Moderate Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) Write the algebraic expression for: "Three times a number decreased by 4." (Let Variable be x)
Correct! "Three times a number" = 3x, "decreased by 4" means - 4, so 3x - 4.
(2) Find the value of 5x – 7 when x = 3.
Perfect! 5(3) - 7 = 15 - 7 = 8.
(3) Identify the variable in the expression 2m + 9.
Excellent! The variable is the letter that represents an unknown value: m.
(4) Write the constant term in the expression 8y – 15.
Great! The constant term has no variable: -15.
(5) If z = 5, find the value of 4z + 2.
Correct! 4(5) + 2 = 20 + 2 = 22.
Short Answer Questions (2 Marks Each)
Answer each question clearly
(1) Form expressions for:
The sum of twice a number and 11 (Let Variable be x):
Four less than a number (Let Variable be x):
Excellent! "Sum of twice a number and 11" = 2x + 11, "Four less than a number" = x - 4.
(2) Evaluate 3x + 4y when x = 2, y = 3.
Perfect! 3(2) + 4(3) = 6 + 12 = 18.
(3) Write an expression for the perimeter of a triangle with sides a, b, c.
Correct! Perimeter = sum of all sides = a + b + c.
(4) Simplify: 2p + 3q + 4p – 5q.
Great! Combining like terms: (2p + 4p) + (3q - 5q) = 6p - 2q.
(5) Subtract (7x – 9) from (12x + 5).
Perfect! (12x + 5) - (7x - 9) = 12x + 5 - 7x + 9 = 5x + 14.
Long Answer Questions (4 Marks Each)
Note: Answer each question with complete steps and clear explanations.
(1) A basket contains x apples and another basket contains 3x + 7 apples. Write an expression for the total number of apples. Find its value if x = 12.
Expression:
Correct! Total = x + (3x + 7) = 4x + 7. When x = 12: 4(12) + 7 = 48 + 7 = 55.
(2) If the cost of 1 notebook is n rupees and the cost of 1 pen is p rupees, write an expression for the total cost of 8 notebooks and 5 pens. Find the cost when n = 15, p = 10.
Expression:
Perfect! Total cost = 8n + 5p. When n = 15, p = 10: 8(15) + 5(10) = 120 + 50 = 170.
(3) A rectangle has length 2x + 3 and breadth x + 2. Write an expression for its perimeter. Simplify it.
Expression:
Excellent! Perimeter = 2(length + breadth) = 2[(2x + 3) + (x + 2)] = 2(3x + 5) = 6x + 10.
(4) Write an expression for the area of a rectangle with length l and breadth b. Evaluate it when l = 12 cm, b = 9 cm.
Expression:
Great! Area = l × b. When l = 12, b = 9: Area = 12 × 9 = 108
(5) The sum of four consecutive odd numbers can be expressed algebraically. Form the expression and simplify it.
Expression:
Correct! Let first odd number = x. Consecutive odds: x, x+2, x+4, x+6. Sum = x + (x+2) + (x+4) + (x+6) = 4x + 12.
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) The coefficient of y in 12y – 8 is:
(a) 12 (b) 8 (c) y (d) –8
Correct! The coefficient is the number multiplied with the variable. Here, 12 is the coefficient of y.
(2) The variable in 7p + 4 is:
(a) 7 (b) 4 (c) p (d) None
Correct! The variable is the letter representing an unknown value: p.
(3) If m = 3, the value of 2m + 5 is:
(a) 6 (b) 11 (c) 8 (d) 5
Correct! 2m + 5 = 2(3) + 5 = 6 + 5 = 11.
(4) The perimeter of a rectangle with length l and breadth b is:
(a) l + b (b) 2(l + b) (c) l × b (d) l – b
Correct! Perimeter = 2(length + breadth) = 2(l + b).
(5) Which of these is an algebraic expression?
(a) 20 (b) x + 7 (c) 5 × 9 (d) 100
Correct! An algebraic expression contains variables. x + 7 has variable x.
(6) The constant term in 9x + 13 is:
(a) 9 (b) x (c) 13 (d) 22
Correct! The constant term has no variable: 13.
(7) The expression for "twice a number added to 6" is:
(a) 2x – 6 (b) 2x + 6 (c) x + 6 (d) 6 – 2x
Correct! "Twice a number" = 2x, "added to 6" means + 6, so 2x + 6.
(8) The value of 3y – 4 when y = 5 is:
(a) 11 (b) 12 (c) 15 (d) 19
Correct! 3y - 4 = 3(5) - 4 = 15 - 4 = 11.
(9) The sum of a and 9 is written as:
(a) a – 9 (b) a + 9 (c) 9 – a (d) 9a
Correct! Sum means addition, so a + 9.
(10) If x = 7, the value of
(a) 7 (b) 14 (c) 21 (d) 49
Correct!
Advanced Algebra Challenge
Determine whether these statements are True or False: