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

01 A student is checking a worked solution. A geometric sequence with ratio r has \(u_n=\)

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

B \(u_1+(n-1)r\) This does not satisfy the stated relationship.

C \(u_1r^n\) This does not satisfy the stated relationship.

D \(u_1r^{n-1}\) There are n−1 ratio multiplications from the first term.

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

02 The standard deviation of the sample mean is

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

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

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

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

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

03 Which response best completes this VCE-style item? For a particle in equilibrium, the vector sum of forces is

A \(m\vec v\) This does not satisfy the stated relationship.

B \(m\vec g\) always This does not satisfy the stated relationship.

C \(\vec0\) Zero net force is the equilibrium condition.

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

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

04 A student is checking a worked solution. A square matrix is invertible exactly when its determinant is

A non-zero A zero determinant means singular.

B one only This does not satisfy the stated relationship.

C negative only This does not satisfy the stated relationship.

D zero This does not satisfy the stated relationship.

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

05 A student is checking a worked solution. If \(a\mid b\) and \(a\mid c\), then

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

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

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

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

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

06 Which response best completes this VCE-style item? The cross product \(\vec a\times\vec b\) is

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

B a scalar This does not satisfy the stated relationship.

C always zero This does not satisfy the stated relationship.

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

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

07 A student is checking a worked solution. The cross product \(\vec a\times\vec b\) is

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

B a scalar This does not satisfy the stated relationship.

C always zero This does not satisfy the stated relationship.

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

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

08 A student is checking a worked solution. For independent random variables X and Y, \(\mathrm{Var}(X+Y)=\)

A \(\mathrm{Var}(X)\mathrm{Var}(Y)\) This does not satisfy the stated relationship.

B \(\mathrm{Var}(X)-\mathrm{Var}(Y)\) This does not satisfy the stated relationship.

C \(\mathrm{Var}(X)+\mathrm{Var}(Y)\) Covariance is zero under independence.

D \(0\) This does not satisfy the stated relationship.

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

09 During a one-minute revision round: For \(dy/dx=f(x)g(y)\), separation gives

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

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

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

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

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

10 Which response best completes this VCE-style item? \(i^2=\)

A 1 This does not satisfy the stated relationship.

B i This does not satisfy the stated relationship.

C 0 This does not satisfy the stated relationship.

D −1 This defines the imaginary unit.

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

11 Which response best completes this VCE-style item? 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

12 During a one-minute revision round: The sum of degrees in an undirected graph equals

A the number of vertices This does not satisfy the stated relationship.

B twice the number of edges Each edge contributes two degree incidences.

C twice the number of vertices This does not satisfy the stated relationship.

D the number of edges This does not satisfy the stated relationship.

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

13 During a one-minute revision round: A square matrix is invertible exactly when its determinant is

A non-zero A zero determinant means singular.

B negative only This does not satisfy the stated relationship.

C one only This does not satisfy the stated relationship.

D zero This does not satisfy the stated relationship.

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

14 During a one-minute revision round: A proof by contradiction begins by assuming

A a numerical example This does not satisfy the stated relationship.

B the conclusion itself This does not satisfy the stated relationship.

C every lemma is false This does not satisfy the stated relationship.

D the negation of the desired conclusion A contradiction disproves the negation.

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

15 Which response best completes this VCE-style item? For independent random variables X and Y, \(\mathrm{Var}(X+Y)=\)

A \(0\) This does not satisfy the stated relationship.

B \(\mathrm{Var}(X)\mathrm{Var}(Y)\) This does not satisfy the stated relationship.

C \(\mathrm{Var}(X)-\mathrm{Var}(Y)\) This does not satisfy the stated relationship.

D \(\mathrm{Var}(X)+\mathrm{Var}(Y)\) Covariance is zero under independence.

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

16 A student is checking a worked solution. The negation of “all integers are positive” is

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

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

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

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

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

17 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

18 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

19 The sum of degrees in an undirected graph equals

A the number of edges This does not satisfy the stated relationship.

B twice the number of edges Each edge contributes two degree incidences.

C the number of vertices This does not satisfy the stated relationship.

D twice the number of vertices This does not satisfy the stated relationship.

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

20 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