Pre-Algebra Final Exam Study Guide

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Questions and Answers

What formula do you use to solve 'At 50 mph how long will it take to go 325 miles'?

Rate/time=Distance or D=R*T

2124 is divisible by which of the following numbers? (Select all that apply)

  • 9 (correct)
  • 5
  • 4 (correct)
  • 2 (correct)
  • 6 (correct)
  • 3 (correct)

In a quadrant plane, Roman numerals go from?

Right to left

What is the result when using the distributive property on -6(y - 3)?

<p>-6y + 18</p> Signup and view all the answers

What is the solution to the equation -7 = n - 6?

<p>n = -1</p> Signup and view all the answers

What is the solution to the equation -54 = -9w?

<p>w = 6</p> Signup and view all the answers

What is the greatest common factor of 20c^3d and 12cd?

<p>2d</p> Signup and view all the answers

Evaluate the expression 9x - (y + z) if x = 3, y = 8, and z = 5.

<p>14</p> Signup and view all the answers

What number is indicated if a number increased by 14 equals 52?

<p>x = 38</p> Signup and view all the answers

What is the product of 7x * 2x^6?

<p>14x^7</p> Signup and view all the answers

What is the product of 15 * 4/5?

<p>12</p> Signup and view all the answers

What is the result of 2 1/4 * (-4/3)?

<p>-3</p> Signup and view all the answers

What is 5 ÷ (-1 1/3)?

<p>-3 3/4</p> Signup and view all the answers

What is the sum of 7/9 + (-2/9)?

<p>5/9</p> Signup and view all the answers

What is the least common multiple of 7c^2 and 21c?

<p>21c^2</p> Signup and view all the answers

If 20 CDs cost $18, what is the cost per CD?

<p>$0.90</p> Signup and view all the answers

Convert 4 ft/min to yards per hour.

<p>80 yd</p> Signup and view all the answers

Convert the percentage 45% to a fraction.

<p>9/20</p> Signup and view all the answers

Convert the percentage 120% to a fraction.

<p>1 1/5</p> Signup and view all the answers

Convert the percentage 0.5% to a fraction.

<p>1/200</p> Signup and view all the answers

What is approximately 40% of 45?

<p>18</p> Signup and view all the answers

If 15 is less than or equal to 5w, then w = 3.

<p>True (A)</p> Signup and view all the answers

What is the solution to the equation n^2 = 81?

<p>n = 9</p> Signup and view all the answers

Use the Pythagorean theorem to find a if b = 2 and c = 7.

<p>a = 6 * 7</p> Signup and view all the answers

Is the relation {(0,0), (-4,3), (10,3), (3,3), (5,8)} a function?

<p>False (B)</p> Signup and view all the answers

What is the percent of change from $56 to $63?

<p>125% increase</p> Signup and view all the answers

What is the percent of change from 68 to 51?

<p>25% decrease</p> Signup and view all the answers

Write a linear equation with a slope of -1 and a y-intercept of 3.

<p>y = -1x + 3</p> Signup and view all the answers

What is the measure of one angle in a quadrilateral?

<p>90 degrees</p> Signup and view all the answers

What is the total degree measure of a hexagon?

<p>720 degrees</p> Signup and view all the answers

What is the volume of a pyramid with a square base of 4 inches and a height of 12 inches?

<p>64 cubic inches</p> Signup and view all the answers

What is the area of a rectangle that measures 4 in by 12 in?

<p>48 in squared</p> Signup and view all the answers

What is the area of a triangle with a base of 10 ft and a height of 17 ft?

<p>56 2/3 feet squared</p> Signup and view all the answers

What is the area of a circle with a radius of 3.5?

<p>38.5 units squared</p> Signup and view all the answers

How do you find the area of a circle?

<p>Area = π * r^2</p> Signup and view all the answers

How do you find the area of a rectangle?

<p>Area = length * width</p> Signup and view all the answers

How do you find the area of a cone?

<p>Area = (1/3) * π * r^2 * h</p> Signup and view all the answers

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Study Notes

Distance, Rate, and Time

  • Use the formula D = R × T to calculate distance.
  • Example: At 50 mph, traveling 325 miles takes 6.5 hours.

Divisibility

  • 2124 is divisible by 2, 3, 4, 6, and 9.

Roman Numerals

  • Roman numerals are arranged on a quadrant plane from right to left.

Distributive Property

  • Apply the distributive property: -6(y - 3) equals -6y + 18.

Solving Equations

  • For -7 = n - 6, solve to find n = -1.
  • For -54 = -9w, rearrange to find w = 6.

Greatest Common Factor

  • The greatest common factor of 20c³d and 12cd is 2d.

Evaluating Expressions

  • Evaluate 9x - (y + z) using x = 3, y = 8, z = 5 to get 14.

Algebraic Expressions

  • If a number increased by 14 equals 52, then x + 14 = 52, yielding x = 38.
  • The product of 7x and 2x⁶ is 14x⁷.

Multiplication and Division

  • 15 multiplied by 4/5 equals 12.
  • 2 1/4 multiplied by -4/3 gives -3.
  • 5 divided by -1 1/3 results in -3 3/4.

Fraction Addition

  • Adding fractions: 7/9 + (-2/9) equals 5/9.

Least Common Multiple

  • The least common multiple of 7c² and 21c is 21c².

Unit Cost

  • To determine the cost per CD, divide $18 by 20 CDs to get $0.90.

Unit Conversion

  • Convert 4 ft/min to yards per hour: 4 ft/min equals 80 yd/hr.

Percent Conversion

  • Convert 45% to a fraction: 45% equals 9/20.
  • Convert 120% to a mixed number: 120% equals 1 1/5.
  • Convert 0.5% to a fraction: 0.5% equals 1/200.

Percent Calculation

  • Approximately 40% of 45 is 18.

Functions

  • If 15 is less than or equal to 5w, true implies w = 3.

Square Roots

  • The solution for n² = 81 is n = 9.

Pythagorean Theorem

  • Using the Pythagorean theorem with b = 2 and c = 7, a equals 6.

Function Relations

  • The relation {(0,0), (-4,3), (10,3), (3,3), (5,8)} represents a function.

Percent of Change

  • From $56 to $63, the percent of change is a 125% increase.
  • From 68 to 51, the percent of change is a 25% decrease.

Linear Equations

  • A linear equation with a slope of -1 and a y-intercept of 3 is expressed as y = -1/m + 3/b.

Angles in Shapes

  • One angle in a quadrilateral measures 90 degrees.
  • The total degree measure of a hexagon is 720 degrees.

Area and Volume Calculations

  • Volume of a pyramid with a square base of 4 in and a height of 12 in is 64 cubic inches.
  • Area of a rectangle measuring 4 in by 12 in is 48 in².
  • Area of a triangle with a base of 10 ft and a height of 17 ft is 56 2/3 ft².
  • Area of a circle with a radius of 3.5 is approximately 38.5 units².

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