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AAI Junior Executive (ATC) Mathematics — practice by topic

Browse 77 questions across 19 Mathematics topics. Choose what you want to revise, then open a question to check its answer and worked solution.

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Mathematics topics

Probability (40)Binomial Theorem (39)Correlation and Regression (39)Geometry (39)Linear Programming (39)Mean (39)Median (39)Permcomb (39)Permutations and Combinations (39)Probability & Statistics (39)Sequences (39)Sequences and Series (39)Integrals (36)Application of Integrals (33)Integral Calculus (33)Probability Density Function (27)Probability Distribution (27)Vectors & 3D Geometry (27)Definite Integration (21)

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A fair coin is tossed twice. How many outcomes are there in the sample space?Read the answer and worked solution →A fair six-sided die is rolled once. What is the probability of getting an even number?Read the answer and worked solution →Find $\displaystyle\int x^4\,dx$.Read the answer and worked solution →Find $\displaystyle\int \sin x\,dx$.Read the answer and worked solution →

Worked practice questions

A fair coin is tossed twice. How many outcomes are there in the sample space?

  1. $2$
  2. $4$
  3. $6$
  4. $8$
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Correct answer: B. $4$

Each toss has 2 possible outcomes (H or T), and the tosses are independent. By the multiplication principle, the sample space has $2 \times 2 = 4$ outcomes: {HH, HT, TH, TT}.

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A fair six-sided die is rolled once. What is the probability of getting an even number?

  1. $\dfrac{1}{6}$
  2. $\dfrac{1}{2}$
  3. $\dfrac{1}{3}$
  4. $\dfrac{2}{3}$
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Correct answer: B. $\dfrac{1}{2}$

The even outcomes are {2, 4, 6}, so the number of favourable outcomes is 3. The total sample space has 6 outcomes. $P(\text{even}) = \dfrac{3}{6} = \dfrac{1}{2}$.

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Find $\displaystyle\int x^4\,dx$.

  1. $5x^5 + C$
  2. $\dfrac{x^5}{5} + C$
  3. $x^5 + C$
  4. $4x^3 + C$
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Correct answer: B. $\dfrac{x^5}{5} + C$

Power rule for integration: $\displaystyle\int x^n\,dx = \dfrac{x^{n+1}}{n+1} + C$ for $n \neq -1$. Plug $n = 4$: $\dfrac{x^5}{5} + C$. Option A is the *derivative* of $x^4$, not the integral. Always check by differentiating your answer.

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