SIMAK UI · Basic Mathematics (Matematika Dasar)

Matrices, Functions and Probability

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

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Given matrix $A = (2413)$ , compute the determinant of $A^{- 1}$ .
If $f (x) = 2 x + 3$ and $g (x) = x^{2} - 1$ , what is the value of $(g \circ f) (2)$ ?
Given the invertible function $f (x) = (3 x + 1) / (2 x - 5)$ for $x \neq = 5/2$ , determine $f^{- 1} (2)$ .
How many distinct 4-letter arrangements can be formed from the letters of the word 'SIMAK'?
A committee of 4 students is to be chosen from a group of 5 boys and 4 girls. What is the probability that the committee contains exactly 2 boys and 2 girls?
Find the domain of definition of the real function $h (x) = (x - 2) / (5 - x)$ .
If $tan θ = 3/4$ with $θ$ in the first quadrant, what is the exact value of $sin (2 θ)$ ?
Given $A = (1324)$ and $B = (5768)$ , compute the trace of the product matrix $A B$ .
If $A$ and $B$ are independent events with $P (A) = 0.4$ and $P (B) = 0.5$ , what is $P (A \cup B)$ ?
What is the slope of the tangent line to the curve $y = 2 x^{3} - 5 x + 4$ at the point where $x = 2$ ?
Find the equation of the tangent line to the parabola $y = x^{2} - 4 x + 3$ at $x = 3$ .
Evaluate the definite integral $\int_{1}^{3} (3 x^{2} - 2 x + 4) d x$ .
A dataset of 10 numbers has mean 15 and variance 4. If each number is multiplied by 3 and then increased by 2, what are the new mean and variance?
A rectangular garden is enclosed by 60 meters of fencing against a straight stone wall (fencing only 3 sides). What is the maximum area that can be enclosed in square meters?
A discrete random variable $X$ takes values 1, 2, 3 with probabilities $0.2$ , $0.5$ , and $0.3$ respectively. What is the expected value $E [X]$ ?
If $lim_{x \to 2} \frac{x ^{2} + a x + b}{x - 2} = 5$ , what is the product $ab$ ?
How many integers between 100 and 999 inclusive contain no digit 7?

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Matrices, Functions and Probability

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