AKU-EBClass X (SSC Part II)CHAPTER-WISE NUMERICALS & WORKED PROBLEMS

Computer Science — Chapter-Wise Physics Numericals & Formula Applications

Step-by-step solved numerical word problems from 2024 & 2025 Annual Papers I & II, Model Papers I & II, and chapter formula banks, mapped to 2025 syllabus SLOs with SI units and KaTeX equations.

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UNIT 8 • 7 NUMERICAL PROBLEMS

Unit 8: Number Systems and Encoding Schemes — Worked Numericals

2025 Syllabus Outcome (8.2.1): apply the binary number system to solve arithmetic problems involving addition, subtraction, multiplication, and division;
📋 Official Checking Hints (Marking Scheme):
  • 1 mark for correct binary addition in part i (10001011210001011_2).
  • 1 mark for correct binary subtraction in part ii (001100020011000_2 or 11000211000_2).
  • 1 mark for correct binary multiplication in part iii (11100001211100001_2).
2025 Syllabus Outcome (): Logic Gates & Truth Tables (Retired 2022 Syllabus Unit 12)
Diagram for Q.4
📋 Official Checking Hints (Marking Scheme):
  • i. 1 mark for correctly writing a logical expression (X = AB + C').
  • ii. 4 marks for correctly filling the truth table (1 mark will be given to fill two possible outputs).
  • Note: round off marks to the nearest whole number.
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2025 Syllabus Outcome (): Logic Gates & Truth Tables (Retired 2022 Syllabus Unit 12)
Diagram for Q.4
📋 Official Checking Hints (Marking Scheme):
  • Part i (3 Marks): 1 mark for NOT gates on A and B (A‾,B‾\overline{A}, \overline{B}); 1 mark for the three OR gates representing (A+B‾)(A + \overline{B}), (A‾+B‾)(\overline{A} + \overline{B}), and (A+B)(A + B) (or equivalent Sum-of-Products gates); 1 mark for combining them with an AND gate to output XX.
  • Part ii (2 Marks): 0.5 mark for each correct row of the 4-row truth table (including intermediate working columns).
2025 Syllabus Outcome (): Logic Gates & Truth Tables (Retired 2022 Syllabus Unit 12)
Diagram for Q.4
📋 Official Checking Hints (Marking Scheme):
  • i. 1 mark for correctly placing NOT gates; 1 mark for correctly placing OR gates; 1 mark for correctly placing any AND gates.
  • ii. 1 mark for writing either both pairs of working space and value of X for TWO or attempting either working space or value of X for any TWO values; 1 mark will be awarded if only the values of X are written or only the working is shown.
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2025 Syllabus Outcome (): Boolean Algebra Truth Tables (Moved to Class IX Unit 2 SLO 2.3.4 in 2025 Syllabus)
📋 Official Checking Hints (Marking Scheme):
  • 1 mark for correct column NOT A.
  • 1 mark for correct column B . C.
  • 1 mark for correct final column X = NOT A + (B . C).
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2025 Syllabus Outcome (): Boolean Algebra Truth Tables (Moved to Class IX Unit 2 SLO 2.3.4 in 2025 Syllabus)
📋 Official Checking Hints (Marking Scheme):
  • 1 mark for column A + B.
  • 1 mark for column NOT(A + B).
  • 1 mark for column X = NOT(A + B) . C.
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2025 Syllabus Outcome (): Boolean Algebra Truth Tables (Moved to Class IX Unit 2 SLO 2.3.4 in 2025 Syllabus)
📋 Official Checking Hints (Marking Scheme):
  • 1 mark for column NOT A.
  • 1 mark for column B . C.
  • 1 mark for column X = NOT A + (B . C).
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Better candidate calculation for Q.6
UNIT 9 • 2 NUMERICAL PROBLEMS

