Midterm Review

Real Numbers

100

What type of number is 0: natural, whole, integer, rational, irrational, or real? Give the smallest set it belongs to.

Whole number

200

What type of number is -7?

Integer

300

Is the square root of 10 rational or irrational?

Irrational

400

Name all sets that -3/4 belongs to from: natural, whole, integer, rational, irrational, real

Rational, and Real

500

Put these numbers into rational and irrational groups:

square root of 25, square root of 7, -4/9, 0.75, pi

Rational: square root of 25, -4/9, 0.75

Irrational: Square root of 7, pi

Square and Cubed Roots

100

Find the square root of 81

9

200

Find the cubed root of -343

-7

300

Find the square root of 169/121

13/11

400

Between which two whole numbers does the square root of 684 lie between?

26 and 27

500

Between which two whole numbers does the cubed root of -3,568 lie between? 

-15 and -16

Scientific Notation

100

Write 4,500,000 in scientific notation

4.5 x 10 ⁶

200

Write 6.2 x 10^-4 in standard form

0.00062

300

Write 0.000000400068 in scientific notation

4.00068 x 10^-7

400

Write 4.008 x 10³ x 10^-6 in standard form

0.004008

500

Write (6 x 10 ^-18) x (8 x 10²²) in standard form

48000

Laws of Exponents

100

Simplify a⁴ x a³

a⁷

200

Simplify a⁹ / a⁵

a⁴

300

Simplify (2x³y²)³

8x⁹y⁶

400

Simplify (a^-6/a^-11)³

a¹⁵

500

Simplify and leave no negative exponents:

6x^-2y⁵ / 2xy⁷

3/x³y²

Pythagorean Theorem

100

Find the hypotenuse

a = 6 

b = 8

c = ?

c = 10

200

Find the missing leg 

c = 13

a = 5

b = 12

300

Do 8, 15, and 17 form A right triangle? Prove it.

Yes. 8² + 15² = 17²

400

A right triangle has legs 12 and 16. Find the hypotenuse then determine whether it forms a Pythagorean triple. 

20, yes it is a Pythagorean triple because 12-16-20 are all whole numbers.

500

Geometry Challenge: A triangle has points A(0,0), B(3,4), and C(7,1). Use the distance formula to fin AB, BC, AC. Then use the Pythagorean theorem to determine whether the triangle is a right triangle.

AB = 5
BC = 5
AC = square root of 50
Yes it is a right triangle.