Important Questions and Answers for Class 8 Maths Chapter 6 Algebra Play 2025-26

1. Multiple choice questions.

1. Which operation do you perform first in the trick: "Think of a number, double it, add four, divide by two, subtract the original number"?

• (a) Add four
• (b) Divide by two
• (c) Subtract the original number
• (d) Double the number

Answer: (d) Double the number

2. In a number pyramid, what determines each number (except the lowest row)?

• (a) Product of numbers below
• (b) Sum of two numbers below
• (c) The larger number below
• (d) The average of numbers below

Answer: (b) Sum of two numbers below

3. Which of the following best describes the relationship between the bottom row and the top number in a pyramid?

• (a) Top is always twice the largest in the bottom row
• (b) Top is always the sum of all numbers in the pyramid
• (c) Top is an expression using all bottom row values
• (d) Top is the product of the bottom row values

Answer: (c) Top is an expression using all bottom row values

4. The final sum of four numbers in a 2×2 calendar grid of consecutive days is always equal to:

• (a) 2 × the largest number in the square
• (b) 4 × the top left number plus 16
• (c) Always 40
• (d) Top left number minus 16

Answer: (b) 4 × the top left number plus 16

2. Very Short Answer (VSA).

1. What is an algebraic trick used to predict a number's transformation?

Answer: An algebraic trick is a series of steps, like doubling and adding, that always lead to a predictable result, explained using variables and algebraic expressions.

2. How is each number in a number pyramid (except the bottom row) calculated?

Answer: Each number is calculated as the sum of the two numbers directly below it in the pyramid, following a fixed rule for construction.

3. In the calendar grid trick, what does the variable a represent?

Answer: The variable a represents the smallest number or the top left number in the selected 2×2 grid of the calendar.

3. Short Answer Questions.

1. If you think of a number, double it, add 4, divide by 2, and subtract the original number, why do you always get 2?

Answer: Let the number be $x$. Double: $2x$. Add 4: $2x+4$. Divide by 2: $x+2$. Subtract original: $x+2-x=2$. The operations always lead back to 2, regardless of $x$, because the rest cancels out.

2. In a number pyramid, the bottom row is 8 and 134. What is the number at the top?

Answer: For a two-row pyramid, the top is $a+b$. So, top number $=8+134=142$. The sum of the two bottom numbers gives the top in this case.

3. For the date trick, if the final answer is 1269, what date did the person choose? Show steps.

Answer: Subtract 165: $1269-165=1104$. The month is 11 (November); day is 04. So, the date is 4th November.

4. A mother is 5 times her daughter’s age now. In 6 years, she’ll be 3 times her daughter’s age. Find the daughter’s age.

Answer: Let daughter’s age = $x$. Mother’s = $5x$. After 6 years: Mother $= 5x+6$, daughter $= x+6$. So, $5x+6=3(x+6) \implies 5x+6=3x+18 \implies 2x=12 \implies x=6$. Daughter is 6 years old.

5. In a 2×2 calendar square, if the sum is 36, what are the numbers?

Answer: $4a+16=36 \implies 4a=20 \implies a=5$. The four numbers are 5, 6, 12, and 13. (Top left: 5; others: 6, 12, 13).

4. True or False Questions.

1. In a number pyramid, every row above the bottom is formed by subtracting the lower numbers.

Answer: False

2. The divisibility trick using difference of a 2-digit number and its reverse will always result in a multiple of 9.

Answer: True

3. In the largest product problem, arranging two smaller digits as a two-digit number and multiplying by the largest digit always gives the highest result.

Answer: False

4. Adding a two-digit number and its reverse is always divisible by 11.

Answer: True

3. Fill in the Blanks Questions.

1. In a 3-row number pyramid with bottom row values $a, b, c$, the topmost value is ____.

Answer: $a+2b+c$

2. For the grid trick, the sum of all four numbers in a 2×2 square is expressed by ____.

Answer: $4a+16$, where $a$ is the top left number

3. If the result of the date trick is 394, the month and date chosen were ____.

Answer: 2nd March (394–165 = 229, so month = 2, day = 29)

4. In the trick with the number sequence 1/3, (1+3)/(5+7), (1+3+5)/(7+9+11), the numerator is always the sum of ____ odd numbers, and the denominator is the sum of ____ consecutive odd numbers.

Answer: first $n$ odd numbers; next $n$ consecutive odd numbers

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