1661 Words7 Pages

Name: ______________________________ (
)
Date: ___________
Class: __________
Revision (Quadratic Equations and Functions)
Question 1
Find the values of k for which the equation x2 + 2x + 16 = 3kx has equal roots.
Question 2
Find the range of values of p such that x 2 + ( p − 3) x + p + 5 > 0 for all values of x.
Question 3
Show that the equation (p + 1)x2 + (2p + 3)x + (p + 2) = 0 has real roots for all real values of p.
Question 4
Find the smallest integer value of m for which the expression 2 x 2 − 5 x + m will always be positive for all real values of x.
Question 5
Find the range of values of m for which the equation 6 x 2 − 3x − 5m = 0 has no real roots.
Question 6
Find the range of values of m for which 2x2 + 5x + m is always positive for all real values of x.
Question 7
x2
Find the values of k for which the equation
= 1 − x has 2 real distinct roots. k −2
Question 8
Find the values of p for which the equation ( p − 2) x 2 − px + 1 + 2 x = 0 has equal roots.
Question 9
(a) Express x 2 + 6 x − 7 in the form ( x − h) 2 + k .
(b) Hence solve the equation x 2 + 6 x − 7 = 0 .
(c) (i) Sketch the graph y = x 2 + 6 x − 7 .
(ii) Mark and label the coordinates of the points where the graph cuts the axes.
(iii) Write down the equation of the line of symmetry.
Question 10
Given that the curve y = x 2 + ax − b crosses the x-axis at values of a and b.
. Find the
1
Question 11
(a) Given that ( x − 3)( x + 4) = ( x + a) 2 − b , state the values of a and b.
(b) Sketch the graph of y = ( x − 3)( x + 4) on the given axes below. You must show clearly the x and y intercept and the line of symmetry. y x
Question 12
The diagram shows the graph of the curve y = ( x + k )(2 − x) , where k is a constant.
The curve meets the y axis at A and the x axis at B and C as shown.
(a) Write down the coordinates of B and find the value of k.
(b) Find the coordinates of A.
(c) Write down

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