{
  "Id": "53ac7411-3851-4f29-a666-764da79dcaf5",
  "Title": "Class 6 Algebra \u2014 Variables, Expressions, and Equations",
  "Subject": "Mathematics",
  "Topic": "Intro to Algebra: variables, expressions, equations, LHS/RHS, and simple properties",
  "Instructions": "Read each question carefully and answer to the best of your ability. Show all working for word problems.",
  "EstimatedMinutes": 35,
  "StudentProfileId": "dd186faa-f489-46ee-84e4-26e2d01e2691",
  "SourceFileName": "manual-input",
  "SessionMaterialId": "6345474f-8265-41ca-9a44-2543c9205d15",
  "GeneratedAt": "2026-08-16T10:51:50.632871Z",
  "Questions": [
    {
      "Id": 1,
      "Type": "true_false",
      "Text": "In algebra, letters can stand for numbers whose values are not fixed.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 2,
      "Type": "true_false",
      "Text": "The expression 3k \u002B 7 is an equation.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 3,
      "Type": "true_false",
      "Text": "In an equation, the equality sign separates the LHS and RHS.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 4,
      "Type": "true_false",
      "Text": "If a and b are numbers, then a \u002B b is always equal to b \u002B a.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 5,
      "Type": "true_false",
      "Text": "The number of days in a week is a variable.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 6,
      "Type": "true_false",
      "Text": "To check if a number is a solution of x \u2212 4 = 9, we can substitute and see if both sides are equal.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 7,
      "Type": "true_false",
      "Text": "The expression 2n has the same value no matter what n is.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 8,
      "Type": "true_false",
      "Text": "If each shape uses 5 matchsticks, then repeating it t times needs 5 \u002B t matchsticks.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 9,
      "Type": "true_false",
      "Text": "If x = 3, then the value of 2x \u002B 1 is 7.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 10,
      "Type": "true_false",
      "Text": "The two sides of an equation are called RHS and RHE.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 11,
      "Type": "multiple_choice",
      "Text": "Which of the following is an equation?",
      "Options": [
        "A. y \u002B 8 = 20",
        "B. 7p \u2212 3",
        "C. m/5",
        "D. 9 \u002B q"
      ],
      "Answer": "A. y \u002B 8 = 20",
      "Points": 2
    },
    {
      "Id": 12,
      "Type": "multiple_choice",
      "Text": "In the formula P = 2(l \u002B b) for a rectangle, which of the following are variables?",
      "Options": [
        "A. Only P",
        "B. l and b only",
        "C. l, b and P",
        "D. None of these"
      ],
      "Answer": "C. l, b and P",
      "Points": 2
    },
    {
      "Id": 13,
      "Type": "multiple_choice",
      "Text": "The statement a \u002B b = b \u002B a shows which property?",
      "Options": [
        "A. Commutative property of addition",
        "B. Distributive property",
        "C. Associative property of subtraction",
        "D. Identity property of multiplication"
      ],
      "Answer": "A. Commutative property of addition",
      "Points": 2
    },
    {
      "Id": 14,
      "Type": "multiple_choice",
      "Text": "If n stands for the number of times a design is repeated and each design uses 4 sticks, which expression gives the total sticks needed?",
      "Options": [
        "A. 4n",
        "B. n \u002B 4",
        "C. n \u2212 4",
        "D. 4 \u2212 n"
      ],
      "Answer": "A. 4n",
      "Points": 2
    },
    {
      "Id": 15,
      "Type": "multiple_choice",
      "Text": "For x = \u22122, what is the value of 5 \u2212 x?",
      "Options": [
        "A. 3",
        "B. 7",
        "C. \u22127",
        "D. \u22123"
      ],
      "Answer": "B. 7",
      "Points": 2
    },
    {
      "Id": 16,
      "Type": "multiple_choice",
      "Text": "Which statement is true?",
      "Options": [
        "A. For x = 4, 3x = 12, so x = 4 solves 3x = 12.",
        "B. The expression r \u002B 9 has an LHS and RHS.",
        "C. If k = 2, then k \u002B 1 = 4.",
        "D. The number of sides of a triangle is a variable."
