Chapter 1 and 2 Review

Real Numbers

1

What is the smallest prime number?

2

2

What is the term for a number that cannot be written as a simple fraction, such as pi?

irrational number

3

prime factorization of 20 expressed with exponents

2² x 5

4

square root of 81 - square root of 25

4

5

Give an example of a perfect square expressed in exponent form

depends on answer

Scientific Notation

1

The number of significant figures in the measurement 0.0045

2

2

The number 35,000 written in proper scientific notation

3.5 x 10⁴

3

standard decimal form of 4.2 x10^-3

0.0042

4

If a city of 4 x 10⁶ people each produces 2 x 10³ kilograms of waste per year, what is the total waste produced by the city, in scientific notation?

8 x 10⁹ kg

5

estimated value of 19.8 + 11.5 if you round every number to one significant figure before calculating

30

Algebra

1

simplified form of 3x + 4y - x + 2y

2x + 6y

2

expanded form of 4(2a - 3)

8a - 12

3

fully factorised form of 15x² - 10x using the highest common factor

5x(3x - 2)

4

A shipping box has a height of 2x, a width of x, and a length of 3x - 1. Find the fully expanded algebraic expression for the volume of the box.

6x³ - 2x²

5

factorised form of the monic quadratic expression x² + 7x + 10

(x + 2)(x + 5)

Exponents

1

simplified form of m⁴ x m⁵

m⁹

2

y-⁸/x^-2 with positive exponents only

x²/y⁸

3

5⁰ + 2^-1

1.5

4

(2a³)³

8a⁹

5

A digital image has a file size of 16 x 2⁵ bytes. If a server compresses the file by dividing its size by 2^-3, what is the new file size expressed as a single base of 2?

2¹² bytes

Random

1

Between 1/3, 0.25, and square root 2, identify the irrational number.

square root 2

2

The number of significant figures in 105.0

4

3

simplified form of p⁵ x p^-2

p³

4

factorise x² - 81

(x - 9)(x + 9)

5

Area of a square whose side length is represented by the term 3x

9x²