COPY: Divisibility Rules and Surface Area

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

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

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

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

<p>432 (C)</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. (C)</p> Signup and view all the answers

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

<p>304 (C)</p> Signup and view all the answers

What should be performed first in the order of operations?

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

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

<p>35 (D)</p> Signup and view all the answers

What does 'BIDMAS' stand for?

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

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

<p>5 (B)</p> Signup and view all the answers

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

<p>Subtraction (C)</p> Signup and view all the answers

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

<p>150 (B)</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 (C)</p> Signup and view all the answers

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

<p>9 (B)</p> Signup and view all the answers

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

<p>126 cm² (A)</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 (D)</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 (B)</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 (C)</p> Signup and view all the answers

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

<p>6 × 16 (D)</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 (A)</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 (C)</p> Signup and view all the answers

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

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

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

<p>480 cm3 (B)</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>$4x^2$ (D)</p> Signup and view all the answers

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

<p>199 cm3 (A)</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 (B)</p> Signup and view all the answers

Which formula correctly calculates the surface area of a cuboid?

<p>$2(lw + lh + wh)$ (C)</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 (B)</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 $10 cm \times 2 cm \times 5 cm$ (B)</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 $20 cm \times 10 cm \times 2.5 cm$ (B)</p> Signup and view all the answers

Which of the following numbers is divisible by 2?

<p>24 (B)</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. (B)</p> Signup and view all the answers

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

<p>1 (A)</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 (C)</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. (A)</p> Signup and view all the answers

Which of the following best describes theoretical probability?

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

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

<p>As a whole number (C)</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 (D)</p> Signup and view all the answers

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