1. 1
   A student is using a scientific calculator to carry out multi-step calculations for a science project involving measurements and statistics.

   (a)

   Using a calculator, evaluate $\sqrt{7.29}$.

   [1 mark]

   • A$2.7$
   • B$3.645$
   • C$1.35$
   • D$14.58$

   (b)

   Using a calculator, evaluate $\frac{15.6 + 4.8^2}{3}$, giving your answer to 2 decimal places.

   [1 mark]

   • A$16.72$
   • B$12.88$
   • C$21.28$
   • D$7.68$

   (c)

   A calculator displays the result of a division as $3.6666666...$. Rounded to 3 significant figures, what should the student write down?

   [1 mark]

   • A$3.7$
   • B$3.66$
   • C$3.667$
   • D$3.67$

   Total for question 1: 3 marks

2. 2
   A student uses a calculator to process a formula from a physics experiment, taking care with the order of operations and rounding at the end rather than during working.

   (a)

   Using a calculator, evaluate $\dfrac{8.4^2 - 3.6}{\sqrt{25}}$, showing the order in which you use the calculator keys and giving your final answer to 2 decimal places.

   [2 marks]

   (b)

   The student's calculator displays an intermediate value of $13.392$ before rounding. Explain why it is important to use the full calculator display value (not the rounded value from part (a)) if further calculations are needed, using an example.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A physics student is using a scientific calculator to evaluate the period of a pendulum using a formula involving square roots and pi, then checking their calculator's memory function is used correctly.

   (a)

   A scientist uses a calculator to evaluate the formula $T = 2\pi\sqrt{\dfrac{l}{g}}$ where $l = 2.5$ metres and $g = 9.8\ \text{m/s}^2$. Calculate $T$, giving your answer to 3 significant figures.

   [3 marks]

   (b)

   The scientist stores the value of $T$ from part (a) in the calculator's memory, then needs to calculate $5T^2$ using the full unrounded value. Explain the correct calculator process to do this without re-typing $T$, and calculate $5T^2$ to 3 significant figures using $T = 3.1735$ (unrounded).

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A student is using a calculator's trigonometric functions and checking that the calculator mode (degrees or radians) is set correctly before using it in a multi-step problem involving compound interest and roots.

   (a)

   A student uses a calculator to evaluate $\dfrac{\sin(38^\circ) \times 12.4}{\cos(52^\circ)}$. Calculate this value, giving your answer to 3 significant figures, and state whether your calculator is in degree mode or radian mode by checking that $\sin(38^\circ) \approx 0.6157$.

   [4 marks]

   (b)

   The student then uses the calculator to work out the value of an investment: $A = 4500\left(1+\dfrac{3.8}{100}\right)^7$. Calculate $A$, giving your answer to the nearest cent, showing the correct order of calculator operations (brackets, then power, then multiplication).

   [4 marks]

   (c)

   The student wants to check part (b)'s answer using estimation. Round each value in $A = 4500\left(1+\dfrac{3.8}{100}\right)^7$ sensibly (e.g. $1.038 \to 1.04$, and keep the power as $7$) to estimate $A$ to 1 significant figure, and comment on whether this estimate supports the calculator answer from part (b).

   [5 marks]

   Total for question 4: 13 marks

End of questions