4MA0 Higher January 2012 Paper 3 Q8
8 A bag contains 60 beads.
\(x\) of the beads are red and the rest are green.
Altaaf takes at random a bead from the bag.
(a) State, in terms of \(x\), the probability that Altaaf takes a red bead. (1)
Altaaf puts his bead back in the bag.
Another 20 red beads are added to those in the bag.
The probability that Altaaf takes a red bead is now doubled.
(b)
(i) Use this information to write down an equation in \(x\) and show that your equation can be expressed as \(8x = 3(x + 20)\)
(ii) Solve \(8x = 3(x + 20)\)
Show your working clearly.
(5)Show your working clearly.
| Scheme | Marks |
|---|---|
| \(x/60\) oe | B1 |
| (1) |
Notes
B1: Must be a fraction or \(0.01\dot{6}x\)
| Scheme | Marks |
|---|---|
| (i) \(2(\text{“}x/60\text{”}) = (x+20)/80\) | M2 |
| \(16(0)x = 6(0)(x + 20)\) or \(80x = 30(x + 20)\) or \(2x/3 = (x + 20)/4\) | A1 dep |
| (ii) \(8x = 3x + 60\) or \(5x = 60\) or 60÷ 5 | M1 |
| 12 | A1 |
| (5) | |
| (Total 6 marks) |
Notes
M2: ( must be an equation) M1 for either \(2(\text{“}x/60\text{”})\) or \((x+20)/80\)
A1 dep: Correct removal of denominators.
Correct removal of denominators.
Simplifying denominators.
A1: Dependent on M1. Can be marked if seen in b(i)