Math Final Exam Study Guide Page 1 of 5

Mathematics 1 Final Exam Review

Ms. Walker

This study guide is a review of everything that will be on the final exam. Sample problems are provided for you to practice.

  • Rules of divisibility

-Tell whether 3,420 is divisible by 2, 3, 5, or 10

-Tell whether 728 is divisible by 4, 6, or 9.

  • Powers and Exponents

-Write 34 as a product

-Write 2  2  2  2  2 using an exponent. Then find the value of the power.

  • Order of Operations

-Find the value of the expression 7 + 3  5.

-Find the value of the expression 36  9 + 12  (7 – 5).

  • Algebra: Variables and Expressions

-Evaluate 19 – a if a = 11.

-Evaluate 3k – 4 if k = 7.

  • Statistics and Graphs [Remember KAATZ: Key, Axis Y, Axis X, 3 Titles, Zero]

-How to read and construct a bar graph

-How to read and construct a line plot

-How to read and construct a box-and-whiskers plot

-How to read and construct a circle graph

-How to read and construct a frequency table

-How to read and construct a pictograph

-Exam Scores - Make a stem-and-leaf plot of the exam scores shown below.

-Find the mean, median, mode, and range of the data below.

Exam Scores
75 83 99 69
95 80 71 88
92 84 79 97
  • Ordering decimals, fractions and percents from least to greatest.

-Order 34.03, 34, 33.98, and 34.1 from least to greatest.

-Order –0.01, 0.01, .42 from least to greatest

-Order the fractions from least to greatest.

-Order 3 7/10%, 3 4/5%, 3.75 and 7/2 from least to greatest.

  • Multiplying and Dividing Decimals

-Find 3.8  5.2

-Find 2.3  0.04.

-Find 6.93  1.8.

-Find 83.2  0.52.

  • Adding and Subtracting Fractions

-Find - Find

-Find - Find 4.

  • Multiplying and Dividing Fractions

-Find - Find

-Find - Find

  • Simplifying Fractions
  • Equivalent Fractions
  • Greatest Common Factor
  • Least Common Multiple
  • Integers

- Find −3 + (−5).- Multiply 5  (−3).

- Find 4 + (−6).- Multiply −9  (−5).

- Find −7 + 3. - Divide −6  3.

- Find −8 − (−5).- Divide −35  (−7).

-Find –4 – 6.

  • Algebra: Solving Equations

-Solve m + 2 = 7- Solve −4x = 24

-Solve c – 2 = – 3.- Solve 3x + 7 = 16.

-Solve 4x – 9 = 15

  • Ratio, Proportion, and Percents

- MARBLES A collection of marbles has 8 blue marbles and 6 green marbles. Write the ratio that compares the number of blue marbles to the number of green marbles.

- CEREAL A 16-ounce box of cereal is priced at $3.68. Find the cost per ounce.

- Solve .

- Write 140% as a fraction in simplest form.

- Write 0.7% as a decimal.

- Find 8% of 400.

- Convert: Fraction to Decimal, Decimal to Fraction, Fraction to Percent, Percent to

Fraction

  • Geometry: Perimeter, Area, Volume, Circumference, Surface Area

-Find the area of a rectangle with length 14 feet and width 9 feet.

-Find the circumference of a circle whose diameter is 7.2 centimeters. Round to the nearest tenth.

-GARDENING Tom is trying to determine the area of his garden so that he will know how much fertilizer to buy. His garden is a circle with a radius of 10 feet. About how much land does Tom’s garden cover?

-Find the volume of the rectangular prism.

-Find the area of the triangle.

-Find the perimeter of a trapezoid with sides of 6 feet, 9 feet, 3 feet and 3 feet.

-Find the surface area of the rectangular prism.

-Know how to find the volume and surface area of a cylinder.

  • Prime and Composite Numbers / Prime Factorization

54 = 2 x 27 = 2 x 3 x 9 = 2 x 3 x 3 x 3 = 2 x 33

  • Mr. Wilson’s students have completed more than 50% of the class work planned for the entire school year. Which fraction could be used to represent a value GREATER than 50%?