      ],
      "Answer": "A. For x = 4, 3x = 12, so x = 4 solves 3x = 12.",
      "Points": 2
    },
    {
      "Id": 17,
      "Type": "multiple_choice",
      "Text": "Which expression represents \u0022six minus half of t\u0022?",
      "Options": [
        "A. 6 \u2212 t/2",
        "B. (6 \u2212 t)/2",
        "C. t/2 \u2212 6",
        "D. 6t/2"
      ],
      "Answer": "A. 6 \u2212 t/2",
      "Points": 2
    },
    {
      "Id": 18,
      "Type": "multiple_choice",
      "Text": "Which value of y makes y \u002B 5 = 2y \u2212 1 true?",
      "Options": [
        "A. 4",
        "B. 5",
        "C. 6",
        "D. 7"
      ],
      "Answer": "C. 6",
      "Points": 2
    },
    {
      "Id": 19,
      "Type": "multiple_choice",
      "Text": "In the equation 4p \u002B 1 = 13, which option correctly identifies the LHS and RHS?",
      "Options": [
        "A. LHS: 4p \u002B 1, RHS: 13",
        "B. LHS: 13, RHS: 4p \u002B 1",
        "C. LHS: p, RHS: 13",
        "D. LHS: 4, RHS: p \u002B 1"
      ],
      "Answer": "A. LHS: 4p \u002B 1, RHS: 13",
      "Points": 2
    },
    {
      "Id": 20,
      "Type": "multiple_choice",
      "Text": "If s stands for any number, which of the following is always equal to s \u002B s?",
      "Options": [
        "A. s^2",
        "B. 2s",
        "C. s/2",
        "D. s \u2212 s"
      ],
      "Answer": "B. 2s",
      "Points": 2
    },
    {
      "Id": 21,
      "Type": "fill_blank",
      "Text": "In algebra, letters like x or y that can take different values are called _____.",
      "Options": [],
      "Answer": "variables",
      "Points": 2
    },
    {
      "Id": 22,
      "Type": "fill_blank",
      "Text": "An equality such as 3k \u2212 2 = 10 is called an _____.",
      "Options": [],
      "Answer": "equation",
      "Points": 2
    },
    {
      "Id": 23,
      "Type": "fill_blank",
      "Text": "The side to the left of the equal sign is called the _____.",
      "Options": [],
      "Answer": "LHS",
      "Points": 2
    },
    {
      "Id": 24,
      "Type": "fill_blank",
      "Text": "In the statement a \u002B b = b \u002B a, the property shown is the _____ property of addition.",
      "Options": [],
      "Answer": "commutative",
      "Points": 2
    },
    {
      "Id": 25,
      "Type": "fill_blank",
      "Text": "To check if a number is a solution, we _____ it into the equation.",
      "Options": [],
      "Answer": "substitute",
      "Points": 2
    },
    {
      "Id": 26,
      "Type": "fill_blank",
      "Text": "If each figure uses 3 matchsticks, then repeating the figure n times needs _____ matchsticks.",
      "Options": [],
      "Answer": "3n",
      "Points": 2
    },
    {
      "Id": 27,
      "Type": "fill_blank",
      "Text": "For x = 5, the value of 2x \u002B 4 is _____.",
      "Options": [],
      "Answer": "14",
      "Points": 2
    },
    {
      "Id": 28,
      "Type": "fill_blank",
      "Text": "A quantity whose value does not change is a _____.",
      "Options": [],
      "Answer": "constant",
      "Points": 2
    },
    {
      "Id": 29,
      "Type": "fill_blank",
      "Text": "Only when LHS equals RHS is a value said to _____ the equation.",
      "Options": [],
      "Answer": "satisfy",
      "Points": 2
    },
    {
      "Id": 30,
      "Type": "fill_blank",
      "Text": "We can use any letter such as p, q, r to _____ a number whose value can change.",
      "Options": [],
      "Answer": "represent",
      "Points": 2
    },
    {
      "Id": 31,
      "Type": "word_problem",
