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Questions and Answers
Which method confirms if a number is divisible by 4?
Which method confirms if a number is divisible by 4?
What is the result when 128 is successively halved to check for divisibility by 4?
What is the result when 128 is successively halved to check for divisibility by 4?
What indicates that 246 is not divisible by 4?
What indicates that 246 is not divisible by 4?
To determine if a number is divisible by 8 using the last three digits, what condition must be met?
To determine if a number is divisible by 8 using the last three digits, what condition must be met?
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Which alternative method checks if a number is divisible by 8?
Which alternative method checks if a number is divisible by 8?
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Which of the following numbers is divisible by 8 based on the last three digits?
Which of the following numbers is divisible by 8 based on the last three digits?
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What is the last digit of a number that is divisible by 4?
What is the last digit of a number that is divisible by 4?
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What was the result of halving the number 2432 three times?
What was the result of halving the number 2432 three times?
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What should be performed first in the order of operations?
What should be performed first in the order of operations?
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Calculate 7 + 4 × 9 − 8. What is the correct answer?
Calculate 7 + 4 × 9 − 8. What is the correct answer?
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What does 'BIDMAS' stand for?
What does 'BIDMAS' stand for?
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Calculate 25 − (2 + 3) × 4. What is the final result?
Calculate 25 − (2 + 3) × 4. What is the final result?
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In the expression 6 + 3 × 2 − 1, which operation is performed last?
In the expression 6 + 3 × 2 − 1, which operation is performed last?
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Calculate 22 + (3 + 5)² × 2. What is the result?
Calculate 22 + (3 + 5)² × 2. What is the result?
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What is the primary purpose of the order of operations in mathematics?
What is the primary purpose of the order of operations in mathematics?
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What will be the result of the calculation 4 × 2 + 5 − 3 × 1?
What will be the result of the calculation 4 × 2 + 5 − 3 × 1?
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What is the total surface area of the cuboid calculated using Method 1?
What is the total surface area of the cuboid calculated using Method 1?
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Which dimension is used to calculate the area of the front and back faces of the cuboid?
Which dimension is used to calculate the area of the front and back faces of the cuboid?
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What is the area of the top and bottom faces of the cuboid calculated using Method 1?
What is the area of the top and bottom faces of the cuboid calculated using Method 1?
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What is the combined area of the two sides of the cuboid according to Method 1?
What is the combined area of the two sides of the cuboid according to Method 1?
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How is the area of rectangle A determined in the net of the cuboid?
How is the area of rectangle A determined in the net of the cuboid?
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What area is calculated for rectangles B and C in the cuboid's net?
What area is calculated for rectangles B and C in the cuboid's net?
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Using Method 2, what is the total surface area of the cuboid derived from its net?
Using Method 2, what is the total surface area of the cuboid derived from its net?
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Which method involves calculating the surface area by considering pairs of faces?
Which method involves calculating the surface area by considering pairs of faces?
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What is the total volume of the original cuboid before any cuts are made?
What is the total volume of the original cuboid before any cuts are made?
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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?
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?
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What is the remaining volume of the shape after the cuboid has been removed?
What is the remaining volume of the shape after the cuboid has been removed?
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What must be the value of x to maintain a total volume of 199 cm3 for the remaining shape?
What must be the value of x to maintain a total volume of 199 cm3 for the remaining shape?
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Which formula correctly calculates the surface area of a cuboid?
Which formula correctly calculates the surface area of a cuboid?
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What is the surface area of a cuboid with dimensions $10 cm \times 10 cm \times 4 cm$?
What is the surface area of a cuboid with dimensions $10 cm \times 10 cm \times 4 cm$?
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What is one way to design a composite shape that can be split into two cuboids with a total volume of 200 cm3?
What is one way to design a composite shape that can be split into two cuboids with a total volume of 200 cm3?
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For a composite shape split into three cuboids totaling 500 cm3, which dimensions could be accurate?
For a composite shape split into three cuboids totaling 500 cm3, which dimensions could be accurate?
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Which of the following numbers is divisible by 2?
Which of the following numbers is divisible by 2?
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What does it mean if a number is divisible by 9?
What does it mean if a number is divisible by 9?
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Which of the following reflects a probability of an event that is certain?
Which of the following reflects a probability of an event that is certain?
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If an event is described as 'rarely' happening, what would its probability likely be?
If an event is described as 'rarely' happening, what would its probability likely be?
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Which of the following statements about divisibility by 3 and 9 is false?
Which of the following statements about divisibility by 3 and 9 is false?
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Which of the following best describes theoretical probability?
Which of the following best describes theoretical probability?
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Which of the following is not a way to represent probability?
Which of the following is not a way to represent probability?
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How would the term 'even chance' be interpreted in relation to probability?
How would the term 'even chance' be interpreted in relation to probability?
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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.
- Method 1: Calculate areas of each pair of opposite faces:
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.
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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.
