TCE Mathematics Methods Level 4: mixed exam-style practice quiz

Criterion 4, Section A style. Solve $\log_2 x + \log_2(x - 2) = 3$.

Criterion 4. The inverse of $f(x) = 2 + \ln(x - 1)$, $x > 1$, is:

Criterion 5, Section A style. The exact value of $\sin\left(\dfrac{5\pi}{6}\right)$ is:

Criterion 5. The solutions of $\tan x = -1$ for $0 \le x \le 2\pi$ are:

Criterion 5. For $y = -3\cos\left(\dfrac{\pi x}{2}\right) + 2$, the amplitude, period and range are:

Criterion 6. The derivative of $y = e^{3x}\sin x$ is:

Criterion 6. The derivative of $y = \tan(2x)$ is:

Criterion 6. The maximum value of $f(x) = x^3 - 3x$ on the interval $-2 \le x \le 3$ is:

Criterion 7. $\displaystyle\int_0^1 e^{2x}\,dx$ is closest to:

Criterion 7. Using the trapezoidal rule with two strips of width 1, the estimate of $\displaystyle\int_0^2 x^2\,dx$ is:

Criterion 8. Each item from a machine is faulty with probability 0.04, independently. In a batch of 50, the probability of at least one faulty item is closest to:

Criterion 8, Section B style. In a random sample of 400 people, 120 support a proposal. An approximate 95 percent confidence interval for the population proportion is: