{
  "Id": "c8f0dc08-ec78-4e3e-8665-8f613c8f0c88",
  "Title": "Introduction to Algebra: Variables, Expressions, and Perimeter \u2014 Practice Worksheet",
  "Subject": "Mathematics",
  "Topic": "Introductory Algebra: variables vs. constants, coefficients, properties, expressions, evaluation, and perimeter rules",
  "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": "f1c128e9-2717-4503-894a-3e2d69c6b01a",
  "GeneratedAt": "2026-09-07T23:28:32.145961Z",
  "Questions": [
    {
      "Id": 1,
      "Type": "true_false",
      "Text": "Algebra uses variables to represent quantities that can change.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 2,
      "Type": "true_false",
      "Text": "In the term 9k, 9 is the variable.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 3,
      "Type": "true_false",
      "Text": "The perimeter of a square with side s is 3s.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 4,
      "Type": "true_false",
      "Text": "The distributive property allows you to expand a(b \u002B c) into ab \u002B ac.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 5,
      "Type": "true_false",
      "Text": "For all real numbers a and b, a \u002B b = b \u002B a.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 6,
      "Type": "true_false",
      "Text": "Variables must always be lowercase letters.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 7,
      "Type": "true_false",
      "Text": "Evaluating 4t \u2212 1 at t = 0 gives 4.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 8,
      "Type": "true_false",
      "Text": "An algebraic expression may include more than one variable.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 9,
      "Type": "true_false",
      "Text": "In 6m \u002B 2n, m and n are the literal coefficients.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 10,
      "Type": "true_false",
      "Text": "Two consecutive even integers differ by 1.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 11,
      "Type": "multiple_choice",
      "Text": "In 12p, which identifies the variable and the numerical coefficient?",
      "Options": [
        "A. Variable: 12; Coefficient: p",
        "B. Variable: p; Coefficient: 12",
        "C. Variable: 12p; Coefficient: 1",
        "D. Variable: 12; Coefficient: 1"
      ],
      "Answer": "B. Variable: p; Coefficient: 12",
      "Points": 2
    },
    {
      "Id": 12,
      "Type": "multiple_choice",
      "Text": "Which statement shows the commutative property of multiplication?",
      "Options": [
        "A. a \u002B (b \u002B c) = (a \u002B b) \u002B c",
        "B. a(b \u002B c) = ab \u002B ac",
        "C. ab = ba",
        "D. (ab)c = a(bc)"
      ],
      "Answer": "C. ab = ba",
      "Points": 2
    },
    {
      "Id": 13,
      "Type": "multiple_choice",
      "Text": "If a = 5, what is the value of 3a \u002B 4?",
      "Options": [
        "A. 11",
        "B. 19",
        "C. 17",
        "D. 34"
      ],
      "Answer": "B. 19",
      "Points": 2
    },
    {
      "Id": 14,
      "Type": "multiple_choice",
      "Text": "Which expression represents \u201Ctwice a number decreased by seven\u201D?",
      "Options": [
        "A. 2x \u002B 7",
        "B. 2x \u2212 7",
        "C. 7 \u2212 2x",
        "D. x/2 \u2212 7"
      ],
      "Answer": "B. 2x \u2212 7",
      "Points": 2
    },
    {
      "Id": 15,
      "Type": "multiple_choice",
      "Text": "A rectangle has length 3x and width x \u002B 2. Which expression equals its perimeter?",
      "Options": [
        "A. 6x \u002B 2x",
        "B. 2(3x \u002B x \u002B 2)",
        "C. 8x \u002B 4",
        "D. 3x(x \u002B 2)"
      ],
      "Answer": "C. 8x \u002B 4",
      "Points": 2
    },
    {
      "Id": 16,
      "Type": "multiple_choice",
