Vidaara.orgClass 11 · Mathematics
CodeVID-M11-05-CT
Linear Inequalities — Full Chapter Test
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- This is a full-length test covering the whole chapter — every topic is included.
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
The solution of $x+3>7$ is:
- A.$x>4$
- B.$x<4$
- C.$x>10$
- D.$x\ge4$
2.
The solution region of a linear inequality in two variables is:
- A.a line
- B.a half-plane
- C.a ray
- D.a point
3.
The solution of a system of inequalities is:
- A.a line
- B.the common region
- C.empty
- D.a ray
4.
Multiplying an inequality by a negative number:
- A.keeps the sign
- B.reverses the sign
- C.makes it zero
- D.removes it
5.
For a strict inequality $(<)$, the boundary line is:
- A.solid
- B.dashed
- C.absent
- D.doubled
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Solve $3x+5<14$.
7.
Does $(1,1)$ satisfy $2x+y\le4$?
8.
Does $(1,1)$ satisfy both $x+y\le4$ and $x\ge0$?
9.
Solve $-4x\ge-12$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Solve $2(x-1)
11.
Determine whether $(2,3)$ satisfies $3x-2y<5$.
12.
Find the corner points of $x\ge0,\ y\ge0,\ x+y\le4$.
13.
Solve $\dfrac{2x-1}{3}\ge\dfrac{x+2}{2}$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Solve $\dfrac{2x-3}{4}+9\ge3+\dfrac{4x}{3}$ and represent the solution on a number line.
15.
Describe the region $2x+3y\le12,\ x\ge0,\ y\ge0$ and give its corner points.
Answer Key
Section A — Multiple Choice Questions
- (A) $x>4$
- (B) a half-plane
- (B) the common region
- (B) reverses the sign
- (B) dashed
Section B — Short Answer (2 marks)
- $x<3$.
- Yes ($3\le4$).
- Yes.
- $x\le3$.
Section C — Short Answer (3 marks)
- $x<5$.
- Yes ($0<5$).
- $(0,0),(4,0),(0,4)$.
- $x\ge8$.
Section D — Long Answer (5 marks)
- $x\le6.3$ (i.e. $x\in(-\infty,6.3]$).
- A triangle with corners $(0,0),(6,0),(0,4)$.
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