### All SSAT Upper Level Math Resources

## Example Questions

### Example Question #31 : Number Concepts And Operations

Define a function as follows:

Evaluate .

**Possible Answers:**

**Correct answer:**

### Example Question #32 : Number Concepts And Operations

Define a function as follows:

Evaluate .

**Possible Answers:**

The correct answer is not among the other responses.

The expression is undefined.

**Correct answer:**

### Example Question #31 : Number Concepts And Operations

Define a function on the real numbers as follows:

Evaluate .

**Possible Answers:**

The expression is undefined.

The correct answer is not among the other responses.

**Correct answer:**

The expression is undefined.

Since even-numbered roots of negative numbers are not defined for real-valued functions, the expression is undefined.

### Example Question #32 : Number Concepts And Operations

Define an operation on the real numbers as follows:

For all real numbers :

.

Evaluate .

**Possible Answers:**

The expression is undefined on the real numbers.

**Correct answer:**

The expression is undefined on the real numbers.

However, is undefined in the real numbers; subsequently, so is .

### Example Question #35 : Number Concepts And Operations

**Possible Answers:**

**Correct answer:**

First multiply the fraction in the numerator.

Now we have

Never divide fractions. We multiply the numerator by the reciprocal of the denominator.

### Example Question #36 : Number Concepts And Operations

Which of these expressions is the greatest?

**Possible Answers:**

All of these expressions are equivalent

Twenty-five percent of one fifth

One fifth of

One fourth of

Twenty percent of one fourth

**Correct answer:**

All of these expressions are equivalent

The easiest way to see that all four are equivalent is to convert each to a decimal product, noting that twenty percent and one-fifth are equal to , and twenty-five percent and one fourth are equal to .

One fourth of 0.2:

One fifth of 0.25:

Twenty-five percent of one fifth:

Twenty percent of one fourth:

### Example Question #1 : How To Multiply

Write .007341 in scientific notation.

**Possible Answers:**

**Correct answer:**

The answer is .

### Example Question #38 : Number Concepts And Operations

If are consecutive negative numbers, which of the following is false?

**Possible Answers:**

**Correct answer:**

When three negative numbers are multiplied together, the product will be negative as well. All the other expressions are true.

### Example Question #21 : Basic Addition, Subtraction, Multiplication And Division

Fill in the circle to yield a true statement:

**Possible Answers:**

**Correct answer:**

The problem is asking for a number whose product with 5 yields a number congruent to 3 in modulo 6 arithmetic - that is, a number which, when divided by 6, yields remainder 3. We multiply 5 by each choice and look for a product with this characteristic.

;

;

;

;

;

The only choice whose product with 5 yields a number congruent to 3 modulo 6 is 3, so this is the correct choice.

### Example Question #40 : Number Concepts And Operations

You are asked to fill in all three circles in the statement

with the *same* number from the set

to make a true statement.

How many ways can you do this?

**Possible Answers:**

One

Five

Two

Four

Three

**Correct answer:**

One

The problem is asking for a number whose cube is a number congruent to 9 in modulo 10 arithmetic - that is, a number whose cube, when divided by 10, yields remainder 9. If the quotient of a number and 10 has remainder 9, then it is an integer that *ends* with the digit "9". Since this makes the cube odd, the number that is cubed must also be odd, so we need only test the five odd integers:

Only 9 fits the criterion, so "one" is the correct response.

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