Past Paper Example 1
AQA Jun 2022 3H Q19
5 marks
Here is the plan of the floor of an L-shaped room.
All lengths are in metres.
All lengths are in metres.
(a) The area of the floor is 75 m2
Show that x2 + x - 90 = 0 [3 marks]
Show that x2 + x - 90 = 0 [3 marks]
(b) By factorising x2 + x - 90 work out the value of x.
You must show your working [2 marks]
You must show your working [2 marks]
Worked Solution & Mark Scheme (5 marks)
Part (a) Solution:
Split the L-shape horizontally into two rectangles: M1
- Bottom rectangle: width x, height x - 2
Area1 = x(x - 2) = x2 - 2x
- Top rectangle: width x - 5, height 3
Area2 = 3(x - 5) = 3x - 15 M1
Total area:
Total Area = x2 - 2x + 3x - 15 = x2 + x - 15
Equate to 75 m2:
x2 + x - 15 = 75 ⇒ x2 + x - 90 = 0 C1
- Bottom rectangle: width x, height x - 2
Area1 = x(x - 2) = x2 - 2x
- Top rectangle: width x - 5, height 3
Area2 = 3(x - 5) = 3x - 15 M1
Total area:
Total Area = x2 - 2x + 3x - 15 = x2 + x - 15
Equate to 75 m2:
x2 + x - 15 = 75 ⇒ x2 + x - 90 = 0 C1
Answer (a): Area = x(x - 2) + 3(x - 5) = x² + x - 15 = 75 => x² + x - 90 = 0
Part (b) Solution:
Find two numbers that multiply to -90 and add to +1: +10 and -9. M1
(x + 10)(x - 9) = 0
x = -10 \quador x = 9
Since length must be positive (x - 5 > 0), x = 9. A1
(x + 10)(x - 9) = 0
x = -10 \quador x = 9
Since length must be positive (x - 5 > 0), x = 9. A1
Answer (b): x = 9