Divisibility Rules and Surface Area
40 Questions
1 Views

Divisibility Rules and Surface Area

Created by
@WellBehavedRomanArt1747

Podcast Beta

Play an AI-generated podcast conversation about this lesson

Questions and Answers

Which method confirms if a number is divisible by 4?

  • The entire number must be divisible by 4.
  • The last two digits must be divisible by 4. (correct)
  • The last digit must be divisible by 4.
  • The last two digits must be divisible by 2.

    • What is the result when 128 is successively halved to check for divisibility by 4?

  • 32
  • 12
  • 16
  • 64 (correct)

    • What indicates that 246 is not divisible by 4?

  • The overall sum of the digits is not divisible by 4.
  • The result after halving is not a whole number. (correct)
  • The last digit is odd.
  • The last two digits are not even.

    • To determine if a number is divisible by 8 using the last three digits, what condition must be met?

    <p>The last three digits must be divisible by 8.</p> Signup and view all the answers

    Which alternative method checks if a number is divisible by 8?

    <p>Halve the number three times.</p> Signup and view all the answers

    Which of the following numbers is divisible by 8 based on the last three digits?

    <p>432</p> Signup and view all the answers

    What is the last digit of a number that is divisible by 4?

    <p>It must be even.</p> Signup and view all the answers

    What was the result of halving the number 2432 three times?

    <p>304</p> Signup and view all the answers

    What should be performed first in the order of operations?

    <p>Operation in brackets</p> Signup and view all the answers

    Calculate 7 + 4 × 9 − 8. What is the correct answer?

    <p>35</p> Signup and view all the answers

    What does 'BIDMAS' stand for?

    <p>Brackets, Indices, Division, Multiplication, Addition, Subtraction</p> Signup and view all the answers

    Calculate 25 − (2 + 3) × 4. What is the final result?

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

    In the expression 6 + 3 × 2 − 1, which operation is performed last?

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

    Calculate 22 + (3 + 5)² × 2. What is the result?

    <p>150</p> Signup and view all the answers

    What is the primary purpose of the order of operations in mathematics?

    <p>To provide a standard convention for calculations</p> Signup and view all the answers

    What will be the result of the calculation 4 × 2 + 5 − 3 × 1?

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

    What is the total surface area of the cuboid calculated using Method 1?

    <p>126 cm²</p> Signup and view all the answers

    Which dimension is used to calculate the area of the front and back faces of the cuboid?

    <p>5 cm and 6 cm</p> Signup and view all the answers

    What is the area of the top and bottom faces of the cuboid calculated using Method 1?

    <p>36 cm²</p> Signup and view all the answers

    What is the combined area of the two sides of the cuboid according to Method 1?

    <p>30 cm²</p> Signup and view all the answers

    How is the area of rectangle A determined in the net of the cuboid?

    <p>6 × 16</p> Signup and view all the answers

    What area is calculated for rectangles B and C in the cuboid's net?

    <p>15 cm² each</p> Signup and view all the answers

    Using Method 2, what is the total surface area of the cuboid derived from its net?

    <p>126 cm²</p> Signup and view all the answers

    Which method involves calculating the surface area by considering pairs of faces?

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

    What is the total volume of the original cuboid before any cuts are made?

    <p>480 cm3</p> Signup and view all the answers

    If a cuboid with dimensions $x cm \times x cm \times 4 cm$ is cut from a corner, which expression represents the volume of the cut-out cuboid?

    <p>$4x^2$</p> Signup and view all the answers

    What is the remaining volume of the shape after the cuboid has been removed?

    <p>199 cm3</p> Signup and view all the answers

    What must be the value of x to maintain a total volume of 199 cm3 for the remaining shape?

    <p>4 cm</p> Signup and view all the answers

    Which formula correctly calculates the surface area of a cuboid?

    <p>$2(lw + lh + wh)$</p> Signup and view all the answers

    What is the surface area of a cuboid with dimensions $10 cm \times 10 cm \times 4 cm$?

    <p>240 cm2</p> Signup and view all the answers

    What is one way to design a composite shape that can be split into two cuboids with a total volume of 200 cm3?

