased by seven
The opposite of the difference of seven and a number
The absolute value of the difference of seven and a number
Seven decreased by the opposite of a number
is seven decreased by , which is the opposite of a number; therefore, is "seven decreased by the opposite of a number."
Example Question #3 : Single Variable Algebra
Which of the following phrases can be represented by the algebraic expression ?
The multiplicative inverse of the difference of nine and a number
The multiplicative inverse of the difference of a number and nine
Nine less than by the multiplicative inverse of a number
One divided into the difference of nine and a number
Nine decreased by the multiplicative inverse of a number
The multiplicative inverse of the difference of nine and a number
is the multiplicative inverse of , which is the difference of nine and a number. Therefore, is "the multiplicative inverse of the difference of nine and a number".
Example Question #4 : Single Variable Algebra
Which of the following phrases can be represented by the algebraic expression
Ten decreased by three times the square root of a number
Ten decreased by the cube root of a number
The cube root of the difference of a number and ten
Ten less than the cube root of a number
Ten less than three times the square root of a number
Ten less than the cube root of a number
is ten less than , which is the cube root of a number; therefore, is "ten less than the cube root of a number".
Example Question #5 : Single Variable Algebra
Which of the following phrases can be represented by the algebraic expression
Negative twenty multiplied by the square root of a number
The square root of the difference of a number and twenty
Twenty decreased by the square root of a number
The square root of the difference of twenty and a number
Twenty less than the square root of a number
Twenty decreased by the square root of a number
is twenty decreased by , which is the square root of a number, so is "twenty decreased by the square root of a number".
Example Question #6 : Single Variable Algebra
Adult tickets to the zoo sell for ; child tickets sell for . On a given day, the zoo sold tickets and raised in admissions. How many adult tickets were sold?
Let be the number of adult tickets sold. Then the number of child tickets sold is .
The amount of money raised from adult tickets is ; the amount of money raised from child tickets is . The sum of these money amounts is , so the amount of money raised can be defined by the following equation:
To find the number of adult tickets sold, solve for :
adult tickets were sold.
Example Question #4 : Single Variable Algebra
Sarah sells lemonade at the concession stands. She charges fifty cents per cup of lemonade, and twenty five cents for refills. What is the equation that represents the total that she will make from the lemonade stand using the variables cups and refills ?
Sarah charges fifty cents per cup of lemonade:
Sarah charges twenty five cents for refills:
Set up the equation by adding the totals.
The answer is:
Example Question #3 : Finding Roots
Solve for :
To solve for , you need to isolate it to one side of the equation. You can subtract the from the right to the left. Then you can add the 6 from the right to the left:
Next, you can factor out this quadratic equation to solve for . You need to determine which factors of 8 add up to negative 6:
Finally, you set each binomial equal to 0 and solve for :
Example Question #1 : Solving Equations
Give the solution set of the equation .
Use the quadratic formula with :
Example Question #161 : Sat Subject Test In Math Ii
A large tub has two faucets. The hot water faucet, if turned all the way up, can fill the tub in 15 minutes; the cold water faucet can do the same in 9 minutes. Which of the following responses is closest to the time it takes to fill the tub if both faucets are turned all the way up?
Work problems can be solved by looking at them as rate problems.
The hot faucet can fill up the tub at a rate of 15 minutes per tub, or tub per minute. The cold faucet, similarly, can fill up the tub at a rate of 9 minutes per tub, or tub per minute.
Suppose the tub fills up in minutes. Then, at the end of this time, the hot faucet has filled up tub, and the cold faucet has filled up tub, for a total of one tub. We can set up this equation and solve for :
Of the five choices, 6 minutes comes closest.
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