Unit 9: Computational Thinking and Algorithm — Worked Numericals

2025 Syllabus Outcome (9.1.1): write algorithms to address the following types of problems: a. conditional algorithm (I. if, II. nested if, III. if else, IV. else if, V. switch), b. iteration algorithm (I. for, II. while, III. do-while, IV. nested loops), c. searching algorithm (I. linear, II. binary), d. sorting algorithm (I. selection, II. bubble);
📋 Official Checking Hints (Marking Scheme):
  • 1 mark for Start/Stop steps and loop initialisation (i = 1 to 10).
  • 1 mark for printing/outputting i inside the For loop body.
  • 1 mark for proper loop termination (EndFor / Next i).
2025 Syllabus Outcome (9.1.2): draw flowcharts related to SLO # 9.1.1.
Diagram for Q.1
📋 Official Checking Hints (Marking Scheme):
  • 0.5 mark for each correctly placed statement number (10 × 0.5 = 5 marks).
  • Note: The pair of statements 9 and 2 can be used in place of the pair of statements 8 and 5 and vice versa.
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UNIT 10 • 22 NUMERICAL PROBLEMS

Unit 10: Programming in JavaScript — Worked Numericals

2025 Syllabus Outcome (10.4.3): write JavaScript code to implement the following statements: a. if statement, b. if-else statement, c. if-else or if-else-if, d. switch statement;
📋 Official Checking Hints (Marking Scheme):
  • 1 mark for reading the menu option using prompt().
  • 4 marks (1 mark per case with break) for handling options 1, 2, 3, 4.
  • 1 mark for the default branch displaying "Invalid Option Selected".
  • 1 mark for reading n and checking if (n < 1).
  • 2 marks for writing the for loop from 1 to n and reading each student's marks.
  • 2 marks for accumulating total and computing average = total / n.
  • 1 mark for displaying Total Marks and Average Marks in the required format.
2025 Syllabus Outcome (10.4.3): write JavaScript code to implement the following statements: a. if statement, b. if-else statement, c. if-else or if-else-if, d. switch statement;
📋 Official Checking Hints (Marking Scheme):
  • 1 mark for reading the number using prompt().
  • 1 mark for testing divisibility by 2 using if (num % 2 === 0).
  • 1 mark for displaying 'Even' and 'Odd' in the if and else branches.
2025 Syllabus Outcome (10.6.2): write JavaScript code to declare and initialise a one-dimensional array with different sizes and data types;
📋 Official Checking Hints (Marking Scheme):
  • 1 mark for valid JavaScript array declaration (const / let / var with bracket notation [...]).
  • 1 mark for initialising elements of all four requested data types (number, string, boolean, and null).
2025 Syllabus Outcome (10.4.3): write JavaScript code to implement the following statements: a. if statement, b. if-else statement, c. if-else or if-else-if, d. switch statement;
📋 Official Checking Hints (Marking Scheme):
  • Give ONE mark for writing each conclusion (THREE required).
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2025 Syllabus Outcome (10.5.3): write JavaScript code to implement the following loops: a. for loop, b. while loop, c. do while loop, d. nested loop;
📋 Official Checking Hints (Marking Scheme):
  • 1 mark for initialisation of counter variable.
  • 1 mark for writing the correct condition using a do-while statement.
  • 1 mark for writing the correct increment statement.
  • Note: No mark deduction if the increment is done anywhere inside the body of the loop.
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2025 Syllabus Outcome (10.5.3): write JavaScript code to implement the following loops: a. for loop, b. while loop, c. do while loop, d. nested loop;
📋 Official Checking Hints (Marking Scheme):
  • 1 mark for declaring correct variables.
  • 1 mark for taking input.
  • 1 mark for writing the correct condition of the while loop.
  • 1 mark for writing the formula for calculating multiple.
  • 1 mark for the increment in the counter variable.
  • 1 mark for writing the output.
  • 1 mark for taking input.
  • 1 mark for printing output.
  • 2 marks for checking vowel using if condition (five operators/cases required).
  • 1 mark for checking a consonant.
  • 1 mark for checking invalid character (default in switch).
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2025 Syllabus Outcome (10.4.3): write JavaScript code to implement the following statements: a. if statement, b. if-else statement, c. if-else or if-else-if, d. switch statement;
📋 Official Checking Hints (Marking Scheme):
