0580.C1.3.07 — Calculate with the following: other powers and roots of numbers.: past paper questions

Real questions on 0580.c1.3.07 — calculate with the following: other powers and roots of numbers.

The newest 20 of 30 written questions. Open one to see it on the real paper.

1. 0980/41 · October/November 2025 · Q19[3]
   The mass of a radioactive substance decays exponentially at a rate of $10\%$ per day. The initial mass of the substance is $20\text{ g}$. Find the number of whole days it takes for the mass of the substance to first be less than $1\text{ g}$.See it on the paper →
2. 0980/21 · October/November 2023 · Q8[1]
   8 Calculate. $7\frac{3}{11}\times 3\frac{3}{10}$See it on the paper →
3. 0980/21 · October/November 2023 · Q10c[2]
   10 Simplify. (c) $(243y^{20}{)}^{\frac{2}{5}}$See it on the paper →
4. 0980/31 · October/November 2023 · Q1d(i)[1]
   (d) Put one pair of brackets in each statement to make it correct. (i) $24-4\times 3+2=62$See it on the paper →
5. 0980/41 · October/November 2023 · Q3a(i)[1]
   (a) The table shows information about some of the planets in the solar system. | Planet | Diameter (km) | Average distance from the Sun (km) | | :--- | :--- | :--- | | Earth | 12 800 | $1.496\times 10^8$ | | Mars | 6 800 | $2.279\times 10^8$ | | Jupiter | 143 000 | $7.786\times 10^8$ | | Saturn | 120 500 | $1.434 \...See it on the paper →
6. 0980/41 · October/November 2023 · Q3a(v)[2]
   (a) The table shows information about some of the planets in the solar system. | Planet | Diameter (km) | Average distance from the Sun (km) | | :--- | :--- | :--- | | Earth | 12 800 | $1.496\times 10^8$ | | Mars | 6 800 | $2.279\times 10^8$ | | Jupiter | 143 000 | $7.786\times 10^8$ | | Saturn | 120 500 | $1.434 \...See it on the paper →
7. 0980/41 · October/November 2023 · Q3b(i)[2]
   (b) One light year is the distance that light travels in a year of 365.25 days. The speed of light is $2.9979\times 10^5$ kilometres per second. (i) Show that one light year is $9.461\times 10^{12}$ km, correct to 4 significant figures.See it on the paper →
8. 0980/41 · October/November 2023 · Q3b(ii)[2]
   (b) One light year is the distance that light travels in a year of 365.25 days. The speed of light is $2.9979\times 10^5$ kilometres per second. (ii) The distance from the Andromeda Galaxy to Earth is $2.40\times 10^{19}$ km. Calculate the time taken for light to travel from this galaxy to Earth. Give your answer in...See it on the paper →
9. 0980/41 · October/November 2022 · Q2a(iii)[1]
   (a) Write (iii) $2090$ correct to 2 significant figures.See it on the paper →
10. 0980/41 · October/November 2022 · Q2d[1]
    (d) Write $0.00701$ in standard form.See it on the paper →
11. 0980/41 · October/November 2022 · Q2e[2]
    (e) Simplify $1.5\times 10^x+1.5\times 10^{x-1}$ giving your answer in standard form.See it on the paper →
12. 0980/12 · May/June 2022 · Q13b[2]
    (b) Find the value of $6789^{\frac{1}{3}}$. Give your answer correct to 2 decimal places.See it on the paper →
13. 0980/12 · May/June 2022 · Q17[1]
    17 $9^x\times 9^2=9^{12}$ Find the value of $x$. $x=$See it on the paper →
14. 0980/42 · May/June 2022 · Q1c[2]
    (c) Work out $\frac{6.39\times 10^4}{2.45\times 10^6}$. Give your answer in standard form.See it on the paper →
15. 0980/31 · October/November 2021 · Q1d(ii)[1]
    (d) Write down (ii) the value of $14^0$.See it on the paper →
16. 0980/31 · October/November 2021 · Q1e(i)[1]
    (e) Calculate. (i) $5^4$See it on the paper →
17. 0980/22 · May/June 2021 · Q2[1]
    2 Calculate $\sqrt[4]{0.0256}$ .See it on the paper →
18. 0980/22 · May/June 2021 · Q8[2]
    8 $a=\frac{b^2}{5c}$ Find $b$ when $a=5.625$ and $c=2$.See it on the paper →
19. 0980/22 · May/June 2021 · Q9[3]
    9 **Without using a calculator**, work out $\frac{2}{3}÷1\frac{3}{7}$. You must show all your working and give your answer as a fraction in its simplest form.See it on the paper →
20. 0980/42 · May/June 2021 · Q3a(i)[1]
    (a) Simplify, giving your answer as a single power of 7. (i) $7^5\times 7^6$See it on the paper →

What examiners said

Putting a pair of correct brackets in each statement was well answered by the majority of candidates. Part (i) was slightly more successful than part (ii).

— Examiner report, October/November 2023, 0980/31 Q1(d)(i) (Cambridge)

The introduction of astronomical units (AU) was implemented well by many, but some candidates used diameters of planets instead of distances from the Sun. The direct method was to multiply the 5.20 AU by the distance from the Sun of Mars divided by the distance from the Sun of Jupiter and this method was seen from the stronger candidates. The other efficient method was to find the number of kilome...

— Examiner report, October/November 2023, 0980/41 Q3(a)(v) (Cambridge)

This was a ‘show that’ question and candidates are expected to show all the steps in a calculation. The conversion of years into seconds was frequently either simply stated as 31 557 600 or with the product 365.25 × 24 × 60 × 60 only partially shown. 3600 was accepted for 60 × 60 but 86 400 × 365.25 was often seen and was not sufficient. The other common error was to omit a value to more than four...

— Examiner report, October/November 2023, 0980/41 Q3(b)(i) (Cambridge)