### All HSPT Math Resources

## Example Questions

### Example Question #31 : Concepts

When evaluating the expression

,

in which order must the operations be carried out?

**Possible Answers:**

Cubing, multiplying, adding

Adding, cubing, multiplying

Adding, multiplying, cubing

Multiplying, cubing, adding

**Correct answer:**

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 #31 : Arithmetic

When evaluating the expression

,

which operation must be performed *last*?

**Possible Answers:**

Exponentiation

Multiplication

Addition

Subtraction

**Correct answer:**

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 #32 : Concepts

When evaluating the expression

,

in which order must the operations be carried out?

**Possible Answers:**

Multiplying, squaring, subtracting

Squaring, subtracting, multiplying

Subtracting, squaring, multiplying

Subtracting, multiplying, squaring

**Correct answer:**

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 on the real numbers as follows:

Which of the following is an undefined quantity?

**Possible Answers:**

**Correct answer:**

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 to be undefined, it must hold that , or .

is the only possible choice; note that , an undefined quantity.

### Example Question #33 : Concepts

When evaluating the expression

,

which operation will be performed *third*?

**Possible Answers:**

The rightmost subtraction

The rightmost addition

The leftmost subtraction

The leftmost addition

**Correct answer:**

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 : Arithmetic

Negative 37 is the square root of what number?

**Possible Answers:**

**Correct answer:**

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 #34 : Concepts

Which of the following four expressions is the greatest?

**Possible Answers:**

**Correct answer:**

By order of operations, multiplication takes precedence over addition, and each is worked right to left. Keeping this in mind:

is the greatest of the four.

### Example Question #38 : Concepts

Which of the following is the least of the four expressions?

**Possible Answers:**

**Correct answer:**

By order of operations, division takes precedence over subtraction, and each is worked right to left. Keeping this in mind:

is the least of the four.

### Example Question #34 : Arithmetic

Solve:

**Possible Answers:**

**Correct answer:**

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.

and so your final answer is .

### Example Question #35 : Concepts

Which of the following is a negative number?

(I)

(II)

(III)

**Possible Answers:**

(II) only

All three

(I) only

(III) only

**Correct answer:**

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.