Class 9 Maths Test Paper Chapter 1, 2 AND 3 | GSEB Board | Detailed Solutions & Marking Scheme
VEDANT CLASSES – IGNITE TEST SERIES
Class: 9
Subject: Mathematics & Science
Board: Gujarat Secondary and Higher Secondary Education Board (GSHSEB)
Chapters: Coordinate Geometry (Point Plotting and Basics of Coordinates), Polynomials, Factorisation by Splitting the Middle Term, Number System
Time: 60 Minutes
Maximum Marks: 30
GENERAL INSTRUCTIONS
All questions are based on NCERT textbook exercises and examples.
All questions are numerical-based only.
Use graph paper wherever required.
Show all necessary calculations.
Internal choice is provided as per sections.
Answer the required number of questions only.
SECTION A – OBJECTIVE QUESTIONS
(7 Marks)
Q.1 Choose the correct option. (3 × 1 = 3)
(i) The coordinates of a point lying 4 units above the origin on the y-axis are:
(A) (4, 0)
(B) (0, 4)
(C) (−4, 0)
(D) (0, −4)
(ii) If p(x) = 2x² − 3x + 4, then p(2) is:
(A) 4
(B) 6
(C) 8
(D) 10
(iii) The factorisation of x² + 9x + 20 is:
(A) (x + 4)(x + 5)
(B) (x − 4)(x − 5)
(C) (x + 10)(x − 2)
(D) (x + 5)(x + 4)
Q.2 Fill in the blanks using the correct option given in brackets. (2 × 1 = 2)
(i) 0.625 = ___/8 (3, 5, 7)
(ii) √64 + √36 = ____ (10, 12, 14)
Q.3 State whether True or False. (2 × 1 = 2)
(i) The point (−5, 0) lies on the x-axis. _______
(ii) √2 + √8 = 3√2. _______
SECTION B – ANSWER ANY 3 QUESTIONS
(3 × 2 = 6)
Q.4 Polynomial Values
(a) Find p(2) for p(x) = x² + 3x − 4.
(b) Find p(−1) for p(x) = 2x² − x + 5.
Q.5 Decimal to Rational Numbers
(a) Express 0.75 in the form p/q.
(b) Express 0.125 in the form p/q.
Q.6 Coordinate Geometry
(a) Plot the point A(3, 2).
(b) Plot the point B(−2, 4).
(c) Write the quadrant of each point.
Q.7 Operations on Radicals
(a) Simplify √49 + √81.
(b) Simplify 3√5 − √5.
Q.8 Factorisation
(a) Factorise x² + 5x + 6.
(b) Verify the factors by multiplication.
SECTION C – ANSWER ANY 3 QUESTIONS
(3 × 3 = 9)
Q.9 Polynomial Evaluation
(a) Find the value of 2x² − 5x + 1 when x = 3.
(b) Find the value of x² + x − 6 when x = −2.
Q.10 Rational and Irrational Numbers
(a) Insert any two rational numbers between 1/3 and 2/3.
(b) Insert one irrational number between 2 and 3.
Q.11 Factorisation by Splitting the Middle Term
(a) Factorise x² + 8x + 15.
(b) Factorise 2x² + 5x + 2.
Q.12 Representation of Irrational Numbers
(a) Construct √5 on the number line.
(b) Mark the position of √5 correct to one decimal place.
Q.13 Coordinate Geometry
(a) Plot the points P(2, −3), Q(−4, −2), and R(−1, 5).
(b) Write the quadrant of each point.
(c) Identify the point nearest to the y-axis.
SECTION D – ANSWER ANY 2 QUESTIONS
(2 × 4 = 8)
Q.14 Operations on Radicals
(a) Simplify 2√12 + √27.
(b) Simplify 4√18 − 2√8.
(c) Hence, find the value of:
(2√12 + √27) + (4√18 − 2√8)
Q.15 Factorisation
(a) Factorise 2x² + 7x + 3.
(b) Factorise 3x² − 14x − 5.
(c) Verify any one factorisation by multiplication.
Q.16 Coordinate Geometry
(a) Plot the points A(4, 3), B(−3, 4), C(−4, −2), and D(5, −3).
(b) Write the quadrant of each point.
(c) Name the point nearest to the x-axis.
(d) Name the point nearest to the y-axis.
