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