That y8 kid 🤣 - bot · guest · Mathematical Methods · Units 1 & 2

01 A student is checking a worked solution. A correlation coefficient near −1 indicates

A a horizontal residual plot only This does not satisfy the stated relationship.

B strong negative linear association Values near −1 show strong negative linear association.

C weak positive association This does not satisfy the stated relationship.

D causation This does not satisfy the stated relationship.

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

02 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 $(4,\infty)$ The logarithm argument must be positive.

D $\mathbb R$ This does not satisfy the stated relationship.

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

03 During a one-minute revision round: A CAS solves $x^3-4x=0$. The full solution set is

A $\{-4,0,4\}$ This does not satisfy the stated relationship.

B $\{0,4\}$ This does not satisfy the stated relationship.

C $\{-2,0,2\}$ Factor x(x−2)(x+2).

D $\{-2,2\}$ This does not satisfy the stated relationship.

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

04 A CAS solves $x^3-4x=0$. The full solution set is

A $\{-2,2\}$ This does not satisfy the stated relationship.

B $\{-4,0,4\}$ This does not satisfy the stated relationship.

C $\{0,4\}$ This does not satisfy the stated relationship.

D $\{-2,0,2\}$ Factor x(x−2)(x+2).

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

05 A student is checking a worked solution. 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 3700 Expected count = trials × probability.

C 10 000 This does not satisfy the stated relationship.

D 370 This does not satisfy the stated relationship.

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

06 Which response best completes this VCE-style item? A CAS returns a decimal root but the question requests an exact value. The best response is to

A use an exact solve command or algebraic form Exact form is required when requested.

B omit the root This does not satisfy the stated relationship.

C round to one decimal place This does not satisfy the stated relationship.

D change the equation This does not satisfy the stated relationship.

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

07 Which response best completes this VCE-style item? On $[0,2\pi]$, $\sin x=1/2$ at

A $5\pi/6,11\pi/6$ This does not satisfy the stated relationship.

B $\pi/6,5\pi/6$ Sine is positive in quadrants I and II.

C $\pi/6,7\pi/6$ This does not satisfy the stated relationship.

D $\pi/3,2\pi/3$ 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? A correlation coefficient near −1 indicates

A a horizontal residual plot only This does not satisfy the stated relationship.

B weak positive association This does not satisfy the stated relationship.

C causation This does not satisfy the stated relationship.

D strong negative linear association Values near −1 show strong negative linear association.

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

09 During a one-minute revision round: If $f(x)=x+2$ and $g(x)=x^2$, then $(g\circ f)(3)=$

A 11 This does not satisfy the stated relationship.

B 7 This does not satisfy the stated relationship.

C 25 f(3)=5, then g(5)=25.

D 13 This does not satisfy the stated relationship.

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

10 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 31 u10=4+9×3=31.

C 27 This does not satisfy the stated relationship.

D 34 This does not satisfy the stated relationship.

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

11 Which response best completes this VCE-style item? $1000 grows by 5% per year for 3 years. Its value is closest to

A $1157.63 $1000(1.05)^3=1157.625$.

B $1050.00 This does not satisfy the stated relationship.

C $1250.00 This does not satisfy the stated relationship.

D $1150.00 This does not satisfy the stated relationship.

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

12 Which response best completes this VCE-style item? A CAS solves $x^3-4x=0$. The full solution set is

A $\{0,4\}$ This does not satisfy the stated relationship.

B $\{-2,2\}$ This does not satisfy the stated relationship.

C $\{-2,0,2\}$ Factor x(x−2)(x+2).

D $\{-4,0,4\}$ This does not satisfy the stated relationship.

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

13 Which response best completes this VCE-style item? For $f(x)=x^2+1$, the tangent gradient at x=3 is

A 6 $f\prime(x)=2x$.

B 7 This does not satisfy the stated relationship.

C 3 This does not satisfy the stated relationship.

D 10 This does not satisfy the stated relationship.

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

14 For $f(x)=x^2+1$, the tangent gradient at x=3 is

A 7 This does not satisfy the stated relationship.

B 10 This does not satisfy the stated relationship.

C 3 This does not satisfy the stated relationship.

D 6 $f\prime(x)=2x$.

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

15 Solve $2^x=10$, correct to two decimal places.

A 5.00 This does not satisfy the stated relationship.

B 3.32 $x=\log_2 10\approx3.32$.

C 2.30 This does not satisfy the stated relationship.

D 10.00 This does not satisfy the stated relationship.

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

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

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

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

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

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

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

17 Which response best completes this VCE-style item? 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 · answered at 100 ms

18 During a one-minute revision round: A CAS returns a decimal root but the question requests an exact value. The best response is to

A round to one decimal place This does not satisfy the stated relationship.

B change the equation This does not satisfy the stated relationship.

C omit the root This does not satisfy the stated relationship.

D use an exact solve command or algebraic form Exact form is required when requested.

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

19 A student is checking a worked solution. An arithmetic sequence has $u_1=4$, common difference 3. Then $u_{10}=$

A 30 This does not satisfy the stated relationship.

B 31 u10=4+9×3=31.

C 34 This does not satisfy the stated relationship.

D 27 This does not satisfy the stated relationship.

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

20 During a one-minute revision round: For X taking 0,1,2 with probabilities 0.2,0.5,0.3, $E(X)=$

A 0.8 This does not satisfy the stated relationship.

B 1.5 This does not satisfy the stated relationship.

C 1.0 This does not satisfy the stated relationship.

D 1.1 0×0.2+1×0.5+2×0.3=1.1.

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