    <p>Design one cuboid of $10 cm \times 4 cm \times 5 cm$ and another $10 cm \times 2 cm \times 5 cm$</p> Signup and view all the answers

    For a composite shape split into three cuboids totaling 500 cm3, which dimensions could be accurate?

    <p>One cuboid of $20 cm \times 10 cm \times 2.5 cm$</p> Signup and view all the answers

    Which of the following numbers is divisible by 2?

    <p>24</p> Signup and view all the answers

    What does it mean if a number is divisible by 9?

    <p>It is always divisible by 3.</p> Signup and view all the answers

    Which of the following reflects a probability of an event that is certain?

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

    If an event is described as 'rarely' happening, what would its probability likely be?

    <p>Close to 0</p> Signup and view all the answers

    Which of the following statements about divisibility by 3 and 9 is false?

    <p>All odd numbers are divisible by 3.</p> Signup and view all the answers

    Which of the following best describes theoretical probability?

    <p>What you expect to happen in theory.</p> Signup and view all the answers

    Which of the following is not a way to represent probability?

    <p>As a whole number</p> Signup and view all the answers

    How would the term 'even chance' be interpreted in relation to probability?

    <p>A probability of 0.5</p> Signup and view all the answers

    Study Notes

    Divisibility Rules

    • A number is divisible by 4 if its last two digits form a number that is divisible by 4.
    • Example: 128 is divisible by 4 because the last two digits, 28, are divisible by 4.
    • An alternative method for testing divisibility by 4 is by halving the number twice. If the final result is a whole number, the original number is divisible by 4.
    • Example: 128 ÷ 2 = 64, then 64 ÷ 2 = 32; since 32 is a whole number, 128 is divisible by 4.

    Testing Divisibility by 8

    • A number is divisible by 8 if its last three digits form a number that is divisible by 8.
    • Example: 2432 is divisible by 8 because the last three digits, 432, are divisible by 8.
    • Alternatively, halving the number three times can confirm divisibility by 8.
    • Example: 2432 ÷ 2 = 1216; 1216 ÷ 2 = 608; 608 ÷ 2 = 304. Since 304 is a whole number, 2432 is divisible by 8.

    Surface Area of a Cuboid

    • The surface area of a cuboid is the total area of its six rectangular faces.
    • Calculation methods:
      • Method 1: Calculate areas of each pair of opposite faces:
        • Front/Back: height × width × 2
        • Top/Bottom: length × height × 2
        • Sides: width × length × 2
        • Total Surface Area = sum of all calculated areas.
      • Method 2: Calculate area of the net, which represents the unfolded shape of the cuboid.

    Order of Operations

    • Mathematical operations follow a specific order:
      • Brackets, Indices, Division/Multiplication (left to right), Addition/Subtraction (left to right).
    • Acronym: BIDMAS.
    • Example calculation: (6 + 3 \times 2 - 1)
      • Result: (= 6 + 6 - 1 = 11).

    Probability Concepts

    • Probability is the measure of the likelihood of an event, ranging from 0 (impossible) to 1 (certain).
    • Probabilities can be expressed as fractions, decimals, or percentages.
    • Everyday language reflects probability: terms like "likely," "possible," "rarely," and "certain" articulate how probably events will occur.
    • Theoretical probability predicts expected outcomes, which may differ from actual results due to the nature of chance events.

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Description

    This quiz covers important concepts related to divisibility rules for numbers, specifically focusing on 4 and 8. It also includes the calculation of the surface area of a cuboid. Test your understanding of these mathematical principles with this engaging quiz.

    More Like This

    Divisibility Rules Quiz
    3 questions

    Divisibility Rules Quiz

    ExceedingPlatypus avatar
    ExceedingPlatypus
    Divisibility Rules Quiz
    5 questions

    Divisibility Rules Quiz: Master the Rules with Flashcards

    EventfulWaterfall avatar
    EventfulWaterfall
    Divisibility Rules Quiz
    5 questions

    Divisibility Rules Quiz

    PrudentSwan avatar
    PrudentSwan
    Divisibility Rules for 3, 6, and 9
    6 questions

    Divisibility Rules for 3, 6, and 9

    AccommodativeHope avatar
    AccommodativeHope
    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser