Paper 2 Section B Practice

Linear Law • 10-Mark Mastery

SPM Paper 2 Section B Specialty

Form 4 Chapter 6: Linear Law (Hukum Linear)

Total Marks: 40 Marks • Time Allowed: 50 Minutes

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A Bahagian A: Non-Linear Reductions [10 Marks]

Answer all questions
Soalan 1 [5 Marks]

Variables $x$ and $y$ are related by the equation $y = \frac{a}{x^2} + b\sqrt{x}$.

(a) By expressing the equation in the linear form $Y = mX + c$, identify $Y, X, m,$ and $c$ such that a straight line can be drawn. [3 marks]

(b) If the straight line passes through $(4, 11)$ and has a $Y$-intercept of $3$, calculate the values of $a$ and $b$. [2 marks]

Soalan 2 [5 Marks]

Diagram below shows a straight line obtained by plotting $\log_{10} y$ against $x$.

(0, 0.6) (4, 1.8) x $\log_{10} y$

The straight line passes through $(0, 0.6)$ and $(4, 1.8)$.

(a) Express $y$ in terms of $x$ in the form $y = ab^x$. [3 marks]

(b) Calculate the value of $y$ when $x = 5$. [2 marks]

B Bahagian B: SPM Paper 2 Section B Full Blueprint [20 Marks]

Answer both 10-mark questions
Soalan 3 (Paper 2 Section B Model) [10 Marks]
Table below shows the values of two variables, $x$ and $y$, obtained from an experiment. The variables are related by the non-linear equation $y = \frac{a}{x} + bx$, where $a$ and $b$ are constants.
x 1.5 2.0 3.0 4.0 5.0 6.0
y 7.83 6.50 5.67 5.75 6.20 6.83

(a) Plot $xy$ against $x^2$, using a scale of $2\text{ cm to } 5\text{ units}$ on the $x^2$-axis and $2\text{ cm to } 5\text{ units}$ on the $xy$-axis. Hence, draw the line of best fit. [5 marks]

(b) Using the graph in (a), find:

(i) The value of $a$ and the value of $b$. [3 marks]

(ii) The value of $y$ when $x = 3.5$. [2 marks]

Soalan 4 (KBAT Newton's Law of Cooling & Outlier Detection) [10 Marks]
A physics laboratory investigation records the excess temperature $\theta$ (°C) of a chemical liquid cooling down over time $t$ (minutes). The cooling process is governed by the law $\theta = \theta_0 e^{-kt}$, which reduces to $\ln \theta = -kt + \ln \theta_0$. Table below shows the experimental recorded data:
t (min) 2 4 6 8 10
θ (°C) 58.0 42.5 40.0 22.8 16.7

(a) Plot $\ln \theta$ against $t$, using a scale of $2\text{ cm to } 2\text{ minutes}$ on the $t$-axis and $2\text{ cm to } 0.5\text{ units}$ on the $\ln \theta$-axis. Hence, draw the line of best fit. [5 marks]

(b) One of the recorded values of $\theta$ is inaccurate due to an erroneous thermocouple reading. State the incorrect temperature reading and deduce its correct value from your graph. [2 marks]

(c) From your graph, determine:

(i) The initial excess temperature $\theta_0$. [2 marks]

(ii) The cooling constant $k$. [1 mark]