Static Members, this Keyword, Number Programs and Roots of Equations (ISC Class 11)

Understand Static Members, the this Keyword, Number Programs and Finding Roots of Equations

class C {
    static int n = 0;          // one copy for the whole class
    int id;                    // one copy per object
    C() { n++; id = n; }
    static int count() { return n; }
}

Box(int l, int b) { this.l = l; this.b = b; }   // l on the left is the field

Static Members, the this Keyword, Number Programs and Finding Roots of Equations: key facts

Quadratic roots

D = b^2 - 4ac | x = (-b + sqrt(D)) / (2a) and (-b - sqrt(D)) / (2a)

Real roots if D >= 0.

Euclid GCD

gcd(a, b) = gcd(b, a % b) | Stop when b = 0

Repeat.

Digit loop

• •digit = n % 10
• •n = n / 10
• •r = r x 10 + digit

Reverse a number.

How to answer Static Members, the this Keyword, Number Programs and Finding Roots of Equations questions

1. 1Write the starting values.
2. 2For each iteration compute the digit or remainder and update the variables.
3. 3Stop when the loop condition fails.
4. 4State the output exactly.

Static Members, the this Keyword, Number Programs and Finding Roots of Equations in real life

The idea, met in an everyday situation. Answer the question in your own words, then compare with the model answer. The one-line hook is what to remember.

Tricks to remember Static Members, the this Keyword, Number Programs and Finding Roots of Equations

Short memory aids. Say each one aloud once, then use it on a question the same day.

• Static = shared

  One copy for the whole class.

  Use it when: Static.

• this.x = x

  Left x is the field, right x the parameter.

  Use it when: this.

• mod and divide by ten

  % 10 takes the digit; / 10 drops it.

  Use it when: Digit programs.

Static Members, the this Keyword, Number Programs and Finding Roots of Equations: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

int r = 0;
while (n > 0) {
    r = r * 10 + n % 10;
    n = n / 10;
}

Where students lose marks in Static Members, the this Keyword, Number Programs and Finding Roots of Equations

The slips examiners see most often, and what to write instead.

• ✗Mistake: Forgetting to update n in the digit loop

  Infinite loop.

  Wrong working

  No n = n / 10

  Right working

  Update n

  ✓Do this: Check the loop variable.

  Usually costs: 2 marks.

• ✗Mistake: Using instance variables in a static method

  No object.

  Wrong working

  static method uses id

  Right working

  Use an object or static data

  ✓Do this: Static methods cannot use this.

  Usually costs: 1-2 marks.

• ✗Mistake: Not using this when names clash

  Shadowing.

  Wrong working

  x = x

  Right working

  this.x = x

  ✓Do this: Qualify the field.

  Usually costs: 2 marks.

Practice questions on Static Members, the this Keyword, Number Programs and Finding Roots of Equations

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

1. Q1 · 1 mark · MCQBoard level

   The keyword that refers to the current object is:
   (a) super (b) this (c) static (d) final

   Hint

   Current object.

   Answer

   (b) this

2. Q2 · 4 marks · Short answerBoard level

   Write a method that returns true if an integer n is a palindrome, and give the result for 121 and 123. (4 marks)

   Hint

   Reverse and compare.

   Answer

   Reverse n into r with the digit loop and return r == original. 121 gives true; 123 reverses to 321 and gives false.

3. Q3 · 5 marks · Long answerHarder board level

   Trace gcd(84, 36) by Euclid's method and state the LCM using LCM = a x b / gcd. Also find the sum of the digits of 9,075 with a loop. (5 marks)

   Hint

   84 % 36 = 12.

   Answer

   (84, 36) to (36, 12) to (12, 0): gcd 12. LCM = 84 x 36 / 12 = 252. Digit sum of 9075 = 5 + 7 + 0 + 9 = 21.

4. Q4 · 4 marks · Short answerHarder board level

   Find the roots of 2x^2 - 7x + 3 = 0 and the nature of roots of x^2 + 2x + 5 = 0. Write the Java condition that tests the discriminant. (4 marks)

   Hint

   D = 49 - 24.

   Answer

   D = 49 - 24 = 25: roots (7 + 5)/4 = 3 and (7 - 5)/4 = 0.5. For x^2 + 2x + 5: D = 4 - 20 = -16 < 0: no real roots. Condition: if (d >= 0) { ... } else { ... }.

5. Q5 · 3 marks · Short answerHOTS / competency

   A class counts its objects with a static variable, but a student declares the count without static and prints it from each of three objects. Predict the output, explain and fix. (3 marks)

   Hint

   Each object has its own copy.

   Answer

   Each object has its own count that starts at 0 and is incremented to 1 in its own constructor, so each prints 1. Declare the counter static so that all objects share one copy; then the prints show 3 after three objects are created.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1. 1.Static variable copies?Show answer

   One for the class.

2. 2.this means?Show answer

   The current object.

3. 3.Euclid stops when?Show answer

   The divisor is zero.

4. 4.D less than 0 means?Show answer

   No real roots.

5. 5.Reverse step?Show answer

   r = r * 10 + n % 10.

Static Members, the this Keyword, Number Programs and Finding Roots of Equations: frequently asked questions