Which statement about the graph of $y = (x + 1)^2(x - 3)$ is correct?

It touches the $x$-axis at $x = -1$, crosses at $x = 3$, and has $y$-intercept $-3$

The graph of $y = \ln x$ is transformed to $y = \ln(x - 2) + 3$. Which statement is correct?

It is translated 2 right and 3 up, with vertical asymptote $x = 2$

The exact solution of $3^{2x} = 5$ is:

$x = \dfrac{\ln 5}{2\ln 3} \approx 0.732$

Criterion 5. The solutions of $\cos(2x) = -\dfrac{1}{2}$ for $0 \le x \le \pi$ are:

$x = \frac{\pi}{3}$ and $x = \frac{2\pi}{3}$

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TCE Mathematics Methods Level 4 criteria 4 to 8: exam-style practice quiz

12 questions. Pick an answer and you'll see why right away. Options are shuffled each attempt, and the review at the end links each missed question to the dot point to revise.

Which statement about the graph of $y = (x + 1)^2(x - 3)$ is correct?
The graph of $y = \ln x$ is transformed to $y = \ln(x - 2) + 3$ . Which statement is correct?
The exact solution of $3^{2x} = 5$ is:
Criterion 5. The solutions of $\cos(2x) = -\dfrac{1}{2}$ for $0 \le x \le \pi$ are:
If $\sin x = \dfrac{3}{5}$ and $\dfrac{\pi}{2} < x < \pi$ , then $\cos x$ equals:
The equation of the tangent to $y = \sqrt{x}$ at $x = 4$ is:
For $f(x) = x^3 - 6x^2$ , the point of inflection is at:
A particle's position is $x(t) = t^3 - 6t^2 + 9t$ metres for $t \ge 0$ seconds. The particle is at rest at:
The area enclosed between $y = x$ and $y = x^2$ is:
Given $f'(x) = \cos(2x)$ and $f(0) = 1$ , the function $f(x)$ is:
A random variable X takes the values 1, 2 and 3 with probabilities 0.5, 0.3 and 0.2. Its mean and variance are:
In a large population, 30 percent of people own a pet bird. For random samples of 100 people, the standard deviation of the sample proportion is closest to: