4400 Higher June 2008 Paper 4 Q20
20
(a) Evaluate \(5 \times 10^{12} + 9 \times 10^{12}\)
Give your answer in standard form. (2)
Give your answer in standard form. (2)
(b) Each of the numbers \(p\), \(q\) and \(r\) is greater than 1 and less than 10
\(p \times 10^{15} + q \times 10^{15} = r \times 10^n\)
\(p + q \gt 10\)
\(p \times 10^{15} + q \times 10^{15} = r \times 10^n\)
\(p + q \gt 10\)
(i) Find the value of \(n\).
(ii) Find an expression for \(r\) in terms of \(p\) and \(q\).
(3)| Scheme | Marks |
|---|---|
| \(14 \times 10^{12}\) oe | M1 |
| \(1.4 \times 10^{13}\) | A1 |
| (2) |
Notes
M1: or 1.4e13
| Scheme | Marks |
|---|---|
| (i) Answer: 16 | B1 |
| (ii) \((p + q) \times 10^{15} = r \times 10^n\) | M1 |
| \((p + q)/10\) oe | A1 |
| (3) | |
| (5 marks) |
Notes
B1: cao
M1: may be seen in (i)
A1: \(0.1(p + q)\), \((p + q) \times 10^{-1}\), \(\dfrac{p \times 10^{15} + q \times 10^{15}}{10^{16}}\)