      "Text": "Which of the following is an algebraic expression?",
      "Options": [
        "A. 4 \u002B 7",
        "B. x/5 \u002B 2",
        "C. 18 \u00D7 3",
        "D. 9 \u2212 1"
      ],
      "Answer": "B. x/5 \u002B 2",
      "Points": 2
    },
    {
      "Id": 17,
      "Type": "multiple_choice",
      "Text": "Which property lets you rewrite 7(n \u002B 3) as 7n \u002B 21?",
      "Options": [
        "A. Commutative property of addition",
        "B. Associative property of multiplication",
        "C. Distributive property",
        "D. Identity property of 0"
      ],
      "Answer": "C. Distributive property",
      "Points": 2
    },
    {
      "Id": 18,
      "Type": "multiple_choice",
      "Text": "For an equilateral triangle with side y, the perimeter is:",
      "Options": [
        "A. y^2",
        "B. 2y",
        "C. 3y",
        "D. 4y"
      ],
      "Answer": "C. 3y",
      "Points": 2
    },
    {
      "Id": 19,
      "Type": "multiple_choice",
      "Text": "What is the constant term in 9 \u2212 5q \u002B 2?",
      "Options": [
        "A. -5",
        "B. 11",
        "C. 9",
        "D. -5q"
      ],
      "Answer": "B. 11",
      "Points": 2
    },
    {
      "Id": 20,
      "Type": "multiple_choice",
      "Text": "If x = 1 and y = 4, what is 2x \u002B 3y?",
      "Options": [
        "A. 10",
        "B. 14",
        "C. 12",
        "D. 18"
      ],
      "Answer": "B. 14",
      "Points": 2
    },
    {
      "Id": 21,
      "Type": "fill_blank",
      "Text": "A symbol that can take different values is called a _____.",
      "Options": [],
      "Answer": "variable",
      "Points": 2
    },
    {
      "Id": 22,
      "Type": "fill_blank",
      "Text": "A number that stays the same in an expression is a _____.",
      "Options": [],
      "Answer": "constant",
      "Points": 2
    },
    {
      "Id": 23,
      "Type": "fill_blank",
      "Text": "In 14z, 14 is the numerical _____.",
      "Options": [],
      "Answer": "coefficient",
      "Points": 2
    },
    {
      "Id": 24,
      "Type": "fill_blank",
      "Text": "The rule a \u00D7 (b \u002B c) = ab \u002B ac is the _____ property.",
      "Options": [],
      "Answer": "distributive",
      "Points": 2
    },
    {
      "Id": 25,
      "Type": "fill_blank",
      "Text": "The perimeter of a polygon is the sum of the lengths of all its _____.",
      "Options": [],
      "Answer": "sides",
      "Points": 2
    },
    {
      "Id": 26,
      "Type": "fill_blank",
      "Text": "The perimeter of a square with side s is _____.",
      "Options": [],
      "Answer": "4s",
      "Points": 2
    },
    {
      "Id": 27,
      "Type": "fill_blank",
      "Text": "When x = 3, the value of 2x \u002B 1 is _____.",
      "Options": [],
      "Answer": "7",
      "Points": 2
    },
    {
      "Id": 28,
      "Type": "fill_blank",
      "Text": "Consecutive odd integers differ by _____.",
      "Options": [],
      "Answer": "2",
      "Points": 2
    },
    {
      "Id": 29,
      "Type": "fill_blank",
      "Text": "An expression built from variables, constants, and operations is an algebraic _____.",
      "Options": [],
      "Answer": "expression",
      "Points": 2
    },
    {
      "Id": 30,
      "Type": "fill_blank",
      "Text": "In 5p \u002B 3q, p and q are the _____ coefficients.",
      "Options": [],
      "Answer": "literal",
      "Points": 2
    },
    {
      "Id": 31,
      "Type": "word_problem",
      "Text": "A herb garden is planted in rows. The first row has 6 plants, and each following row has 4 more plants than the previous row. The number of plants in row r is given by 6 \u002B 4(r \u2212 1). How many plants are in row 8? Show your working.",
      "Options": [],
