Copyright © Ed2Net Learning, Inc. 1 Review #1 Grade 8

Copyright © Ed2Net Learning, Inc.2 Compare & Order Rational Numbers Rational numbers are numbers that can be written as the ratio of two integers where zero is not the denominator. Rational Numbers are in various forms: integers, percents, and positive and negative fractions and decimals In order to compare rational numbers, rewrite all numbers so that they are in the same form :  Either all decimals or  all fractions with a common denominator

Copyright © Ed2Net Learning, Inc.3 Compare & Order Rational Numbers To compare two positive fractions, find equivalent fractions that have a common denominator. Then compare the numerators to determine which fraction was smaller. To compare a positive fraction and a positive decimal, find equivalent decimal for the fraction and then compare the digits in the two decimals that have the same place value. To compare two negative fractions, find equivalent fractions that have a common denominator. Then compare the numerators; whichever numerator is closer to zero is the largest fraction.

Copyright © Ed2Net Learning, Inc.4 Irrational Numbers Irrational numbers are numbers that cannot be written as the ratio of two integers.  Examples π; √2 Square Root of a given number is a number that when multiplied by itself equals the given number.  Example √16 = 4  The side length of a square is the square root of the area of the square.

Copyright © Ed2Net Learning, Inc.5 Irrational Numbers To estimate the value of an irrational number such as √6  Determine between which 2 consecutive numbers √6 would be located on a number line. √6 would be located between 2 and 3 since 2 2 is 4 and 3 2 is 9. 6 is closer to 4 than it is to 9; so √6 will be less than halfway (2.5). A good estimate would for √6 would be 2.4 You can check the estimate by squaring it is 5.76 which is close to 6.

Copyright © Ed2Net Learning, Inc.6 1) Identify the irrational number. 2.3, √3, √169, -4, a)2.3 b)√3 c)√169 d)3 4

Copyright © Ed2Net Learning, Inc.7 2) Which number sentence puts the following set of numbers in ascending order ? 2.3, √5, √2, -4, c) -4, √2, 3, √5, b) -4, √2, 3, 2.3, √5 2 4 a) -4, 3, √2, 2.3, √5 2 4 d) None of the above.

Copyright © Ed2Net Learning, Inc.8 3) Matt has to chose the irrational number listed below that is closest to 6. Which number should Matt chose? a) √12 b) √14 c) √31 d) √37

Copyright © Ed2Net Learning, Inc.9 4) Michael jumped feet; John jumped 93 7/12 feet and Roger jumped feet. Who jumped the farthest? a) Michael b) John c) Roger d) All of the above

Copyright © Ed2Net Learning, Inc.10 Pythagorean Theorem The Pythagorean Theorem shows how the legs and hypotenuse of a right triangle are related. legs hypotenuse In a right triangle, the two shortest sides are legs. The longest side, which is opposite the right angle, is the hypotenuse.

Copyright © Ed2Net Learning, Inc.11 In words: In a right angled triangle, the square of the length of the hypotenuse is equal to the sum of the square of the lengths of the legs. In Symbols: a 2 +b 2 = c 2. a b c If we know the lengths of two sides of a right angled triangle, then Pythagoras' Theorem allows us to find the length of the third side. Pythagorean Theorem

Copyright © Ed2Net Learning, Inc.12 hypotenuse = 2. shorter leg longer leg = shorter leg. √3 C 30º 60º 2s A B s √3s Using the Pythagorean theorem, we find that The converse of Pythagorean Theorem allows you to substitute the lengths of the sides of a triangle into the equation : c 2 = a 2 +b 2 to check whether a triangle is a right triangle, if the Pythagorean equation is true the triangle is a right triangle Triangle

Copyright © Ed2Net Learning, Inc.13 1) What is the length of the third side of the triangle shown in the figure? [Given a = 9.6 cm and b = 12.8 cm] 9.6 cm 12.8 cm x a)17 cm b)15 cm c)14 cm d)16 cm

Copyright © Ed2Net Learning, Inc.14 2) The hypotenuse of a right triangle is 40 meters long, and one of its leg is 18 meters long. Find the length of the other leg. a)32.3 m b)35.7 m c)36.2 m d)36.5 m

Copyright © Ed2Net Learning, Inc.15 3) A ramp used in skateboarding competitions is shown below. How high is the ramp? a)12.3 m b)14.2 m c)12.7 m d)13.2 m 20 m 15 m

Copyright © Ed2Net Learning, Inc.16 4) A ladder that is 10 feet long leans against a building. The bottom of the ladder is 4 feet away from the base. How far up the side of the building does the ladder reach? a)7.2 ft b)10.2 ft c)8.2 ft d)9.2 ft

Copyright © Ed2Net Learning, Inc.17 Scientists have developed a shorter method to express very large numbers. This method is called scientific notation. Scientific Notation is based on powers of the base number 10. The second number is called the base. It must always be 10 in scientific notation. The base number 10 is always written in exponent form. In the number 1.23 x the number 11 is referred to as the exponent or power of ten. Scientific notation The number 123,000,000,000 in scientific notation is written as : 1.23 ×10 11 The first number 1.23 is called the coefficient. It must be greater than or equal to 1 and less than 10.

