Save My Exams! – The Home of Revision
For more awesome GCSE and A level resources, visit us at www.savemyexams.co.uk/
Inequalities
Question Paper
Level
A LEVEL
Exam Board
Edexcel GCE
Subject
Mathematics
Module
Core 1
Topic
Algebra
Sub-Topic
Inequalities
Booklet
Question Paper
Time Allowed:
88 minutes
Score:
/ 73
Percentage:
/100
Grade Boundaries:
C1 Algebra – Inequalities
1.
PhysicsA dMathsTutor.co
Find the set of values of x for which
(a)
3(x – 2) < 8 – 2x
(2)
(b)
(2x – 7)(1 + x) < 0
(3)
(c)
both 3(x – 2) < 8 – 2x and (2x – 7)(1 + x) < 0
(1)
(Total 6 marks)
___________________________________________________________________________
f(x) = x2 + 4kx + (3 + 11k), where k is a constant.
2.
(a)
Express f(x) in the form (x + p)2 + q, where p and q are constants to be found in
terms of k.
(3)
Given that the equation f(x) = 0 has no real roots,
(b)
find the set of possible values of k.
(4)
Given that k = 1,
(c)
sketch the graph of y = f(x), showing the coordinates of any point at which the
graph crosses a coordinate axis.
(3)
(Total 10 marks)
___________________________________________________________________________
2
PhysicsA dMathsTutor.co
C1 Algebra – Inequalities
3.
Find the set of values of x for which
(a)
4x – 3 > 7 – x
(2)
(b)
2x2 – 5x – 12 < 0
(4)
(c)
both 4x – 3 > 7 – x and 2x2 – 5x – 12 < 0
(1)
(Total 7 marks)
___________________________________________________________________________
4.
The equation kx 2 + 4 x + (5 − k ) = 0 , where k is a constant, has 2 different real solutions
for x.
(a)
Show that k satisfies
k 2 − 5 k + 4 > 0.
(3)
(b)
Hence find the set of possible values of k.
(4)
(Total 7 marks)
___________________________________________________________________________
5.
The equation x2 + kx + (k + 3) = 0, where k is a constant, has different real roots.
(a)
Show that k 2 – 4k – 12 > 0.
(2)
(b)
Find the set of possible values of k.
(4)
(Total 6 marks)
___________________________________________________________________________
3
C1 Algebra – Inequalities
6.
PhysicsA dMathsTutor.co
The equation 2x2 – 3x – (k + 1) = 0, where k is a constant, has no real roots.
Find the set of possible values of k.
(Total 4 marks)
___________________________________________________________________________
7.
Find the set of values of x for which
(a)
3(2x + 1) > 5 – 2x,
(2)
(b)
2x2 – 7x + 3 > 0,
(4)
(c)
both 3(2x + 1) > 5 – 2x and 2x2 – 7x + 3 > 0.
(2)
(Total 8 marks)
___________________________________________________________________________
8.
The width of a rectangular sports pitch is x metres, x > 0. The length of the pitch is 20 m
more than its width. Given that the perimeter of the pitch must be less than 300 m,
(a)
form a linear inequality in x.
(2)
Given that the area of the pitch must be greater than 4800 m2,
(b)
form a quadratic inequality in x.
(2)
(c)
by solving your inequalities, find the set of possible values of x.
(4)
(Total 8 marks)
___________________________________________________________________________
4
C1 Algebra – Inequalities
9.
PhysicsA dMathsTutor.co
Find the set of values for x for which
(a)
6x – 7 < 2x + 3,
(2)
(b)
2x2 – 11x + 5 < 0,
(4)
(c)
both 6x – 7 < 2x + 3 and 2x2 – 11x + 5 < 0.
(1)
(Total 7 marks)
___________________________________________________________________________
10.
Find the set of values of x for which
(2x + 1)(x – 2) > 2(x + 5).
(Total 7 marks)
___________________________________________________________________________
11.
Solve the inequality
10 + x 2 > x( x − 2) .
(Total 3 marks)
___________________________________________________________________________
5