      "Answer": "Step 1: Substitute r = 8 into 6 \u002B 4(r \u2212 1): 6 \u002B 4(8 \u2212 1)\nStep 2: Compute inside parentheses: 6 \u002B 4(7) = 6 \u002B 28\nStep 3: Add: 6 \u002B 28 = 34\nAnswer: 34 plants",
      "Points": 5
    },
    {
      "Id": 32,
      "Type": "word_problem",
      "Text": "A rectangle has length 3x \u002B 2 and width x \u2212 1. If x = 4, find its perimeter. Use P = 2(l \u002B w).",
      "Options": [],
      "Answer": "Step 1: Compute length l = 3(4) \u002B 2 = 12 \u002B 2 = 14\nStep 2: Compute width w = 4 \u2212 1 = 3\nStep 3: Find l \u002B w = 14 \u002B 3 = 17\nStep 4: Perimeter P = 2(17) = 34\nAnswer: 34 units",
      "Points": 5
    },
    {
      "Id": 33,
      "Type": "word_problem",
      "Text": "Mira has n stickers. Leo has 2n \u002B 3 stickers. If n = 12, how many stickers does Leo have?",
      "Options": [],
      "Answer": "Step 1: Substitute n = 12 into 2n \u002B 3: 2(12) \u002B 3\nStep 2: Multiply and add: 24 \u002B 3 = 27\nAnswer: 27 stickers",
      "Points": 5
    },
    {
      "Id": 34,
      "Type": "word_problem",
      "Text": "Evaluate 5(a \u002B 2) \u2212 3a when a = 4. Show each algebraic step.",
      "Options": [],
      "Answer": "Step 1: Expand using distributive property: 5a \u002B 10 \u2212 3a = 2a \u002B 10\nStep 2: Substitute a = 4: 2(4) \u002B 10 = 8 \u002B 10\nStep 3: Add: 18\nAnswer: 18",
      "Points": 5
    },
    {
      "Id": 35,
      "Type": "word_problem",
      "Text": "Notebooks cost $2.25 each and pens cost $0.75 each. Write an expression for the total cost of 4 notebooks and 6 pens, then compute its value.",
      "Options": [],
      "Answer": "Step 1: Form the expression: Total = 4(2.25) \u002B 6(0.75)\nStep 2: Multiply: 4(2.25) = 9.00 and 6(0.75) = 4.50\nStep 3: Add: 9.00 \u002B 4.50 = 13.50\nAnswer: $13.50",
      "Points": 5
    },
    {
      "Id": 36,
      "Type": "word_problem",
      "Text": "An equilateral triangle has side length 12.3 cm. Find its perimeter.",
      "Options": [],
      "Answer": "Step 1: Use P = 3a for equilateral triangle with side a\nStep 2: Substitute a = 12.3: P = 3(12.3) = 36.9\nAnswer: 36.9 cm",
      "Points": 5
    },
    {
      "Id": 37,
      "Type": "word_problem",
      "Text": "A square has side length y \u002B 1 meters. If y = 6, find the perimeter of the square.",
      "Options": [],
      "Answer": "Step 1: Compute side: y \u002B 1 = 6 \u002B 1 = 7\nStep 2: Perimeter of a square P = 4s = 4(7) = 28\nAnswer: 28 meters",
      "Points": 5
    },
    {
      "Id": 38,
      "Type": "word_problem",
      "Text": "The sum of two consecutive odd integers is 36. Find the two integers.",
      "Options": [],
      "Answer": "Step 1: Let the integers be n and n \u002B 2\nStep 2: Write equation: n \u002B (n \u002B 2) = 36 \u2192 2n \u002B 2 = 36\nStep 3: Solve: 2n = 34 \u2192 n = 17; next is n \u002B 2 = 19\nAnswer: 17 and 19",
      "Points": 5
    },
    {
      "Id": 39,
      "Type": "word_problem",
      "Text": "A row of n adjacent squares is built from matchsticks. The total number of matchsticks is M = 3n \u002B 1. How many matchsticks are needed for 9 squares?",
      "Options": [],
      "Answer": "Step 1: Substitute n = 9 into M = 3n \u002B 1\nStep 2: Compute: M = 3(9) \u002B 1 = 27 \u002B 1 = 28\nAnswer: 28 matchsticks",
      "Points": 5
    },
    {
      "Id": 40,
      "Type": "word_problem",
      "Text": "A rectangle\u2019s length is triple its width. If its perimeter is 64 units, find the rectangle\u2019s width and length.",
      "Options": [],
      "Answer": "Step 1: Let width be w and length be 3w; perimeter P = 2(l \u002B w) = 64\nStep 2: Set up equation: 2(3w \u002B w) = 64 \u2192 2(4w) = 64 \u2192 8w = 64\nStep 3: Solve for w: w = 8; then l = 3w = 24\nAnswer: Width = 8 units, Length = 24 units",
      "Points": 5
    }
  ],
  "TotalPoints": 100
}