SACE Stage 2 Mathematical Methods: mixed exam-style practice quiz

The derivative of $f(x) = x^2\ln x$ is:

A population is modelled by $P = 5e^{0.4t}$ (thousands), with $t$ in years. The time taken to reach 60 thousand is closest to:

The stationary point of $y = xe^{-2x}$ is:

$\displaystyle\int_0^{\pi/2} \sin(2x)\,dx$ equals:

The area enclosed between $y = 4 - x^2$ and the $x$-axis is:

A random variable X takes the values 0, 1, 2 and 3 with probabilities 0.2, 0.4, 0.3 and 0.1. The standard deviation of X is:

A student guesses all 8 questions of a quiz, each with 4 options. The probability of exactly 2 correct is closest to:

A continuous random variable has density $f(x) = 2x$ for $0 \le x \le 1$. $P(X > 0.5)$ equals:

IQ-style test scores are modelled by $X \sim N(100, 15^2)$. $P(X > 130)$ is closest to:

Checkout times have mean 50 s and standard deviation 12 s. For random samples of 36 customers, $P(\bar{X} > 53)$ is closest to:

A random sample of 100 has $\bar{x} = 24.6$ and $s = 5$. An approximate 95 percent confidence interval for the population mean is:

$\ln 12 - \ln 3 + 2\ln 2$ simplifies to: