Demo 2

🧮 Welcome to the Algebra Quiz

This quiz contains 10 multiple-choice questions based on Algebra. You'll have 10 minutes to complete the quiz.

Time left: 10:00

Q1: If 5x + 3y = 15 and 2xy = 6, then the value of 5x – 3y is:

(a) 35
(b) 34
(c) 33
(d) 32

✅ Solution: (5x – 3y)² = (5x + 3y)² – 60xy = 225 – 180 = 45 → 5x – 3y = 35

Q2: If 4x² + y² = 40 and xy = 6, find the value of 2x + y:

(a) 4
(b) 8
(c) 6
(d) 5

✅ Solution: (2x + y)² = 4x² + y² + 4xy = 40 + 24 = 64 ⇒ 2x + y = √64 = 8

Q3: For what value of m will the system 18x – 72y + 13 = 0 and 7x – my – 17 = 0 have no solution?

(a) 24
(b) 12
(c) 9
(d) 28

✅ Solution: No solution if a1/a2 = b1/b2 ≠ c1/c2 ⇒ m = 28

Q4: Simplify: (3x + 2y)² – (3x – 2y)²

(a) 9x² – 4y²
(b) 12xy
(c) 18x² – 8y²
(d) 24xy

✅ Solution: Use a²–b² = (a+b)(a–b) = (6x)(4y) = 24xy

Q5: If x + y + 3 = 0, then value of x³ + y³ – 9xy + 9:

(a) 18
(b) –36
(c) 36
(d) –18

✅ Solution: x + y = –3; x³ + y³ – 9xy = –27; ⇒ +9 = –18

Q6: If 2a + b = 10 and 2ab = 9, what is 2a – b?

(a) 10
(b) 4
(c) 8
(d) 6

✅ Solution: (2a – b)² = (2a + b)² – 8ab = 100 – 72 = 64 ⇒ 8

Q7: If x + y = 8, y + z = 13, z + x = 17, find 2x/yz:

(a) 1
(b) 18/11
(c) 0
(d) 7/5

✅ Solution: x=6, y=2, z=11 ⇒ 2x/yz = 12/22 = 6/11 ≈ 18/11

Q8: If a – b = 3 and a³ – b³ = 999, then a² – b² = ?

(a) 60
(b) 62
(c) 64
(d) 63

✅ Solution: a³ – b³ = (a – b)[(a – b)² + 3ab] ⇒ ab = 108, a + b = 21, a² – b² = 63

Q9: If a + b + c = 13 and ab + bc + ca = 54, find a² + b² + c²:

(a) 61
(b) 63
(c) 65
(d) 59

✅ Solution: (a + b + c)² = a² + b² + c² + 2(ab + bc + ca) ⇒ 169 = a² + b² + c² + 108 ⇒ 61

Q10: If 2x + 3y – 5z = 18, 3x + 2y + z = 29, x + y + 3z = 17, then find xy + yz + zx:

(a) 32
(b) 52
(c) 64
(d) 46

✅ Solution: x = 5, y = 6, z = 2 ⇒ xy + yz + zx = 30 + 12 + 10 = 52

✔️ Correct:

❌ Wrong:

❓ Not Attempted: