EFSMaths
|EFSMaths |Forming Equations (Application) |
| |Grade B-A* |
| |Algebra is usually used to write |
| |equations so that we can solve |
| |them for a particular variable |
Solving Problems with Quadratics
(Forming Equations, Substitution, Operations with –ve numbers )
Grade B
Grade A
Grade A*
[pic]
The area of the shape is 25 cm2.
a) Show that 6x2 + 17x – 39 = 0
b) Calculate the length of the shortest side
GCSE A* Q1
The diagram shows a 6-sided shape.
All the corners are right angles.
All the measurements are given in centimetres.
[pic]
Diagram NOT
accurately drawn
The area of the shape is 85 cm2.
(a) Show that 9x2 – 17x – 85 = 0
(3)
(b) (i) Solve 9x2 – 17x – 85 = 0
Give your solutions correct to 3 significant figures.
x = ........... or x = ...................
(ii) Hence, work out the length of the shortest side of the 6-sided shape.
................................. cm
(4)
(Total 7 marks)
GCSE A* Q2
[pic]
The diagram shows a trapezium.
The lengths of three of the sides of the trapezium are x – 5, x + 2 and x + 6.
All measurements are given in centimetres.
The area of the trapezium is 36 cm2.
(a) Show that x2 – x – 56 = 0
(4)
(b) Solve the equation x2 – x – 56 = 0
…………………
Hence find the length of the shortest side of the trapezium.
…………………… cm
(4)
(Total 8 marks)
GCSE A* Q3
[pic]
The diagram shows a trapezium. The area of the trapezium is 400 cm2.
(a) Show that x2 + 20x = 400
(2)
(b) Find the value of x.
Give your answer correct to 3 decimal places.
.....................................
(3)
(Total 5 marks)
-----------------------
2x
3x
Area = 150 cm2
x + 5
Area = 26 cm2
x + 3
................
................
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