Composite Functions
You're viewing free preview questions — 4 questions previewing here — subscribe to unlock 218 more, plus the Full Question Bank, Mock Papers & Worksheets.Upgrade

Composite Functions — Free MYP5 Mathematics (Extended) Practice Questions

1Questionf(g(x)) conceptConcept Practice
2 marks~3 minCriterion A
A construction team is installing a ramp for accessibility compliance. The ramp forms a right triangle: the horizontal base measures (x+1)(x + 1) m and the vertical rise measures 2x2x m, where x=2x = 2.

Building regulations require that the ramp angle θ\theta (opposite the vertical rise) must not exceed 55°55° to be approved.
a
Calculate the value of θ\theta. [1]
b
Advise the construction team whether the ramp should be approved, justifying your answer using your result from part (a). [1]
Question diagram

Solutions

2QuestionInterpret compositeAssessment Practice
2 marks~3 minCriterion D
A toy factory models the painting cost CC (in dollars) of a car as a function of its surface area AA (in cm²), and the surface area as a function of a single dimension dd (in cm), such that A(d)=6d2A(d) = 6d^2 and C(A)=0.05AC(A) = 0.05A.
a
Explain how the composite function C(A(d))C(A(d)) models the total painting cost in terms of dimension dd, showing the chain of dependence d→A→Cd \rightarrow A \rightarrow C. [1]
b
Interpret what a doubling of dimension dd means for the painting cost, and justify whether this composite model is sufficient for a factory manager to use when pricing larger car models. [1]
Question diagram

Solutions

3QuestionEvaluate compositeConcept Practice
2 marks~3 minCriterion C
A delivery company charges a handling fee then applies a distance multiplier. The handling fee function is f(x)=x+2f(x) = x + 2 and the distance multiplier is g(x)=3xg(x) = 3x, where xx is the base cost in dollars.
a
Calculate f(g(x))f(g(x)) and g(f(x))g(f(x)) for x=1,2,3,4x = 1, 2, 3, 4. [1]
b
A customer claims the order of operations does not affect the final charge. Justify whether this claim is correct, using your results from part (a). [1]

Solutions

4QuestionEvaluate compositeAssessment Practice
8 marks~12 minCriterion B
A computer simulation models the spread of a notification through a network. At each step, every active node activates exactly one new node and remains active. The number of active nodes at step nn is modelled by f(x)=2x+1f(x) = 2x + 1, applied repeatedly from x1=1x_1 = 1. The sequence is defined by xk+1=f(xk)x_{k+1} = f(x_k) for all positive integers kk.
a
Calculate the first five terms of the sequence. [2]
b
Deduce a formula for xnx_n in terms of nn, showing clearly how the pattern in part (a) leads to your general expression. [2]
c
Prove by mathematical induction that your formula holds for all positive integers nn. [2]
d
The network has a capacity of 1000 active nodes. Using your formula, advise the network administrator at which step they should intervene to prevent the capacity being exceeded, justifying your answer with reference to the simulation. [2]

Solutions

Questions 5-222

Unlock these questions with Premium

Sign Up →

That's every free question here — 4 of 222.

+218 more questions, plus Mock Papers & Worksheets, are waiting in Premium.

Upgrade