Algebra Class 6

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Class 6 Algebra Worksheet (Advanced Level)

Section A: Solve for the Variable

1. Solve for $x$:
   a) $5x + 7 = 27$
   b) $3(x - 4) = 18$
   c) $2x + 3 = 5x - 9$
   d) $6x - 4 = 2x + 16$

2. If $y + 8 = 3y - 10$, find the value of $y$.

3. Solve: $\frac{x}{3} + 7 = 12$.

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Section B: Word Problems

4. A number is doubled and then decreased by 5. The result is 19. Find the number.

5. The sum of three consecutive numbers is 72.
   a) Find the numbers.
   b) Verify your answer.

6. A father’s age is three times his son’s age. Five years ago, the father was four times his son’s age. Find their current ages.

7. A car travels $3x$ kilometres in 2 hours and $2x$ kilometres in the next hour.
   a) Write an expression for the total distance travelled in 3 hours.
   b) If $x = 40$, find the total distance.

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Section C: Simplify the Expressions

8. Simplify:
   a) $2x + 3x - 4 + 7$
   b) $5(2y + 1) - 3(y - 4)$
   c) $4x + 7 - 3x + 5x - 2$

9. If $a = 2$ and $b = 3$, find the value of:
   a) $2a + 3b$
   b) $a^2 + b^2$
   c) $5a - 2b$

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Section D: Higher-Order Thinking

10. A rectangle's length is $3x + 5$ cm and its breadth is $x + 2$ cm.
    a) Write an expression for its perimeter.
    b) Write an expression for its area.
    c) If $x = 4$, find the perimeter and area.

11. The sum of a number and its square is 90. Find the number.

12. A farmer has $x$ cows. Each cow gives 5 litres of milk daily. Write an expression for:
    a) The total milk produced in a day.
    b) The total milk produced in $7$ days.
    c) If $x = 10$, find the milk produced in $7$ days.

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