{
  "Id": "cc2ae969-7458-48d7-99a6-30a04c63406f",
  "Title": "Algebra Basics: Variables, Expressions, and Patterns \u2014 Practice Worksheet",
  "Subject": "Mathematics",
  "Topic": "Introductory Algebra (variables, expressions, properties, perimeters, and patterns)",
  "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": "algebra.pdf",
  "SessionMaterialId": "728a742e-a3d5-49b9-bfb9-a467d0a1562f",
  "GeneratedAt": "2026-07-25T12:24:43.407148Z",
  "Questions": [
    {
      "Id": 1,
      "Type": "true_false",
      "Text": "A symbol like k used to represent a changing quantity is called a variable.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 2,
      "Type": "true_false",
      "Text": "The expression 4 \u002B x represents 4 multiplied by x.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 3,
      "Type": "true_false",
      "Text": "In the expression 9p - 6, 9 is a coefficient.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 4,
      "Type": "true_false",
      "Text": "The perimeter of a square with side s equals 2s.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 5,
      "Type": "true_false",
      "Text": "If a = 3, then 2a \u002B 1 equals 7.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 6,
      "Type": "true_false",
      "Text": "The distributive property lets us rewrite 7(m \u002B 2) as 7m \u002B 14.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 7,
      "Type": "true_false",
      "Text": "For whole-number n, the product 3n can be an even number only.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 8,
      "Type": "true_false",
      "Text": "The expressions y \u002B y \u002B y and 3y are equivalent.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 9,
      "Type": "true_false",
      "Text": "If each box has q pens, then 5 boxes contain q \u002B 5 pens.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 10,
      "Type": "true_false",
      "Text": "For any numbers a and b, a \u002B b = b \u002B a is an example of the associative property.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 11,
      "Type": "multiple_choice",
      "Text": "Which expression represents \u201C12 more than a number t\u201D?",
      "Options": [
        "A. t \u002B 12",
        "B. 12t",
        "C. t - 12",
        "D. 12 - t"
      ],
      "Answer": "A. t \u002B 12",
      "Points": 2
    },
    {
      "Id": 12,
      "Type": "multiple_choice",
      "Text": "\u201CSubtract 9 from the product of m and n\u201D is written as:",
      "Options": [
        "A. 9mn",
        "B. mn - 9",
        "C. m - 9n",
        "D. 9 - mn"
      ],
      "Answer": "B. mn - 9",
      "Points": 2
    },
    {
      "Id": 13,
      "Type": "multiple_choice",
      "Text": "Which is equivalent to 6(x \u002B 4)?",
      "Options": [
        "A. 6x \u002B 24",
        "B. 10x",
        "C. 6x \u002B 4",
        "D. 24x"
      ],
      "Answer": "A. 6x \u002B 24",
      "Points": 2
    },
    {
      "Id": 14,
      "Type": "multiple_choice",
      "Text": "Find the value of 3x - 5 when x = 4.",
      "Options": [
        "A. 7",
        "B. 12",
        "C. -1",
        "D. 17"
      ],
      "Answer": "A. 7",
      "Points": 2
    },
    {
      "Id": 15,
      "Type": "multiple_choice",
      "Text": "Identify the property: (p \u002B q) \u002B r = p \u002B (q \u002B r).",
      "Options": [
        "A. Commutative of addition",
        "B. Associative of addition",
        "C. Distributive over addition",
        "D. Additive identity"
      ],
      "Answer": "B. Associative of addition",
      "Points": 2
    },
    {
      "Id": 16,
      "Type": "multiple_choice",
      "Text": "Perimeter of a rectangle with length L and breadth B is:",
