Wazari Exam (Iraq Baccalaureate) - Scientific Branch · Mathematics

Probability, sequences and logarithms

18 practice questions, each with the answer and an explanation.

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Find the coefficient of $x^{2}$ in the expansion of $(2 x + 1)^{6}$ .
A fair coin is tossed 5 times. What is the probability of exactly 2 heads?
A fair coin is tossed 6 times. What is the probability of exactly 3 heads?
A fair coin is tossed 8 times. What is the probability of exactly 4 heads?
A fair coin is tossed 7 times. What is the probability of exactly 5 heads?
A fair coin is tossed 10 times. What is the probability of exactly 3 heads?
Bag I holds 3 red and 2 white balls; bag II holds 1 red and 4 white balls. A bag is chosen at random and a ball drawn is red. What is the probability that it came from bag I?
Bag I holds 2 red and 3 white balls; bag II holds 4 red and 1 white balls. A bag is chosen at random and a ball drawn is red. What is the probability that it came from bag I?
Bag I holds 4 red and 1 white balls; bag II holds 2 red and 6 white balls. A bag is chosen at random and a ball drawn is red. What is the probability that it came from bag I?
Find the sum to infinity of the geometric series $18 + 12 + 8 + \dots$
Find the sum to infinity of the geometric series $20 + 15 + \frac{45}{4} + \dots$
Evaluate $lo g_{2} 32 - lo g_{3} 27$ .
Evaluate $lo g_{2} 64 - lo g_{5} 25$ .
Evaluate $lo g_{3} 81 - lo g_{2} 8$ .
If $x_{1}$ and $x_{2}$ are the real roots of $2^{2 x} - 10 \cdot 2^{x} + 16 = 0$ , what is $x_{1} + x_{2}$ ?
If $x_{1}$ and $x_{2}$ are the real roots of $3^{2 x} - 10 \cdot 3^{x} + 9 = 0$ , what is $x_{1} + x_{2}$ ?
If $x_{1}$ and $x_{2}$ are the real roots of $2^{2 x} - 5 \cdot 2^{x} + 4 = 0$ , what is $x_{1} + x_{2}$ ?
If $x_{1}$ and $x_{2}$ are the real roots of $3^{2 x} - 12 \cdot 3^{x} + 27 = 0$ , what is $x_{1} + x_{2}$ ?

Probability, sequences and logarithms

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