Straight-Line Graphs Structured Questions | Cambridge O Level Additional Mathematics

Question 1 of 4 · 11 marks

Straight-Line Graphs · 4 - Linear Law Experimental Data & Power Models

3 parts

Additional Mathematics 4037 · Question 1Paper 2 · Calculator[11 marks]

The variables $x$ and $y$ are believed to be connected by the non-linear relationship $y = a x^b$ , where $a$ and $b$ are constants.

(a)

Express this equation in linear form $Y = mX + c$ , clearly defining $Y, X, m,$ and $c$ in terms of $\lg y, \lg x, a,$ and $b$ .

[2]

(b)

An experiment yields a straight line when $\lg y$ is plotted against $\lg x$ . The line passes through the points $(0.301, 0.903)$ and $(0.903, 2.107)$ .

[6]

(i)

Calculate the gradient of the line, giving your answer correct to 2 decimal places, and deduce the value of $b$ .

[3]

(ii)

Calculate the value of constant $a$ , giving your answer to 3 significant figures.

[3]

(c)

Using your values of $a$ and $b$ , estimate the value of $y$ when $x = 5.0$ .

[3]