      "Options": [
        "A. L \u002B B",
        "B. 2(L \u002B B)",
        "C. 4(L \u002B B)",
        "D. LB"
      ],
      "Answer": "B. 2(L \u002B B)",
      "Points": 2
    },
    {
      "Id": 17,
      "Type": "multiple_choice",
      "Text": "If each packet holds 25 cookies, how many cookies are in k packets?",
      "Options": [
        "A. k \u002B 25",
        "B. 25 - k",
        "C. 25k",
        "D. 25/k"
      ],
      "Answer": "C. 25k",
      "Points": 2
    },
    {
      "Id": 18,
      "Type": "multiple_choice",
      "Text": "Which inequality represents \u201Cx is at least 7\u201D?",
      "Options": [
        "A. x = 7",
        "B. x \u003E 7",
        "C. x \u003E= 7",
        "D. x \u003C 7"
      ],
      "Answer": "C. x \u003E= 7",
      "Points": 2
    },
    {
      "Id": 19,
      "Type": "multiple_choice",
      "Text": "Which pair could represent two consecutive even integers?",
      "Options": [
        "A. 2n and 2n \u002B 1",
        "B. 2n and 2n \u002B 2",
        "C. n and n \u002B 1",
        "D. 2n - 1 and 2n \u002B 1"
      ],
      "Answer": "B. 2n and 2n \u002B 2",
      "Points": 2
    },
    {
      "Id": 20,
      "Type": "multiple_choice",
      "Text": "If s is the side length of a square, which expression gives its area?",
      "Options": [
        "A. 4s",
        "B. s \u002B s",
        "C. s^2",
        "D. 2s"
      ],
      "Answer": "C. s^2",
      "Points": 2
    },
    {
      "Id": 21,
      "Type": "fill_blank",
      "Text": "A number that does not change in value is called a _____.",
      "Options": [],
      "Answer": "constant",
      "Points": 2
    },
    {
      "Id": 22,
      "Type": "fill_blank",
      "Text": "The expression for \u201C7 multiplied by n\u201D is _____.",
      "Options": [],
      "Answer": "7n",
      "Points": 2
    },
    {
      "Id": 23,
      "Type": "fill_blank",
      "Text": "The coefficient of x in 5x \u002B 2 is _____.",
      "Options": [],
      "Answer": "5",
      "Points": 2
    },
    {
      "Id": 24,
      "Type": "fill_blank",
      "Text": "The perimeter of a square with side a is _____.",
      "Options": [],
      "Answer": "4a",
      "Points": 2
    },
    {
      "Id": 25,
      "Type": "fill_blank",
      "Text": "The expression \u201Cthe sum of y and 11\u201D can be written as _____.",
      "Options": [],
      "Answer": "y\u002B11",
      "Points": 2
    },
    {
      "Id": 26,
      "Type": "fill_blank",
      "Text": "When like terms are combined, 4k \u002B 3k becomes _____.",
      "Options": [],
      "Answer": "7k",
      "Points": 2
    },
    {
      "Id": 27,
      "Type": "fill_blank",
      "Text": "If x = 2 and y = 3, then x \u002B 2y equals _____.",
      "Options": [],
      "Answer": "8",
      "Points": 2
    },
    {
      "Id": 28,
      "Type": "fill_blank",
      "Text": "Using the distributive property, 9(t \u002B 1) is rewritten as _____.",
      "Options": [],
      "Answer": "9t\u002B9",
      "Points": 2
    },
    {
      "Id": 29,
      "Type": "fill_blank",
      "Text": "\u201Cr exceeds s\u201D can be expressed as _____.",
      "Options": [],
      "Answer": "r\u003Es",
      "Points": 2
    },
    {
      "Id": 30,
      "Type": "fill_blank",
      "Text": "If each letter in a pattern uses 4 matchsticks, the total for n letters is _____.",
      "Options": [],
      "Answer": "4n",
      "Points": 2
    },
    {
      "Id": 31,
      "Type": "word_problem",
      "Text": "A student buys 3 notebooks at p rupees each and one pen for 12 rupees. Write an expression for the total cost and find the amount when p = 18.",
      "Options": [],
      "Answer": "Step 1: Total cost expression = 3p \u002B 12\nStep 2: Substitute p = 18 \u2192 3(18) \u002B 12 = 54 \u002B 12\nAnswer: 66 rupees",
