elephant · guest · Specialist Mathematics · Units 3 & 4

01 For a particle in equilibrium, the vector sum of forces is

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

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

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

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

Written for icaijy.com · U3–4 · Mechanics · answered at 2502 ms

02 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 7159 ms

03 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 9977 ms

04 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 14466 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 18467 ms

06 During a one-minute revision round: A vector equation of a line is

A \(\vec r=\vec a+\lambda\vec d\) A point plus a scalar multiple of a direction defines the line.

B \(\vec r=\lambda\) This does not satisfy the stated relationship.

C \(\vec r=\vec a\times\vec d\) This does not satisfy the stated relationship.

D \(\vec r=\vec a\cdot\vec d\) This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Vector lines · answered at 25271 ms

07 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 31414 ms

08 A student is checking a worked solution. The scalar projection of a onto non-zero b is

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

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

C \(\frac{\vec a\cdot\vec b}{|\vec b|}\) Divide the dot product by the magnitude of b.

D \(\frac{|\vec b|}{|\vec a|}\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Geometry · answered at 35633 ms

09 Which response best completes this VCE-style item? If position is \(\vec r(t)\), acceleration is

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

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

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

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

Written for icaijy.com · U3–4 · Kinematics · answered at 42167 ms

10 During a one-minute revision round: A connected graph with n vertices and n−1 edges is a

A cycle This does not satisfy the stated relationship.

B multigraph necessarily This does not satisfy the stated relationship.

C complete graph This does not satisfy the stated relationship.

D tree This is a standard characterisation of a tree.

Written for icaijy.com · U1–2 · Graph theory · answered at 45480 ms

11 Which response best completes this VCE-style item? Two non-zero vectors are perpendicular when their dot product is

A 0 The dot product includes cos 90° = 0.

B −1 always This does not satisfy the stated relationship.

C their magnitude product This does not satisfy the stated relationship.

D 1 This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Vectors · answered at 49111 ms

12 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 57780 ms

13 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 59701 ms