  • 1 mark for calculating the sum of the three angles (sum = a1 + a2 + a3;).
  • 1 mark for writing the if condition checking whether sum == 180 (and printing that the triangle is valid).
  • 1 mark for writing the else branch printing that the formation of the triangle is not possible.
2025 Syllabus Outcome (10.5.4): write the output of a given program having a loop and selection structures;
📋 Official Checking Hints (Marking Scheme):
  • 1 mark for correctly completing Iteration 1 (x = 14, y = 20, Output = 14).
  • 1 mark for correctly completing Iteration 2 (x = 16, y = 20, Output = 16).
  • 1 mark for correctly completing Iteration 3 (x = 18, y = 20, Output = 18) and showing x = 20, y = 20 where the loop terminates.
2025 Syllabus Outcome (10.4.3): write JavaScript code to implement the following statements: a. if statement, b. if-else statement, c. if-else or if-else-if, d. switch statement;
📋 Official Checking Hints (Marking Scheme):
  • 1 mark for variable declaration (int year;).
  • 1 mark for taking user input (scanf("%d", &year);).
  • 2 marks for writing the correct leap-year condition (year % 4 == 0 or full Gregorian rule (year % 400 == 0) || (year % 4 == 0 && year % 100 != 0)).
  • 2 marks for printing the appropriate output in both if and else blocks.
  • 1 mark for declaring and initialising the first two terms (t1 = 0, t2 = 1) and loop variables.
  • 2 marks for writing the for loop structure for 10 terms (for (i = 1; i <= 10; i++)).
  • 2 marks for computing the next Fibonacci term (nextTerm = t1 + t2; t1 = t2; t2 = nextTerm;).
  • 1 mark for printing the series output accurately.
2025 Syllabus Outcome (10.4.3): write JavaScript code to implement the following statements: a. if statement, b. if-else statement, c. if-else or if-else-if, d. switch statement;
📋 Official Checking Hints (Marking Scheme):
  • 1 mark for writing each correct condition (THREE required).
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2025 Syllabus Outcome (10.5.4): write the output of a given program having a loop and selection structures;
📋 Official Checking Hints (Marking Scheme):
  • 1 mark for writing correct value of n and output of each iteration (THREE required).
  • No marks will be awarded if either n or output is missing.
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Better candidate calculation for Q.3
2025 Syllabus Outcome (10.4.3): write JavaScript code to implement the following statements: a. if statement, b. if-else statement, c. if-else or if-else-if, d. switch statement;
📋 Official Checking Hints (Marking Scheme):
  • 1 mark for declaring the correct variables.
  • 1 mark for taking the input.
  • 1 mark for writing each correct condition using correct operators (FOUR required).
  • 1 mark for declaring correct variables.
  • 1 mark for taking input.
  • 1 mark for writing correct for loop.
  • 1 mark for writing print statement inside loop.
  • 1 mark for the formula for adding even numbers.
  • 1 mark for writing the output.
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2025 Syllabus Outcome (10.3.8): simplify an expression by using the order of precedence of operators;
📋 Official Checking Hints (Marking Scheme):
  • 1 mark for inputting current (I) and voltage (V).
  • 1 mark for calculating power using programming multiplication operator (P = I * V).
  • 1 mark for outputting power (PRINT P).
  • 0.5 mark for each correct evaluation (4 × 0.5 = 2 marks).
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2025 Syllabus Outcome (10.5.4): write the output of a given program having a loop and selection structures;
📋 Official Checking Hints (Marking Scheme):
  • 1 mark for tracing Z = 1, 2, 3 at Line 50.
  • 1 mark for tracing X = 12, 24, 48 at Line 60.
  • 1 mark for tracing Output = 12, 24, 48 at Line 70.
  • 1 mark for tracing Y = 12, 24, 48 at Line 80.
  • 1 mark for correctly rewriting the statement (IF-block executes when condition is true and ELSE-block executes when condition is false).
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2025 Syllabus Outcome (10.6.3): apply the process of traversing using all types of loops for input, output, and manipulation of elements;
📋 Official Checking Hints (Marking Scheme):
  • 1 mark for part (a): Numeric data type.
  • 1 mark for part (b): Inputs 15 numbers and calculates/prints the square of each input number.
  • 1 mark for part (c): 30 FOR X = 1 TO 22.
  • 1 mark for part (d): 50 PRINT A(X) - 5.
