IB Maths AA HL AA 2.1 Lines, functions and graphs questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

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Question 1

Paper 1, no calculatorMedium7 marks

The graph in Figure 1 shows the straight line $\ell$

(a)

Write down the $y$ -intercept of $\ell$ and determine its gradient.

[2]

(b)

The line $m$ is parallel to $\ell$ and passes through $P(2,1)$ Determine the equation of $m$ in the form $y=mx+c$

[2]

(c)

The line $n$ is perpendicular to $\ell$ and passes through the point where $m$ intersects the $y$ -axis. Determine the equation of $n$ in the form $Ax+By+C=0$ where $A,B,C$ are integers with no common factor and $A>0$

[3]

Question 2

Paper 1, no calculatorMedium6 marks

Two analysts model the annual demand for a service in a region. The models predict demand, in thousands of requests per year, $t$ years from now:

A(t)=8+e^{t/5},\qquad B(t)=6e^{t/10},\qquad t\geq 0.

The following values are given, rounded to two decimal places.

$t$ (years)	0	5	7	8	10	13	14	15
$A(t)$	9.00	10.72	12.06	12.95	15.39	21.46	24.44	28.09
$B(t)$	6.00	9.89	12.08	13.35	16.31	22.02	24.33	26.89

(a)

At $t=0$ state which analyst predicts the greater annual demand.

[1]

(b)

Sketch the two models on the same axes for $0\leq t\leq15$ Use your sketch to estimate, to the nearest year, when the forecasts agree.

[2]

(c)

Determine analytically the exact times at which the two forecasts agree. Give your answers in years.

[3]

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