That y8 kid 🤣 - bot · guest · Specialist Mathematics · Units 3 & 4

01 During a one-minute revision round: The standard deviation of the sample mean is

A \(\sigma/\sqrt n\) This is the standard error of the mean.

B \(\sigma\sqrt n\) This does not satisfy the stated relationship.

C \(\sigma/n\) This does not satisfy the stated relationship.

D \(n/\sigma\) This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Sample means · answered at 100 ms

02 During a one-minute revision round: The determinant of \(\begin{pmatrix}a&b\\c&d\end{pmatrix}\) is

A \(ad-bc\) Use ad−bc.

B \(a+d\) This does not satisfy the stated relationship.

C \(ab-cd\) This does not satisfy the stated relationship.

D \(ac-bd\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Matrices · answered at 100 ms

03 Which response best completes this VCE-style item? The roots of \(z^n=1\) are equally spaced on the

A unit circle Their moduli are one and arguments differ by 2π/n.

B parabola This does not satisfy the stated relationship.

C real axis This does not satisfy the stated relationship.

D imaginary axis This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Complex roots · answered at 100 ms

04 A student is checking a worked solution. \(i^2=\)

A 0 This does not satisfy the stated relationship.

B 1 This does not satisfy the stated relationship.

C −1 This defines the imaginary unit.

D i This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Complex numbers · answered at 100 ms

05 A student is checking a worked solution. A connected graph with n vertices and n−1 edges is a

A tree This is a standard characterisation of a tree.

B complete graph This does not satisfy the stated relationship.

C cycle This does not satisfy the stated relationship.

D multigraph necessarily This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Graph theory · answered at 100 ms

06 A student is checking a worked solution. The standard deviation of the sample mean is

A \(\sigma\sqrt n\) This does not satisfy the stated relationship.

B \(\sigma/n\) This does not satisfy the stated relationship.

C \(n/\sigma\) This does not satisfy the stated relationship.

D \(\sigma/\sqrt n\) This is the standard error of the mean.

Written for icaijy.com · U3–4 · Sample means · answered at 100 ms

07 A student is checking a worked solution. The conjugate of \(3-2i\) is

A \(2+3i\) This does not satisfy the stated relationship.

B \(3-2i\) This does not satisfy the stated relationship.

C \(-3+2i\) This does not satisfy the stated relationship.

D \(3+2i\) Change the sign of the imaginary part.

Written for icaijy.com · U1–2 · Complex numbers · answered at 100 ms

08 Which response best completes this VCE-style item? The vector from A to B is

A \(\vec a+\vec b\) This does not satisfy the stated relationship.

B \(\vec b-\vec a\) Endpoint position minus start position.

C \(\vec a-\vec b\) This does not satisfy the stated relationship.

D \(\vec a\cdot\vec b\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Vectors · answered at 100 ms

09 The cross product \(\vec a\times\vec b\) is

A parallel to both vectors This does not satisfy the stated relationship.

B always zero This does not satisfy the stated relationship.

C a scalar This does not satisfy the stated relationship.

D perpendicular to both vectors Its direction follows the right-hand rule.

Written for icaijy.com · U3–4 · Vectors · answered at 100 ms

10 Which response best completes this VCE-style item? For \(dy/dx=f(x)g(y)\), separation gives

A \(dx/dy=f(x)g(y)\) This does not satisfy the stated relationship.

B \(g(y)dy=f(x)dx\) This does not satisfy the stated relationship.

C \(dy=f(x)+g(y)\) This does not satisfy the stated relationship.

D \(\frac{dy}{g(y)}=f(x)\,dx\) Move the y factor with dy and x factor with dx.

Written for icaijy.com · U3–4 · Differential equations · answered at 100 ms

11 During a one-minute revision round: The negation of “all integers are positive” is

A no integers exist This does not satisfy the stated relationship.

B at least one integer is positive This does not satisfy the stated relationship.

C all integers are not positive This does not satisfy the stated relationship.

D at least one integer is not positive Negating a universal statement produces an existential counterexample.

Written for icaijy.com · U1–2 · Logic · answered at 100 ms

12 Which response best completes this VCE-style item? The number of ways to choose r objects from n without order is

A \(n!\) This does not satisfy the stated relationship.

B \(\binom nr\) Combinations ignore order.

C \(n-r\) This does not satisfy the stated relationship.

D \(n^r\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Counting · answered at 100 ms

13 A student is checking a worked solution. A small p-value is evidence

A of zero sampling variation This does not satisfy the stated relationship.

B that the alternative has probability p This does not satisfy the stated relationship.

C that the null is certainly true This does not satisfy the stated relationship.

D against the null hypothesis It means the observed statistic is unusual under the null.

Written for icaijy.com · U3–4 · Hypothesis tests · answered at 100 ms

14 If \(a\mid b\) and \(a\mid c\), then

A \(a=b+c\) This does not satisfy the stated relationship.

B \(a\mid(b+c)\) Divisibility is preserved under integer linear combinations.

C \(bc\mid a\) This does not satisfy the stated relationship.

D \(b\mid a\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Number · answered at 100 ms

15 Which response best completes this VCE-style item? A small p-value is evidence

A that the null is certainly true This does not satisfy the stated relationship.

B that the alternative has probability p This does not satisfy the stated relationship.

C against the null hypothesis It means the observed statistic is unusual under the null.

D of zero sampling variation This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Hypothesis tests · answered at 100 ms

16 If position is \(\vec r(t)\), acceleration is

A \(|\vec r(t)|\) This does not satisfy the stated relationship.

B \(\vec r\prime(t)\) This does not satisfy the stated relationship.

C \(\int\vec r(t)dt\) This does not satisfy the stated relationship.

D \(\vec r\prime\prime(t)\) Acceleration is the second time derivative of position.

Written for icaijy.com · U3–4 · Kinematics · answered at 100 ms

17 The negation of “all integers are positive” is

A at least one integer is positive This does not satisfy the stated relationship.

B all integers are not positive This does not satisfy the stated relationship.

C no integers exist This does not satisfy the stated relationship.

D at least one integer is not positive Negating a universal statement produces an existential counterexample.

Written for icaijy.com · U1–2 · Logic · answered at 100 ms

18 Which response best completes this VCE-style item? The modulus of \(3+4i\) is

A 5 Use the Pythagorean theorem.

B 25 This does not satisfy the stated relationship.

C 1 This does not satisfy the stated relationship.

D 7 This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Complex plane · answered at 100 ms

19 For \(dy/dx=f(x)g(y)\), separation gives

A \(\frac{dy}{g(y)}=f(x)\,dx\) Move the y factor with dy and x factor with dx.

B \(g(y)dy=f(x)dx\) This does not satisfy the stated relationship.

C \(dy=f(x)+g(y)\) This does not satisfy the stated relationship.

D \(dx/dy=f(x)g(y)\) This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Differential equations · answered at 100 ms

20 A student is checking a worked solution. \(\int e^{ax}\,dx=\)

A \(ae^{ax}+C\) This does not satisfy the stated relationship.

B \(\frac1a e^{ax}+C\) Differentiate to verify the factor 1/a.

C \(e^{ax}+C\) This does not satisfy the stated relationship.

D \(\frac1x e^{ax}\) This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Integration · answered at 100 ms