      "Points": 5
    },
    {
      "Id": 32,
      "Type": "word_problem",
      "Text": "The side length of an equilateral triangle is x cm. Write a rule for its perimeter and evaluate it for x = 9 cm.",
      "Options": [],
      "Answer": "Step 1: Perimeter of an equilateral triangle = 3x\nStep 2: Substitute x = 9 \u2192 3(9)\nAnswer: 27 cm",
      "Points": 5
    },
    {
      "Id": 33,
      "Type": "word_problem",
      "Text": "There are b bags with 6 apples in each. If 4 apples are eaten, how many apples remain? Also find the number when b = 7.",
      "Options": [],
      "Answer": "Step 1: Total apples = 6b\nStep 2: Apples remaining = 6b - 4\nStep 3: For b = 7 \u2192 6(7) - 4 = 42 - 4\nAnswer: 38 apples",
      "Points": 5
    },
    {
      "Id": 34,
      "Type": "word_problem",
      "Text": "A taxi charges a base fare of 50 rupees plus 15 rupees per kilometer for d kilometers. Write the expression for the fare and compute it for d = 8.",
      "Options": [],
      "Answer": "Step 1: Fare expression = 50 \u002B 15d\nStep 2: Substitute d = 8 \u2192 50 \u002B 15(8) = 50 \u002B 120\nAnswer: 170 rupees",
      "Points": 5
    },
    {
      "Id": 35,
      "Type": "word_problem",
      "Text": "Let the smaller of two consecutive odd integers be 2n \u002B 1. Their sum is 40. Find n and the two integers.",
      "Options": [],
      "Answer": "Step 1: Consecutive odd integers = 2n \u002B 1 and 2n \u002B 3\nStep 2: Sum = (2n \u002B 1) \u002B (2n \u002B 3) = 4n \u002B 4\nStep 3: Set 4n \u002B 4 = 40 \u2192 4n = 36 \u2192 n = 9\nAnswer: n = 9; integers are 19 and 21",
      "Points": 5
    },
    {
      "Id": 36,
      "Type": "word_problem",
      "Text": "A rectangular garden has width w meters and length that is 3 meters more than the width. Write the perimeter in terms of w and find it when w = 10.",
      "Options": [],
      "Answer": "Step 1: Length = w \u002B 3\nStep 2: Perimeter P = 2(w \u002B (w \u002B 3)) = 2(2w \u002B 3)\nStep 3: Simplify P = 4w \u002B 6; for w = 10 \u2192 4(10) \u002B 6\nAnswer: 46 meters",
      "Points": 5
    },
    {
      "Id": 37,
      "Type": "word_problem",
      "Text": "Evaluate 4a \u002B 2(3a - 5) for a = 7, showing the use of the distributive property.",
      "Options": [],
      "Answer": "Step 1: Expand 2(3a - 5) = 6a - 10\nStep 2: 4a \u002B (6a - 10) = 10a - 10\nStep 3: Substitute a = 7 \u2192 10(7) - 10 = 70 - 10\nAnswer: 60",
      "Points": 5
    },
    {
      "Id": 38,
      "Type": "word_problem",
      "Text": "A jar has 500 mL of juice. After pouring 4 glasses of g mL each, how much juice is left? Also find the amount left when g = 120.",
      "Options": [],
      "Answer": "Step 1: Total poured = 4g\nStep 2: Juice left = 500 - 4g\nStep 3: For g = 120 \u2192 500 - 4(120) = 500 - 480\nAnswer: 20 mL",
      "Points": 5
    },
    {
      "Id": 39,
      "Type": "word_problem",
      "Text": "A pattern uses M(n) = 5n \u002B 2 matchsticks for the nth figure. How many matchsticks are needed for the 12th figure?",
      "Options": [],
      "Answer": "Step 1: Use the rule M(n) = 5n \u002B 2\nStep 2: Substitute n = 12 \u2192 M(12) = 5(12) \u002B 2 = 60 \u002B 2\nAnswer: 62 matchsticks",
      "Points": 5
    },
    {
      "Id": 40,
      "Type": "word_problem",
      "Text": "On a class trip, each of x students pays 320 rupees. The bus costs 4500 rupees. Write an expression for the money left after paying for the bus and evaluate it for x = 20.",
      "Options": [],
      "Answer": "Step 1: Total collected = 320x\nStep 2: Money left = 320x - 4500\nStep 3: For x = 20 \u2192 320(20) - 4500 = 6400 - 4500\nAnswer: 1900 rupees",
      "Points": 5
    }
  ],
  "TotalPoints": 100
}