quadratic equations: completing the square · 2020. 10. 13. · solving equations &...
TRANSCRIPT
Quadratic Equations: Completing the square
Question Paper 1
20 minutes
/17
/100
Time Allowed:
Score:
Percentage:
1
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9 8 7 6 5 4 3
>84% 71% 58% 45% 33% 21% 0%
Grade Boundaries:
U
<15%
Level GCSE
Subject Mathematics
Topic Solving Equations & Inequalities
Sub-Topic Quadratic Equations: Completing the Square
Booklet Question Paper 1
The expression x2 – 8x + 21 can be written in the form (x – a)2 + b for all values of x.
(a) Find the value of a and the value of b.
a = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
b = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
The equation of a curve is y = f(x) where f(x) = x2 – 8x + 21
The diagram shows part of a sketch of the graph of y = f(x).
The minimum point of the curve is M.
(b) Write down the coordinates of M.
(. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .)
(1)
(Total 4 marks)
y = f(x)y
O
M
x
1
3
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16 x
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(Total 2 marks)
13 Write 2 + 6 x + a)2 + b where a and b are integers.
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total 2 marks)
3
2
5
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13
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12 The diagram shows a cuboid ABCDEFGH.
AB = 7 cm, AF = 5 cm and FC = 15 cm.
Calculate the volume of the cuboid.Give your answer correct to 3 significant figures.
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(Total for Question 12 is 4 marks)
F
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DG
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11 Write x 2 + 2x – 8 in the form (x + m ) 2 + n where m and n are integers.
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(Total 2 marks)
17 Solve x2 – 6x – 8 = 0
Write your answer in the form a ± b where a and b are integers.
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(Total 3 marks)
4
5
6
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23 (a) Write 2x2 + 16x + 35 in the form a(x + b)2 + c where a, b, and c are integers.
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(3)
(b) Hence, or otherwise, write down the coordinates of the turning point of the graphof y = 2x2 + 16x + 35
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(1)
(Total 4 marks)
20
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22 There are y black socks and 5 white socks in a drawer.
Joshua takes at random two socks from the drawer.
The probability that Joshua takes one white sock and one black sock is 611
(a) Show that 3y2 – 28y + 60 = 0
(4)
(b) Find the probability that Joshua takes two black socks.
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(3)
(Total for Question 22 is 7 marks)
6
7
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