$$A = \frac{1}{6} \pi \times 4^2$

Area $$A = l \times w$$, Perimeter $$P = 2(l + w)$$

Question 1

Which of the following statements about square roots is correct?

Accepted Answer

The square root of a positive number $$x is $$defined as $$\sqrt{x}.$$

Question 2

Given two lines in a plane, which condition must be true for them to be perpendicular?

Accepted Answer

Their slopes are negative reciprocals of each other.

Question 3

Which property distinguishes congruent shapes from similar shapes?

Accepted Answer

Congruent shapes have the same shape, angles, proportions, and size.

Question 4

A circle has a radius of $$r. $$What is the area of the circle?

Accepted Answer

$$A = \pi r^2$

Question 5

A small circle of radius $$a is $$placed inside a large circle of radius $$b. $$What is the area of the region between the two circles?

Accepted Answer

$$A = \pi b^2$ - \pi a^2$

Question 6

What is the formula for the circumference of a circle with radius $$r$$?

Accepted Answer

$$C = 2\pi r$$

Question 7

The radius of a circle is $$4. $$What is the area of a $$60^\circ$$ sector?

Accepted Answer

$$A = \frac{1}{6} \pi 	imes 4^2$

Question 8

What is the relationship between a central angle and the arc it intercepts in a circle?

Accepted Answer

The central angle is equal to the arc's angle.

Question 9

Given the equation $$(x-3)^2$$ + $$(y+2)^2 = 49$, what is the center and radius of the circle?

Accepted Answer

Center $$(3, -2)$$, radius $$7$$

Question 10

What is the area and perimeter of an equilateral triangle with side length $$s$$?

Accepted Answer

Area $$A = \frac{\sqrt{3}}{4}s^2$, Perimeter P = 3s$

Question 11

A rectangle has length $$l$$ and width $$w. $$What is its area and perimeter?

Accepted Answer

Area $$A = l 	imes w$$, Perimeter $$P = 2(l + w)$$

Question 12

What is the surface area and volume of a rectangular prism with length $$l$$, width $$w$$, and height $$h$$?

Accepted Answer

Surface area $$SA = 2(lw + lh + wh)$$, Volume $$V = lwh$$

Question 13

A cylinder has radius $$r$$ and height $$h. $$What is its lateral area?

Accepted Answer

$$LA = 2\pi r h$$

Question 14

What is the surface area and volume of a sphere with radius $$r$$?

Accepted Answer

Surface area $$SA = 4\pi r^2$, Volume V$$ = \frac{4}{3}\pi $$r^3$$

Question 15

A right triangle has legs $$a = 6$$ and $$b = 8. $$What is the length of the hypotenuse?

Accepted Answer

$$c = \sqrt{6^2$ + 8^2$} = 10$$

Question 16

Which of the following best describes the difference between surface area and volume?

Accepted Answer

Surface area is measured in square units, volume in cubic units.

Question 17

If the circumference of a circle is $$C = 31.4$$, what is the radius?

Accepted Answer

$$r = \frac{31.4}{2\pi}$$

Question 18

A sector of a circle has a central angle of $$90^\circ$$ and radius $$r. $$What is the area of the sector?

Accepted Answer

$$A = \frac{1}{4}\pi r^2$

Foundations of Geometry and Measurement for Trigonometry

Study Guide - Practice Questions