Number Theory

Practice Questions

SAT Subject Test in Math II › Number Theory

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1

Sets

The above represents a Venn diagram. The universal set is the set of all positive integers.

Let be the set of all multiples of 2; let be the set of all multiples of 3; let be the set of all multiples of 5.

As you can see, the three sets divide the universal set into eight regions. Suppose each positive integer was placed in the correct region. Which of the following numbers would be in the same region as 873?

2

Sets

The above represents a Venn diagram. The universal set is the set of all positive integers.

Let be the set of all multiples of 2; let be the set of all multiples of 3; let be the set of all multiples of 5.

As you can see, the three sets divide the universal set into eight regions. Suppose each positive integer was placed in the correct region. Which of the following numbers would be in the same region as 873?

3

$\overline{x}$ denotes the complex conjugate of .

If $x = \frac{1}{10} - \frac{1}{5} i$ , then evaluate $\overline{x}^{2} - x^{2}$ .

4

is a complex number; $\overline{x}$ denotes the complex conjugate of .

$x \cdot \overline{x} = 84$

Which of the following could be the value of ?

5

The fraction $\frac{5+3i}{2-2i}$ is equivalent to which of the following?

6

Multiply:

$-3 i \cdot 8i \cdot 5i \cdot 6i$

7

Evaluate:

$\left ( 7+3i\right )^{2}$

8

Let be a complex number. $\overline{x}$ denotes the complex conjugate of .

$x+\overline{ x} = 20$ and $x \overline{ x} = 200$ .

How many of the following expressions could be equal to ?

(a)

(b)

(c)

(d)

9

Multiply: $\left ( 4+ 7i\right )(4 - 7i)$

10

$\overline{x}$ denotes the complex conjugate of .

If $x = \frac{1}{10} - \frac{1}{5} i$ , then evaluate $\overline{x}^{2} - x^{2}$ .

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