1/5, 4/10, ½ 2/3

  • Which inequality is TRUE?

25% >7/8 , 7/8 <0.83

  • Associative Property of Addition (The way numbers are groups does not change sum or product) (3 + 4) + 5 = 3 + (4 + 5)
  • Commutative Property of Addition (order does not change sum or product)

4 + 3 = 3 + 4

  • Identity Property (The sum of any number and 0 is the number)

5 + 0 = 5

  • Multiplicative Identity (The product of any number and 1 is the number)

7 x 1 - 7

  • Distributive Property

2(7 +4) = 2 x 7 + 2 x 4 What is equivalent to 5(n-9) = 5n-45

  • Change

Kathy’s lunch cost $4.52. If she pays with a $20 bill, how much change should she receive?

$15.48, $15.58, $16.48, $16.52

  • The distance from Josie’s house to school is 4.25 blocks. What is the total number of blocks she walks directly to and from school during a 5-day school week?
  • Miguel, Sara and Joey ride to school together. Miguel rides a distance of 2.25 miles to Sara’s house. Then they go to Joey’s house, which is 1.625 miles past Sara’s house and 5.25 miles from school. What is the total distance in miles, from Miguel’s house to school?
  • Profit or loss for a product
  • Discount and Sales Tax

A store is having a 30%-off sale on all games. Lance wants a board game that cost $26.95 after the discount is applied. What is the discounted price of the game to the nearest cent?

A girl purchased treats for the class party. The sales tax was 6 1/2 %. The total cost of the items was $33.21, what the cost of the treats after the sales tax was applied?

  • Circle J is shown below.

Which line segment is a radius of Circle J? What line segment is the chord of Circle J?

  • Lines, Angles, Triangles

Identify the following: Right Angle, Acute Angle, Obtuse Angle, Straight Line, Parallel Lines, Perpendicular Lines, Supplementary Angles, Complementary Angles, Equilateral Triangle, Isosceles Triangle, Scalene Triangle, Acute Triangle. YOU SHOULD KNOW THE DEGREES AND MEASURES OF THE OUTSIDE AND INSIDE OF THE SHAPES.

  • Scale Drawings

A house and a storage shed are built with the geometrically similar roof parts shown below.

What is the length of the side labeled with a measure of x feet?

  • Quadrants and Coordinate Grids

You should know the coordinate grids with the corresponding [negative and positive] ordered pairs. You should also be able to identify and plot points on a grid.

  • Measure of angles, shapes, missing measure
  • Translation, Rotation, Reflection
  • Square, Square Root, Missing Numbers in Pattern, Patterns in a Table
  • Absolute Value
  • Ratios: There were 5 tables and 12 balls, what is the ration of tables to balls?

5:12 * 5/12 * 5 out of 12 [REMEMBER: ALL RATIOS ARE TO BE REDUCED]

  • Measures of Central Tendency: Mean, Median, Mode, Range
  • Circumference and Area of a Circle

Figure the circumference when given the radius and the diameter

  • C= pi x diameter * pi x 2 x radius
  • Area = pi x radius2
  • Scientific Notation

5 x 104 = 50,0000 9.3 x 105 = 930,000

  • Rounding Off Numbers (To the nearest tenth, and to the nearest hundredth)
  • Two-Dimensional Figures

Identify a shape by its sides: Triangle (3) Quadrilateral (4) Pentagon (5) Hexagon (6) Heptagon (7) Octagon (8) Nonagon (10)

  • Rectangle, Square, Parallelogram, Rhombus, Trapezoid
  • Regular Polygon, Irregular Polygon (Not regular)

Similar, Congruent, Symmetry

Three-Dimensional Figures

  • Identify: Prism (shape of the base tells the name of the prism: Rectangular prism, triangular prism, square prism/cube), Pyramid(shape of the base tells the name of the pyramid: triangular pyramid, square pyramid), Cone, Cylinder, Sphere