      "Text": "A scout badge requires 6 matchsticks. Write an expression for the number of matchsticks needed for t badges. Then find how many matchsticks are needed for 9 badges. Show your working.",
      "Options": [],
      "Answer": "Step 1: Let T be the total number of matchsticks. T = 6t\nStep 2: Substitute t = 9 into T = 6t\nStep 3: T = 6 \u00D7 9 = 54\nAnswer: 54 matchsticks",
      "Points": 5
    },
    {
      "Id": 32,
      "Type": "word_problem",
      "Text": "Find the number m if m \u2212 5 = 11. Show your working.",
      "Options": [],
      "Answer": "Step 1: m \u2212 5 = 11\nStep 2: Add 5 to both sides \u2192 m = 11 \u002B 5\nStep 3: m = 16\nAnswer: m = 16",
      "Points": 5
    },
    {
      "Id": 33,
      "Type": "word_problem",
      "Text": "The perimeter P of a rectangle is given by P = 2(l \u002B b). If l = 13 cm and b = 9 cm, find P. Show your working.",
      "Options": [],
      "Answer": "Step 1: P = 2(l \u002B b)\nStep 2: Substitute l = 13 and b = 9 \u2192 P = 2(13 \u002B 9)\nStep 3: P = 2(22) = 44\nAnswer: 44 cm",
      "Points": 5
    },
    {
      "Id": 34,
      "Type": "word_problem",
      "Text": "Evaluate the expression 4y \u002B 9 when y = \u22123. Show your working.",
      "Options": [],
      "Answer": "Step 1: 4y \u002B 9 with y = \u22123\nStep 2: 4(\u22123) \u002B 9 = \u221212 \u002B 9\nStep 3: \u221212 \u002B 9 = \u22123\nAnswer: \u22123",
      "Points": 5
    },
    {
      "Id": 35,
      "Type": "word_problem",
      "Text": "Check whether x = 8 is a solution of the equation 3x \u002B 1 = 25. Show your working.",
      "Options": [],
      "Answer": "Step 1: Compute LHS with x = 8 \u2192 3(8) \u002B 1 = 24 \u002B 1 = 25\nStep 2: RHS is 25\nStep 3: LHS = RHS, so x = 8 satisfies the equation\nAnswer: Yes, x = 8 is a solution",
      "Points": 5
    },
    {
      "Id": 36,
      "Type": "word_problem",
      "Text": "Twice a number increased by 5 equals 21. Find the number. Show your working.",
      "Options": [],
      "Answer": "Step 1: Let the number be n. Then 2n \u002B 5 = 21\nStep 2: Subtract 5 from both sides \u2192 2n = 16\nStep 3: Divide both sides by 2 \u2192 n = 8\nAnswer: 8",
      "Points": 5
    },
    {
      "Id": 37,
      "Type": "word_problem",
      "Text": "Solve for k: k/3 \u002B 2 = 8. Show your working.",
      "Options": [],
      "Answer": "Step 1: k/3 \u002B 2 = 8\nStep 2: Subtract 2 from both sides \u2192 k/3 = 6\nStep 3: Multiply both sides by 3 \u2192 k = 18\nAnswer: k = 18",
      "Points": 5
    },
    {
      "Id": 38,
      "Type": "word_problem",
      "Text": "Each crate holds 24 bottles. Write an expression for the total bottles in p crates and find the total for p = 11. Show your working.",
      "Options": [],
      "Answer": "Step 1: Total bottles B = 24p\nStep 2: Substitute p = 11 \u2192 B = 24 \u00D7 11\nStep 3: B = 264\nAnswer: 264 bottles",
      "Points": 5
    },
    {
      "Id": 39,
      "Type": "word_problem",
      "Text": "The sum of two consecutive integers is 37. Find the two integers. Show your working.",
      "Options": [],
      "Answer": "Step 1: Let the first integer be n, the next is n \u002B 1\nStep 2: n \u002B (n \u002B 1) = 37 \u2192 2n \u002B 1 = 37\nStep 3: 2n = 36 \u2192 n = 18\nAnswer: 18 and 19",
      "Points": 5
    },
    {
      "Id": 40,
      "Type": "word_problem",
      "Text": "The total cost c (in rupees) of buying n notebooks is given by c = 12n \u002B 15, where 15 is a fixed delivery fee. Find c when n = 5. Show your working.",
      "Options": [],
      "Answer": "Step 1: c = 12n \u002B 15\nStep 2: Substitute n = 5 \u2192 c = 12(5) \u002B 15\nStep 3: c = 60 \u002B 15 = 75\nAnswer: Rs 75",
      "Points": 5
    }
  ],
  "TotalPoints": 100
}