iGCSE Mathematics (0580) :E1.1 Identify and use natural numbers.iGCSE Style Questions Paper 4

(a)(i) $2 \times 5 \times 7$

Break down 70 into prime numbers: 70 ÷ 2 = 35, 35 ÷ 5 = 7, and 7 is prime.

(a)(ii) 14

Prime factors of 112 are $2^4 \times 7$. HCF is the product of common prime factors with lowest powers: $2 \times 7$.

(a)(iii) $560x^4y^5$

Take highest powers of all prime factors and variables from both numbers: $2^4 \times 5 \times 7 \times x^4 \times y^5$.

(b)(i) $a^8$

Subtract exponents when dividing: $a^{12-4} = a^8$.

(b)(ii) $\frac{c}{8}$

Multiply numerators and denominators: $\frac{5bc}{40b} = \frac{c}{8}$ after simplifying.

(c) $x = 5.5$

Subtract 4 from both sides: $2x = 11$. Then divide by 2: $x = 5.5$.

(d) $x = -2$

Multiply both sides by 5: $34 + 2x = 20 – 5x$. Collect like terms: $7x = -14$, so $x = -2$.

(e)(i) 11

Substitute values: $P = 7 + \sqrt[3]{(-8)^2} = 7 + \sqrt[3]{64} = 7 + 4 = 11$.

(e)(ii) $m = \pm \sqrt{(P – d)^3}$

Subtract d: $P – d = \sqrt[3]{m^2}$. Cube both sides: $(P – d)^3 = m^2$. Take square root.