TMUA Pure Mathematics 2 β Questions and Answers
Question 1: Find the sum of the infinite geometric series 3 + 1 + 1/3 + 1/9 + β¦
- 9/2 (Correct answer)
- 4
- 3/2
- 9
Correct answer: 9/2
The first term a = 3 and common ratio r = 1/3, so S = a/(1-r) = 3/(2/3) = 9/2.
Question 2: If f(x) = xΒ³ β 3xΒ² + 4, find the x-coordinates of the stationary points.
- x = 0 and x = 2 (Correct answer)
- x = 1 and x = 3
- x = β1 and x = 2
- x = 0 and x = β2
Correct answer: x = 0 and x = 2
f'(x) = 3xΒ² β 6x = 3x(x β 2) = 0 gives x = 0 and x = 2.
Question 3: What is the value of logβ(8) β logβ(2)?
- 2 (Correct answer)
- 3
- 1
- 4
Correct answer: 2
logβ(8) = 3 and logβ(2) = 1, so the difference is 2.
Question 4: Solve |2x β 3| = 7.
- x = 5 or x = β2 (Correct answer)
- x = 5 or x = 2
- x = β5 or x = 2
- x = 7 or x = β7
Correct answer: x = 5 or x = β2
Setting 2x β 3 = 7 gives x = 5; setting 2x β 3 = β7 gives x = β2.
Question 5: The quadratic xΒ² + bx + 16 = 0 has a repeated root. What is |b|?
- 8 (Correct answer)
- 4
- 16
- 2
Correct answer: 8
A repeated root requires discriminant bΒ² β 4(16) = 0, so bΒ² = 64 and |b| = 8.
Question 6: What is the exact value of tan(135Β°)?
- β1 (Correct answer)
- 1
- β2
- ββ2
Correct answer: β1
tan(135Β°) = tan(180Β° β 45Β°) = βtan(45Β°) = β1.
Question 7: If the binomial expansion of (1 + kx)β΅ has a second-term coefficient of 20, find k.
- 4 (Correct answer)
- 2
- 5
- 10
Correct answer: 4
The second term is 5kΒ·x, so 5k = 20 gives k = 4.
TMUA Pure Mathematics 2
Find the sum of the infinite geometric series 3 + 1 + 1/3 + 1/9 + β¦