iGCSE Mathematics (0580) : C2.4 Use and interpret positive, negative and zero indices. iGCSE Style Questions Paper 3

(a) Ans: 120,020

One hundred twenty thousand = 120,000
And twenty = 20
Combined: 120,000 + 20 = 120,020

(b) Ans: 59

59 × 59 = 3,481
Therefore, \( \sqrt{3481} = 59 \)

(c)(i) Ans: \( \frac{5}{8} \)

Total parts = 8
Shaded parts = 5
Fraction shaded = \( \frac{5}{8} \)

(c)(ii) Ans: 37.5%

Unshaded fraction = \( \frac{3}{8} \)
Percentage unshaded = \( \frac{3}{8} \times 100 = 37.5\% \)

(d) Ans: \( \frac{7}{29} \) < 0.268 < 27% < \( \frac{5}{17} \)

Convert all to decimals:
\( \frac{7}{29} \approx 0.241 \)
0.268
27% = 0.27
\( \frac{5}{17} \approx 0.294 \)

(e) Ans: 0.4

0.3728 rounded to 1 decimal place:
Look at second decimal (7) which ≥5, so round up:
0.4

(f) Ans: 1

Any non-zero number to the power of 0 equals 1:
\(19^\circ = 1\)

(g) Ans: 127.5 ≤ h < 128.5

When rounded to nearest meter (128m), the actual height h satisfies:
127.5m ≤ h < 128.5m

(h) Ans: 18

Prime factors:
126 = 2 × 3² × 7
180 = 2² × 3² × 5
Common factors: 2 × 3² = 18

(i) Ans: \( \sqrt{37} \) (or any other irrational between 6 and 7)

Since \( \sqrt{36} = 6 \) and \( \sqrt{49} = 7 \),
\( \sqrt{37} \approx 6.08276… \) is irrational and between 6 and 7