------------------- END OF QUESTION PAPER -------------------
ANSWER KEY WITH MARKING SCHEME
SECTION A (7 Marks)
Q.1
(i) (B) (0, 4) [1 Mark]
(ii) p(2) = 2(2²) − 3(2) + 4
= 8 − 6 + 4
= 6
Answer: (B) 6 [1 Mark]
(iii) x² + 9x + 20
= x² + 5x + 4x + 20
= x(x + 5) + 4(x + 5)
= (x + 5)(x + 4)
Answer: (A) [1 Mark]
Q.2
(i) 0.625 = 5/8 [1 Mark]
(ii) √64 + √36 = 8 + 6 = 14 [1 Mark]
Q.3
(i) True [1 Mark]
(ii) True
√2 + √8 = √2 + 2√2 = 3√2 [1 Mark]
SECTION B (Answer Any 3)
(3 × 2 = 6)
Q.4
(a) p(2) = 2² + 3(2) − 4
= 4 + 6 − 4
= 6 [1 Mark]
(b) p(−1) = 2(−1)² − (−1) + 5
= 2 + 1 + 5
= 8 [1 Mark]
Q.5
(a) 0.75 = 75/100 = 3/4 [1 Mark]
(b) 0.125 = 125/1000 = 1/8 [1 Mark]
Q.6
(a) Correct plotting of A(3, 2) [0.5 Mark]
(b) Correct plotting of B(−2, 4) [0.5 Mark]
(c) A lies in Quadrant I and B lies in Quadrant II [1 Mark]
Q.7
(a) √49 + √81
= 7 + 9
= 16 [1 Mark]
(b) 3√5 − √5
= 2√5 [1 Mark]
Q.8
(a) x² + 5x + 6
= x² + 2x + 3x + 6
= x(x + 2) + 3(x + 2)
= (x + 2)(x + 3) [1 Mark]
(b) Verification by multiplication:
(x + 2)(x + 3)
= x² + 3x + 2x + 6
= x² + 5x + 6 [1 Mark]
SECTION C (Answer Any 3)
(3 × 3 = 9)
Q.9
(a) For x = 3:
2x² − 5x + 1
= 2(3²) − 5(3) + 1
= 18 − 15 + 1
= 4 [1.5 Marks]
(b) For x = −2:
x² + x − 6
= (−2)² + (−2) − 6
= 4 − 2 − 6
= −4 [1.5 Marks]
Q.10
(a) Two rational numbers between 1/3 and 2/3:
Examples: 4/9 and 5/9 [2 Marks]
(b) One irrational number between 2 and 3:
√5 ≈ 2.236 [1 Mark]
Q.11
(a) x² + 8x + 15
= x² + 3x + 5x + 15
= x(x + 3) + 5(x + 3)
= (x + 3)(x + 5) [1.5 Marks]
(b) 2x² + 5x + 2
= 2x² + 4x + x + 2
= 2x(x + 2) + 1(x + 2)
= (2x + 1)(x + 2) [1.5 Marks]
Q.12
(a) Correct construction of √5 on the number line [2 Marks]
(b) √5 ≈ 2.2 (correct to one decimal place) [1 Mark]
Q.13
(a) Correct plotting of all points [1.5 Marks]
(b)
P(2, −3) → Quadrant IV
Q(−4, −2) → Quadrant III
R(−1, 5) → Quadrant II [1 Mark]
(c) Distance from y-axis = |x-coordinate|
|2| = 2
|−4| = 4
|−1| = 1
Hence, R(−1, 5) is nearest to the y-axis. [0.5 Mark]
SECTION D (Answer Any 2)
(2 × 4 = 8)
Q.14
(a)
2√12 + √27
= 2(2√3) + 3√3
= 4√3 + 3√3
= 7√3 [1 Mark]
(b)
4√18 − 2√8
= 4(3√2) − 2(2√2)
= 12√2 − 4√2
= 8√2 [1 Mark]
(c)
(2√12 + √27) + (4√18 − 2√8)
= 7√3 + 8√2 [2 Marks]
Q.15
(a)
2x² + 7x + 3
= 2x² + 6x + x + 3
= 2x(x + 3) + 1(x + 3)
= (2x + 1)(x + 3) [1 Mark]
(b)
3x² − 14x − 5
= 3x² − 15x + x − 5
= 3x(x − 5) + 1(x − 5)
= (3x + 1)(x − 5) [2 Marks]
(c) Verification of any one factorisation [1 Mark]
Q.16
(a) Correct plotting of all points [1 Mark]
(b)
A(4, 3) → Quadrant I
B(−3, 4) → Quadrant II
C(−4, −2) → Quadrant III
D(5, −3) → Quadrant IV [1 Mark]
(c) Distance from x-axis = |y-coordinate|
A → 3
B → 4
C → 2
D → 3
Nearest to x-axis: C(−4, −2) [1 Mark]
(d) Distance from y-axis = |x-coordinate|
A → 4
B → 3
C → 4
D → 5
Nearest to y-axis: B(−3, 4) [1 Mark]
------------------- TOTAL MARKS: 30 -------------------
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