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 29 written questions. Open one to see it on the real paper.

1. 0580/13 · May/June 2026 · Q18a[1]
   18 (a) Write down the value of $\sqrt[3]{27}$.See it on the paper →
2. 0580/02 · Specimen 2025 · Q1[1]

   1-mark question — its maths and diagrams are best seen on the paper.

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3. 0580/02 · Specimen 2025 · Q11[2]

   2-mark “Find” question — its maths and diagrams are best seen on the paper.

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4. 0580/02 · Specimen 2025 · Q12a[2]

   2-mark question — its maths and diagrams are best seen on the paper.

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5. 0580/02 · Specimen 2025 · Q12b[2]

   2-mark question — its maths and diagrams are best seen on the paper.

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6. 0580/11 · October/November 2025 · Q23a[1]
   $a^8\times a^x=a^{15}$ Find the value of $x$. $x=$See it on the paper →
7. 0580/11 · October/November 2025 · Q23b[1]
   (b) $(b^7{)}^y=b^{21}$ Find the value of $y$.See it on the paper →
8. 0580/22 · October/November 2025 · Q18[3]
   18 Rationalise the denominator and simplify. $\frac{20}{4+\sqrt{6}}$See it on the paper →
9. 0580/23 · October/November 2025 · Q12a[1]
   12 (a) Write down the value of $73^0$.See it on the paper →
10. 0580/23 · October/November 2025 · Q12b[2]
    (b) Find the value of $\frac{7}{3^{-2}}$.See it on the paper →
11. 0580/23 · October/November 2025 · Q12c[2]
    (c) Write $27\times 81^2$ in the form $3^n$.See it on the paper →
12. 0580/43 · October/November 2025 · Q3[1]
    3 $G=\frac{4}{5}{m}^{2}n$ Find the value of $G$ when $m=6$ and $n=15.$See it on the paper →
13. 0580/43 · October/November 2025 · Q6a[1]
    6 Simplify. (a) $\frac{y^5}{y^2}$See it on the paper →
14. 0580/43 · October/November 2025 · Q6b[2]
    6 Simplify. (b) $3x^3\times 5x^5$See it on the paper →
15. 0580/43 · October/November 2025 · Q9[1]

    1-mark “Draw” question — its maths and diagrams are best seen on the paper.

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16. 0580/43 · October/November 2025 · Q13[3]
    13 The point $(5,1024)$ lies on the curve $y=c^x$, where $c$ is a whole number. Find the $y$-coordinate of the point on the curve with $x$-coordinate $-2$.See it on the paper →
17. 0580/13 · May/June 2025 · Q3b[1]
    (b) Work out the value of $2^4$.See it on the paper →
18. 0580/13 · May/June 2025 · Q5b[1]
    5 Find the next term in each sequence. (b) 1, 2, 4, 8, 16, ...See it on the paper →
19. 0580/11 · May/June 2024 · Q20a[1]
    20 (a) Find the value of $137^0$.See it on the paper →
20. 0580/11 · May/June 2024 · Q21[2]

    2-mark “Calculate” question — its maths and diagrams are best seen on the paper.

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What examiners said

A large majority were correct here. Some gave their answer as 137 or 0.

— Examiner report, May/June 2024, 0580/11 Q20(a) (Cambridge)

Many candidates gave as the answer, 203, the value on the calculator display. This needs to be manually turned into a standard form number. Often this second stage was not attempted. Of those that did try to change the form, some had more than one figure before the decimal point. There was a mark for converting their wrong answer to standard form correctly, but this mark was very rarely given as c...

— Examiner report, May/June 2024, 0580/11 Q21 (Cambridge)

This question caused difficulty for many candidates. Either candidates did not read the question carefully enough or they were unsure how to express numbers to one significant figure. Many opted to round the figures to the nearest integer or to one decimal place. Other candidates put the numbers in their calculators as written in the question, then rounded the displayed value to 1sf. Candidates sh...

— Examiner report, October/November 2023, 0580/11 Q18 (Cambridge)