🔥 HIGHER COMPLEXITY SET (With Proper Sections & Case Study)
TOPICS: Number play, Geometric twins, Operations with integers, Another peek beyond the point.
SECTION A – MCQs
- Prove algebraically that square of any odd number is odd. (Objective based)
- If vertically opposite angles are (3x+10)° and (5x−20)°, find x.
- Temperature is −6°C at midnight and rises 3°C per hour. When will it reach 15°C?
- 225.5 km covered in 2.5 hours. Find speed.
- Which congruency rule applies in right triangle with hypotenuse and one side equal?
- Assertion–Reason (Integers rule based)
SECTION B – Short Answer
- Simplify:
(−12) + 36 ÷ (−6) − (−5) × (−2) - Evaluate using distributive property:
125 × (−64) + (−64) × (−75)
- Find petrol required if mileage is 13.75 km/l to cover 192.5 km.
SECTION D – Case Study (Higher Level – Algebra Based)
In a competitive exam:
+4 marks for correct
−1 mark for wrong
A student attempted 25 questions and scored 55 marks.
(a)
Let number of correct answers be x.
Form equation and find number of correct and wrong answers.
(b)
If another student scored 10 marks with 8 correct answers, find wrong answers.
(c)
What is minimum correct answers required to get positive score?
Answer Key
🔥 ANSWER KEY – HIGHER COMPLEXITY SET
SECTION A
- Odd number = 2n+1
Square = (2n+1)²
= 4n² + 4n +1
= 2(2n²+2n) +1 → odd ✔ - 3x+10 = 5x−20
30 = 2x
x = 15 - From −6°C to 15°C
Increase = 21°C
21 ÷ 3 = 7 hours - Speed = 225.5 ÷ 2.5
= 90.2 km/h - RHS
- Both true and correct explanation
SECTION B
(−12) + 36 ÷ (−6) − (−5) × (−2)
= −12 − 6 − 10
= −28
125 × (−64) + (−64) × (−75)
= (−64)(125 − 75)
= (−64)(50)
= −3200
- Petrol required
192.5 ÷ 13.75
= 14 litres
SECTION D – Case Study
(a)
Let correct = x
Wrong = 25 − x
4x − (25 − x) = 55
4x − 25 + x = 55
5x = 80
x = 16 correct
Wrong = 9
(b)
4(8) − x = 10
32 − x = 10
x = 22 wrong
(c)
For positive score:
4x − (25 − x) > 0
5x > 25
x > 5
Minimum correct = 6
