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

01 During a one-minute revision round: If position is \(\vec r(t)\), acceleration is

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

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

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

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

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

02 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

03 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

04 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 100 ms

05 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

06 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

07 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

08 A geometric sequence with ratio r has \(u_n=\)

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

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

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

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

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

09 A student is checking a worked solution. 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 \(g(y)dy=f(x)dx\) 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

10 The determinant of \(\begin{pmatrix}a&b\\c&d\end{pmatrix}\) is

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

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

C \(ad-bc\) Use ad−bc.

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

Written for icaijy.com · U1–2 · Matrices · 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 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 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

14 Which response best completes this VCE-style item? A square matrix is invertible exactly when its determinant is

A negative only This does not satisfy the stated relationship.

B zero This does not satisfy the stated relationship.

C non-zero A zero determinant means singular.

D one only This does not satisfy the stated relationship.

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

15 Which response best completes this VCE-style item? \(\int e^{ax}\,dx=\)

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

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

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

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

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

16 A connected graph with n vertices and n−1 edges is a

A complete graph This does not satisfy the stated relationship.

B tree This is a standard characterisation of a tree.

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

17 A vector equation of a line is

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

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

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

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 100 ms

18 \(\cos(A-B)=\)

A \(\cos A\cos B+\sin A\sin B\) Use the cosine difference identity.

B \(\cos A\cos B-\sin A\sin B\) This does not satisfy the stated relationship.

C \(\cos A-\cos B\) This does not satisfy the stated relationship.

D \(\sin A\cos B\) This does not satisfy the stated relationship.

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

19 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

20 A student is checking a worked solution. The roots of \(z^n=1\) are equally spaced on the

A parabola This does not satisfy the stated relationship.

B real axis This does not satisfy the stated relationship.

C imaginary axis This does not satisfy the stated relationship.

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

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