admin · Mathematical Methods · Units 3 & 4

01 During a one-minute revision round: The area between \(y=x\) and the x-axis from 0 to 4 is

A 4 This does not satisfy the stated relationship.

B 8 \(\int_0^4x\,dx=8\).

C 32 This does not satisfy the stated relationship.

D 16 This does not satisfy the stated relationship.

Written for icaijy.com · U3–4 · Area · answered at 15264 ms

02 During a one-minute revision round: A simulation estimates a probability as 0.37 from 10 000 trials. The expected count is

A 9630 This does not satisfy the stated relationship.

B 370 This does not satisfy the stated relationship.

C 3700 Expected count = trials × probability.

D 10 000 This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Probability simulation · answered at 24481 ms

03 For \(f(x)=\log(x-4)\), the domain is

A \([4,\infty)\) This does not satisfy the stated relationship.

B \(({-\infty},4)\) This does not satisfy the stated relationship.

C \(\mathbb R\) This does not satisfy the stated relationship.

D \((4,\infty)\) The logarithm argument must be positive.

Written for icaijy.com · U1–2 · Domain restrictions · answered at 30585 ms

04 A student is checking a worked solution. A residual is defined as

A observed value minus predicted value Residual = y−ŷ.

B observed times predicted This does not satisfy the stated relationship.

C predicted minus observed only This does not satisfy the stated relationship.

D gradient minus intercept This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Modelling · answered at 42441 ms

05 Which response best completes this VCE-style item? An arithmetic sequence has \(u_1=4\), common difference 3. Then \(u_{10}=\)

A 30 This does not satisfy the stated relationship.

B 27 This does not satisfy the stated relationship.

C 31 u10=4+9×3=31.

D 34 This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Sequences · answered at 51264 ms

06 During a one-minute revision round: In a sample, 40 of 100 students play sport and 10 play sport and music. \(P(\text{music}\mid\text{sport})=\)

A 0.50 This does not satisfy the stated relationship.

B 0.40 This does not satisfy the stated relationship.

C 0.25 10 of the 40 sport players also play music.

D 0.10 This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Two-way tables · not answered before time expired