Copyright © Ed2Net Learning, Inc.18 Exponents The "exponent" stands for how many times the thing is being multiplied. The thing that's being multiplied is called the "base". This process of using exponents is called "raising to a power", where the exponent is the "power". "5 3 " is "five, raised to the third power". Example 1: 2 x 2 x 2 x 2 x 2 = 2 5 i.e., 2 raised to the fifth power Exponential notation is an easier way to write a number as a product of many factors.

Copyright © Ed2Net Learning, Inc.19 Whole numbers can be expressed in standard form, in factor form and in exponential form. Exponential notation makes it easier to write a number as a factor repeatedly. A number written in exponential form is a base raised to an exponent. The exponent tells us how many times the base is used as a factor. Write 10 3, 3 6, and 1 8 in factor form and in standard form. Exponential Form Factor Form Standard Form × 10 × 101, ×3 ×3 × 3 × 3 × ×1 × 1 ×1 × 1 × 1 × 1 × 11

Copyright © Ed2Net Learning, Inc.20 If a negative number is raised to an even power, the result will be positive. (-2) 4 = - 2 × - 2 × - 2 × - 2 = 16 If a negative number is raised to an odd power, the result will be negative. (-2) 5 = - 2 × - 2 × - 2 × - 2 × - 2 = -32 The negative number must be enclosed by parentheses to have the exponent apply to the negative term. Note that (-2) 4 = - 2 × - 2 × - 2 × - 2 = 16 and -2 4 = -(2 × 2 × 2 × 2) = -16

Copyright © Ed2Net Learning, Inc.21 Write in scientific notation: 35,800 Place the decimal point between the first two non-zero numbers, 3 and 5. Since the 3 was in the ten-thousands place, the power of 10 is The number in the scientific notation is 3.58 × To change the number from scientific notation into standard notation, you can also count the number of times the decimal point moved to determine the power of ,800 = = 3.58 × 10 4 Decimal point moves 4 places to the left.

Copyright © Ed2Net Learning, Inc.22 To change the number from scientific notation into standard notation, begin with place value indicated by the power of 10. Add zeroes as place holders when necessary = = 7.9 × Write in scientific notation: Decimal point moves 3 places to the right.

Copyright © Ed2Net Learning, Inc.23 1) Pluto’s mean distance from Sun is 3,670, miles. What is this number in the scientific notation? a)3.67 × 10 9 miles b)3.67 × 10 8 miles c)3.67 × 10 7 miles d)3.67 × miles

Copyright © Ed2Net Learning, Inc.24 2) To write 3.18 ×10 7 in standard form, how many times will the decimal point move? a)7 places to the right. b)5 places to the right. c)7 places to the left. d)5 places to the right.

Copyright © Ed2Net Learning, Inc.25 3) Which number is the largest? a)3.67 × b)3.67 × c)3.67 × d)3.67 ×

Copyright © Ed2Net Learning, Inc.26 4) A movie grossed nearly $6.7 × What is this number in standard form? a)$ b)$6,700,000 c)$670,000 d)$67,000,000

Copyright © Ed2Net Learning, Inc.27 Surface area The surface area of a solid figure is the sum of the areas of all faces of the figure. The surface area of a rectangular solid is expressed in square units. An area of study closely related to solid geometry is nets of a solid. Imagine making cuts along some edges of a solid and opening it up to form a plane figure. The plane figure is called the net of the solid.

Copyright © Ed2Net Learning, Inc.28 In general, Surface Area of solid figures = 2 x area of the base +perimeter of the base x height If, B = area of the base P = perimeter of the base h = height SA = Surface Area Then, SA = 2B +Ph

Copyright © Ed2Net Learning, Inc.29 Cubes A cube is a three-dimensional figure with all edges of the same length. If s is the length of one of its sides, then SA = 2(s 2 ) + (4s)s = 6s 2 s s s ss s s s s

Copyright © Ed2Net Learning, Inc.30 Rectangular prism l w h l w h SA = 2B + Ph SA = 2(lw) + (2l + 2w)h = 2(lw + lh + wh)

Copyright © Ed2Net Learning, Inc.31 1) The perimeter of one face of a cube is 48 cm. What is its surface area? a)862 cm 2 b)864 cm 2 c)866 cm 2 d)868 cm 2

Copyright © Ed2Net Learning, Inc.32 2) Which of the given boxes has the greatest surface area? a)Box A b)Box B c)Box C d)All have equal surface area A B C 1ft 4ft 2ft 3ft 6ft 2ft

Copyright © Ed2Net Learning, Inc.33 3) Each small cube in the rectangular prism below has edges of length 2 centimeters. What is the surface area of the prism in square centimeters? a)220 cm 2 b)222 cm 2 c)224 cm 2 d)208 cm 2

Copyright © Ed2Net Learning, Inc.34 4) What is the surface area of the box with the given dimensions? a)1134 cm 2 b)1224 cm 2 c)1194 cm 2 d)1154 cm 2

Copyright © Ed2Net Learning, Inc. 35 Great Job today!