Back to speedrun
RUN REVIEW · Specialist Mathematics · Units 3 & 4 · Tech-free

That y8 kid 🤣 - bot · guest

11 Sep 2026, 9:23 p.m.

20Serious score
01 Which response best completes this VCE-style item? 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

02 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 100 ms

03 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

04 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 100 ms

05 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

06 During a one-minute revision round: The vector from A to B is
A \(\vec b-\vec a\) Endpoint position minus start position.
B \(\vec a-\vec b\) This does not satisfy the stated relationship.
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

07 Which response best completes this VCE-style item? \(\cos(A-B)=\)
A \(\cos A-\cos B\) This does not satisfy the stated relationship.
B \(\cos A\cos B+\sin A\sin B\) Use the cosine difference identity.
C \(\cos A\cos B-\sin A\sin B\) 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

08 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

09 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

10 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

11 Which response best completes this VCE-style item? The standard deviation of the sample mean is
A \(n/\sigma\) This does not satisfy the stated relationship.
B \(\sigma/n\) This does not satisfy the stated relationship.
C \(\sigma\sqrt n\) 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

12 The scalar projection of a onto non-zero b is
A \(\frac{|\vec b|}{|\vec a|}\) This does not satisfy the stated relationship.
B \(\frac{\vec a\cdot\vec b}{|\vec b|}\) Divide the dot product by the magnitude of b.
C \(|\vec a||\vec b|\) This does not satisfy the stated relationship.
D \(\vec a\times\vec b\) This does not satisfy the stated relationship.

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

13 During a one-minute revision round: \(i^2=\)
A i This does not satisfy the stated relationship.
B 0 This does not satisfy the stated relationship.
C 1 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

14 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 100 ms

15 A student is checking a worked solution. The sum of degrees in an undirected graph equals
A twice the number of edges Each edge contributes two degree incidences.
B the number of vertices This does not satisfy the stated relationship.
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

16 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

17 A student is checking a worked solution. The vector from A to B is
A \(\vec a\cdot\vec b\) 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 \(\vec a+\vec b\) This does not satisfy the stated relationship.

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

18 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

19 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

20 During a one-minute revision round: A small p-value is evidence
A that the alternative has probability p This does not satisfy the stated relationship.
B that the null is certainly true This does not satisfy the stated relationship.
C of zero sampling variation 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

Run it again