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§ Coding·Grade 10

Algorithms & Variables Worksheets

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Easy

10 problems

Medium

20 problems

Hard

20 problems

Mixed

30 problems

Free printable algorithms & variables worksheets with step-by-step answer keys. Every worksheet is uniquely generated so students never see the same problems twice. Topics covered range from single variable update: x = x op value at the easy level through to while-loop with termination condition at the advanced level.

LK20.10

What is algorithms & variables?

An algorithm is a step-by-step sequence of instructions designed to solve a specific problem or perform a calculation. Variables serve as containers that store and update values as the algorithm executes. Together, algorithms and variables form the foundation of computational problem-solving, where each instruction modifies variable values according to predetermined rules.

Why it matters

Algorithms and variables power everything from GPS navigation systems that calculate optimal routes through millions of possible paths, to banking software that processes over 150 billion transactions annually. Search engines use algorithms with thousands of variables to rank web pages in milliseconds. In manufacturing, robotic assembly lines follow algorithmic instructions while tracking variables like temperature (within 2-degree tolerances) and production counts. Video games update player scores, health points, and inventory items through variable assignments executed 60 times per second. Financial trading algorithms analyze market variables and execute trades worth $5 trillion daily. Even simple applications like calculating tax on a $47.50 purchase rely on algorithmic steps that update price variables through multiplication and addition operations.

Common mistakes to watch for

  • ✗Confusing the assignment operator with equality: writing x = 5 to mean 'x equals 5' when it actually means 'assign 5 to x', leading to errors like thinking x = x + 1 is impossible instead of recognizing it updates x by adding 1
  • ✗Forgetting to trace variable updates step-by-step: jumping from x = 3 through a loop that adds 4 three times and incorrectly stating x = 7 instead of the correct x = 15
  • ✗Misunderstanding conditional execution: assuming score = score - 5 always executes when the condition is if score > 20, missing that score = 18 would remain unchanged at 18
  • ✗Mixing up loop iteration counts: believing 'repeat 5 times: x = x × 2' starting with x = 1 gives x = 10 instead of x = 32

Questions teachers ask

What is the difference between an algorithm and a variable?+
An algorithm is the sequence of instructions, while a variable is a storage location for data. For example, in the algorithm 'add 3 to x', the algorithm is the instruction to add, and x is the variable holding the value being modified.
How do you trace through an algorithm with variables?+
Follow each step in order, updating variable values as instructed. Start with initial values, then execute each operation. For x = 5; x = x × 2; x = x + 1, trace: x starts at 5, becomes 10, then becomes 11.
What does x = x + 1 mean in programming?+
This updates the variable x by adding 1 to its current value. If x contains 7, then x = x + 1 changes x to 8. The equals sign means 'assign' rather than mathematical equality.
How do conditional statements work with variables?+
Conditional statements check a variable's value before executing instructions. In 'if score > 15: score = score + 10', the addition only happens when the condition is true. A score of 12 remains unchanged.
Why do loops require careful variable tracking?+
Each loop iteration modifies variables, and the effects accumulate. A loop that doubles a variable 3 times transforms x = 2 into x = 16 (2→4→8→16), not x = 8. Missing iterations leads to incorrect final values.
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Pick a difficulty

Click any level to open the generator with that difficulty pre-selected.

Beginner

Generate →
Concepts
Single variable update: x = x op value
Range
operands: 1–20
Steps
2 steps
Example
x = 7; x = x + 3. What is x?

Easy

Generate →
Concepts
If-condition with one variable update
Range
x: 6–20, threshold varies
Steps
2 steps
Example
x = 10; if x > 5: x = x − 3

Medium

Generate →
Concepts
Loop with fixed iterations (for-loop trace)
Range
4–6 iterations, ops: ×2, ×3, +3
Steps
2 steps
Example
x = 1; repeat 5 times: x = x × 2

Hard

Generate →
Concepts
While-loop with termination condition
Range
start: 1–200, various halving/subtracting ops
Steps
2 steps
Example
x = 100; while x > 10: x = x // 2

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