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This file is useful for igcse edexcel maths olevel. it has exam questions about calculus and finding the maximum or minimum point of a graph
Typology: Exercises
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20 (a) Express 7 + 12 x โ 3 x^2 in the form a + b ( x + c ) 2 where a , b and c are integers.
................................................................................. (3)
C is the curve with equation y = 7 + 12 x โ 3 x^2 The point A is the maximum point on C
(b) Use your answer to part (a) to write down the coordinates of A
(Total for Question 20 is 4 marks)
1 )January 2022 1H # 20
23 (a) Express 2 x^2 โ 12 x + 3 in the form a ( x + b )^2 + c where a , b and c are integers.
....................................................... (3)
The curve C has equation y = 2( x + 4) 2 โ 12( x + 4) + 3
The point M is the minimum point on C
(b) Find the coordinates of M
(Total for Question 23 is 5 marks)
22 The diagram shows a sketch of part of the curve with equation y = x^2 โ p x
where p is a positive constant.
Diagram NOT accurately drawn
y
x
For all values of p , the curve has exactly one turning point and this turning point is a minimum shown as the point T in the sketch.
For the curve where the x coordinate of T is โ
(a) find the value of p
p = ....................................................... (4)
4 ) June 2022 1HR # 22
The line with equation y = k is a tangent to the curve with equation y = x^2 โ
x
(b) Find the value of k
k = ....................................................... (3)
(Total for Question 22 is 7 marks)
20 The curve with equation y 2 x^4 64 x has a minimum point.
Find an equation of the tangent to the curve at the minimum point. Show clear algebraic working.
................................................................
(Total for Question 20 is 4 marks)
19 ABCED is a five-sided shape.
Diagram NOT accurately drawn
A (^) x cm B
y cm
ABCD is a rectangle. CED is an equilateral triangle.
AB = x cm BC = y cm
The perimeter of ABCED is 100 cm. The area of ABCED is R cm^2
(a) Show that R = x x 4
7 ) November 2021 1H # 19
21 The curve C has equation y = f( x ) where f( x ) = 9 โ 3( x + 2)^2 The point A is the maximum point on C.
(a) Write down the coordinates of A.
The curve C is transformed to the curve S by a translation of
(b) Find an equation for the curve S.
.............................................................................................................. (1)
The curve C is transformed to the curve T. The curve T has equation y = 3( x + 2)^2 โ 9
(c) Describe fully the transformation that maps curve C onto curve T.
.............................................................................................................. (1)
8 ) November 2021 2H # 21
(2 x + 5) cm
( x + 1) cm
(3 โ x ) cm
Diagram NOT accurately drawn
The diagram shows a cuboid of volume V cm 3
(a) Show that V = 15 + 16 x โ x^2 โ 2 x^3
9 ) January 2020 1H # 15
20 The radius of a right circular cylinder is x cm.
The height of the cylinder is
x ฯ x
cm.
The volume of the cylinder is V cm^3
Find the maximum value of V Give your answer correct to the nearest whole number.
10 ) January 2023 1H
......................................................
(Total for Question 20 is 5 marks)
......................................................
(Total for Question 17 is 5 marks)