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2025 Syllabus Outcome (10.5.3): write JavaScript code to implement the following loops: a. for loop, b. while loop, c. do while loop, d. nested loop;
📋 Official Checking Hints (Marking Scheme):
  • 1 mark for inputting total number of items.
  • 2 marks for loop inputting each item's price and accumulating Total Price.
  • 1 mark for calculating Tax = Total Price * 0.13.
  • 1 mark for calculating and printing Total Bill = Total Price + Tax.
  • 2 marks for conditional check (Total Bill <= 10000 vs > 10000) and outputting Service Charges (250 or 500).
  • 1 mark for inputting kilometres travelled (D).
  • 2 marks for condition D <= 5 calculating fare = D * 30.
  • 2 marks for condition D > 5 calculating fare = (5 * 30) + ((D - 5) * 25).
  • 1 mark for adding fixed charges of 50 rupees.
  • 1 mark for outputting the final bill.
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2025 Syllabus Outcome (10.3.1): write a JavaScript program to solve arithmetic problems by using arithmetic operators;
📋 Official Checking Hints (Marking Scheme):
  • 1 mark for inputting Principal Amount (P), Interest Rate (I/R), and Number of Years (Y/T).
  • 1 mark for calculating Simple Interest S = (P * I * Y) / 100 using programming arithmetic operators (* and /).
  • 1 mark for displaying Simple Interest in output.
  • 2 marks for completing all 5 remaining relational operations and their programming symbols.
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2025 Syllabus Outcome (10.6.1): explain the array concerning the array name, size, index number, and arrangement of elements in the memory;
📋 Official Checking Hints (Marking Scheme):
  • 1 mark for part (a): One-dimensional array.
  • 1 mark for part (b): It contains only one subscript/index per element (or has one column of values).
  • 1 mark for part (c): 10 (or X$(10)).
  • 1 mark for part (d): String data type because of the '′signattachedtothearraynameX' sign attached to the array name X (or because it stores text/city names).
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2025 Syllabus Outcome (10.6.3): apply the process of traversing using all types of loops for input, output, and manipulation of elements;
📋 Official Checking Hints (Marking Scheme):
  • 2 marks for FOR loop running from 1 to 150.
  • 2 marks for inputting the first four digits of each book's barcode.
  • 3 marks for computing Step 1, Step 2, Step 3, and Step 4 (Remainder using MOD 10).
  • 2 marks for IF-ELSE condition setting check digit to 0 or (10 - Remainder) and printing the check digit.
  • 2 marks for declaring arrays A(15), B(15), and C(15).
  • 2 marks for FOR loop running from 1 to 15.
  • 2 marks for inputting values into A(T) and B(T).
  • 2 marks for adding C(T) = A(T) + B(T).
  • 1 mark for printing the elements of array C(T).
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2025 Syllabus Outcome (10.5.3): write JavaScript code to implement the following loops: a. for loop, b. while loop, c. do while loop, d. nested loop;
📋 Official Checking Hints (Marking Scheme):
  • 1 mark for part (a): Output A (5 asterisks).
  • 4 marks for part (b): Initialising Count = 0, WHILE Count <= 4, PRINT "*", Count = Count + 1, and WEND.
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2025 Syllabus Outcome (): Legacy GW-BASIC Built-in Functions (ABS, SQR, LEFT$ — Retired 2012 Syllabus)
📋 Official Checking Hints (Marking Scheme):
  • 1 mark for Box 1 output: 115.46.
  • 1 mark for Box 2 output: 5.
  • 1 mark for Box 3 output: Kent.
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2025 Syllabus Outcome (10.6.4): write a program that stores numeric values in a one-dimensional array using a for loop and obtains the highest, lowest, and average values.
📋 Official Checking Hints (Marking Scheme):
  • 1 mark for initialising SUM = 0 and MAX = 0.
  • 2 marks for FOR loop running from 1 to 55 and inputting weight W.
  • 2 marks for accumulating SUM = SUM + W and updating MAX using IF W > MAX THEN MAX = W.
  • 1 mark for calculating AVG = SUM / 55.
  • 1 mark for printing AVG and MAX.
  • 1 mark for inputting Weight (W) and Height (H).
  • 2 marks for calculating BMI = W / (H * H) or W / H^2.
  • 4 marks for conditional statements checking the 4 BMI ranges and printing the respective Weight Category (1 mark per category).
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Better candidate calculation for Q.8