1. 1
   A student is using a scientific calculator to evaluate a series of expressions during a mock exam revision session.

   (a)

   Use a calculator to evaluate $\sqrt[3]{2744}$.

   [1 mark]

   • A14
   • B44
   • C196
   • D9.06 (to 3 s.f.)

   (b)

   Use a calculator to evaluate $(2.4 \times 10^{5}) \times (3 \times 10^{-2})$, giving your answer in standard form.

   [1 mark]

   • A$0.72 \times 10^{3}$
   • B$7.2 \times 10^{7}$
   • C$7.2 \times 10^{3}$
   • D$7.2 \times 10^{-3}$

   (c)

   The student's calculator displays the result of a calculation as "1.44E13". What value does this represent, written in standard form?

   [1 mark]

   • A$1.44 \times 13$
   • B$1.44 \times 10^{-13}$
   • C$14.4 \times 10^{13}$
   • D$1.44 \times 10^{13}$

   Total for question 1: 3 marks

2. 2
   A plumber uses the formula $C = 45 + 12h$ to calculate the cost, in pounds, of a call-out lasting $h$ hours, entering values directly into a calculator.

   (a)

   Use a calculator to find the cost of a call-out lasting 3.5 hours.

   [2 marks]

   (b)

   For a different job, the plumber's calculator shows a total cost of £141. Use inverse operations to work out how many hours, $h$, the call-out lasted.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A scientist measures the mass of one bacterial sample as $3.6 \times 10^{-5}$ grams and needs to use her calculator to work with this value in standard form calculations, checking her answers by estimation.

   (a)

   Use a calculator to find the total mass, in grams, of 250 identical samples. Give your answer in standard form.

   [3 marks]

   (b)

   Show, by using estimation, that the answer to part (a) is reasonable.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   An engineer is using a calculator to work with trigonometric functions and standard form values while designing a support strut for a bridge.

   (a)

   An engineer is designing a support strut for a bridge. The strut makes an angle of $37°$ with a horizontal beam of length 12 m, and the strut is the hypotenuse of the right-angled triangle formed. Use a calculator to find the length of the strut, correct to 3 significant figures.

   [4 marks]

   (b)

   The force, in newtons, acting along a second strut is given by $F = \dfrac{2.4 \times 10^{6} \times \sin(52°)}{3 \times 10^{2}}$. Use a calculator to find the value of $F$, giving your answer in standard form correct to 2 significant figures.

   [4 marks]

   (c)

   A third strut forms a right-angled triangle with a vertical support of height 9 m and a horizontal beam of length 12 m. The engineer's calculator gives the angle between the strut and the horizontal beam as $36.87°$. Show, using estimation and an inverse trigonometric calculation, that this angle is correct to 2 decimal places.

   [5 marks]

   Total for question 4: 13 marks

End of questions