HSPT Math : Concepts
Study concepts, example questions & explanations for HSPT Math
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Example Questions
Example Question #31 : Concepts
When evaluating the expression
in which order must the operations be carried out?
Adding, multiplying, cubing
Multiplying, cubing, adding
Cubing, multiplying, adding
Adding, cubing, multiplying
Cubing, multiplying, adding
According to the order of operations, since no grouping symbols are present (the parentheses are setting apart a negative number, not an operation), the exponentiation (the cubing) is worked first, then the multiplication, then the addition.
Example Question #32 : Concepts
When evaluating the expression
which operation must be performed last?
Exponentiation
Addition
Subtraction
Multiplication
Addition
According to the order of operations, since no grouping symbols are present (the parentheses are setting apart a negative number, not an operation), the exponentiation must be performed first, followed by the multiplication. The remaining subtraction and addition are performed in left-to-right order, so the subtraction is worked next, and the addition is the final operation performed.
Example Question #33 : Concepts
When evaluating the expression
in which order must the operations be carried out?
Subtracting, multiplying, squaring
Subtracting, squaring, multiplying
Squaring, subtracting, multiplying
Multiplying, squaring, subtracting
Subtracting, squaring, multiplying
According to the order of operations, the operation inside the parentheses, which is the subtraction, is performed first. This leaves a multiplication and an exponentiation (the squaring); by the order of operations, the squaring is performed next, then the multiplication.
Example Question #31 : Concepts
Define an operation 
Which of the following is an undefined quantity?
If both the base and exponent of an exponential expression are integers, then the expression is undefined if and only if the base is 0 and the exponent is 0 or negative. For 
Example Question #34 : Concepts
When evaluating the expression
which operation will be performed third?
The rightmost subtraction
The leftmost addition
The rightmost addition
The leftmost subtraction
The rightmost addition
In the order of operations, additions and subtractions are performed left to right. Therefore, the four operations are performed in the following order: leftmost addition, leftmost subtraction, rightmost addition, rightmost subtraction. Therefore, the rightmost addition is performed third.
Example Question #35 : Concepts
Negative 37 is the square root of what number?
The square root of a number is the number which, when squared - multiplied by itself - yields that number as its result. Recall that when two negative numbers are multiplied together they result in a positive numbers.
Therefore, negative 37 is the square root of
Example Question #37 : Arithmetic
Which of the following four expressions is the greatest?
By order of operations, multiplication takes precedence over addition, and each is worked right to left. Keeping this in mind:
Example Question #36 : Concepts
Which of the following is the least of the four expressions?
By order of operations, division takes precedence over subtraction, and each is worked right to left. Keeping this in mind:
Example Question #37 : Concepts
Solve:
Whenever you multiple an odd number of negative values togther, you will end with a negative number.
Then you just need to multiple your actual values together.
Example Question #38 : Concepts
Which of the following is a negative number?
(I)
(II)
(III)
(III) only
(I) only
All three
(II) only
All three
(I) and (II) are both negative, since the product or quotient of a negative number and a positive number is negative.
The sum of a negative number and a positive number assumes the sign of the number with the greater absolute value. Since in (III), the negative number has the higher absolute value (200 versus 180), the sign of the sum is negative.
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