Unit 1: Real And Complex Numbers - Mathematics For Class IX (Science Group) - Solved Exercise 1.2 - By Miss Aira Shakir

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Unit 1: Real And Complex Numbers
Exercise 1.2

By Miss Aira Shakir
1. Recognize the properties of real numbers used in the following:

2. Fill the correct real number in the following to make the real numbers property correct.

3. Fill in the blanks to make the property correct/true.
(i) 5 < 8 and 8 < 10 ⇒ 5 < 10
(ii) 10 > 8 and 8 > 5 ⇒ 10 > 5 (OR 5 < 10)
(iii) 3 < 6 ⇒ 3 + 9 < 6 + 9
(iv) 4 < 6 ⇒ 4 + 8 < 6 + 8
(v) 8 > 6 ⇒ 6 + 8 > 6 + 6

4. Fill the following blanks which make property correct/true:
(i) 5 < 7 ⇒ 5 x 12 < 7 x 12
(ii) 7 > 5 ⇒ 7 x 12 > 5 x 12
(iii) 6 > 4 ⇒ 6 x (-7)  < x 4 x (-7)
(iv) 2 < 8 ⇒ 2 x (-4)  > 8 x (-4)

5. Find the additive and multiplicative inverse of the following real numbers.

Introduction to Coordinate Geometry / Analytic Geometry - Chapter No. 16 -Math Class IX - Prepared By Team Of Ustani G, Free Educational Team, KARACHI

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Chapter No. 16: Introduction to Coordinate Geometry / Analytic Geometry
MCQs Preparation Of IX Math

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Free Educational Team, KARACHI

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Projection Of A Side Of A Triangle - Chapter No. 15 -Math Class IX - Prepared By Team Of Ustani G, Free Educational Team, KARACHI

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Chapter No. 15: Projection Of A Side Of A Triangle - Triangles
MCQs Preparation Of IX Math

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(a) congruent
(b) concurrent ✓
(c) parallel
(d) perpendicular

30. The common point of three or more than three lines is called ________.
(a) central point
(b) point of concurrency ✓
(c) vertex
(d) centroid

31. In right angled triangle if one angle is 30°, then other angle will be _________.
(a) 15°
(b) 30°
(c) 45°
(d) 60° ✓

32. In right angled triangle if one angle is 60°, then other angle will be _________.
(a) 15°
(b) 30° ✓
(c) 45°
(d) 60°


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Theorems Related with Area - Chapter No. 14 -Math Class IX - Prepared By Team Of Ustani G, Free Educational Team, KARACHI

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Chapter No. 14: Theorems Related with Area - Triangles
MCQs Preparation Of IX Math

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(c) A = L × W ✓
(d) A = L²

14. Area of parallelogram is _________.
(a) A = ½Base × Heigth
(b) A = Base × Heigth ✓
(c) A = L × W
(d) A = L²

15. If the length and breadth of a rectangle are ‘a’ and ‘b’ then its area will be:
(a) 𝑎 + 𝑏
(b) 𝑎 × 𝑏 ✓
(c) 𝑎 − 𝑏
(d) 𝑎 = 𝑏

16. In most cases similar figures have ________ areas.
(a) same
(b) different ✓
(c) equal
(d) congruent

17. All congruent figures have ________ areas.
(a) same ✓
(b) different
(c) zero
(d) non-congruent

18. Area of a geometrical figure is always _______ real number.
(a) zero
(b) positive ✓
(c) negative
(d) rational


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Practical Geometry - Triangles - Chapter No. 13 -Math Class IX - Prepared By Team Of Ustani G, Free Educational Team, KARACHI

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Chapter No. 13: Practical Geometry - Triangles
MCQs Preparation Of IX Math

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(a) base
(b) perpendicular
(c) hypotenuse ✓
(d) none

8. In the figure, the value of 𝑥 is:
(a) 6cm
(b) 8cm ✓
(c) 10cm
(d) 16cm

9. In the figure, the value of 𝑥 is:
(a) 5cm
(b) 8cm
(c) 12cm ✓
(d) 18cm

10. In the figure, the value of 𝑥 is:
(a) 2cm
(b) 1cm ✓
(c) √2 cm
(d) 3cm

11. In right angles triangle greater angle is ___________.
(a) 30°
(b) 60°
(c) 90° ✓
(d) 120°

12. In right angled triangle on angle is 90° and other two angles are ___________.
(a) obtuse
(b) acute ✓
(c) right
(d) supplementary

13. If hypotenuse of an isosceles right angled triangle is √2 then each of other side is:
(a) 1cm ✓
(b) 2cm
(c) 3cm
(d) 4cm

14. In right angled triangle which side is the longest side?
(a) perpendicular
(b) base
(c) hypotenuse ✓
(d) none of these

15. In right angled triangle, if 𝑚∠B=90° then which of the following is true?
(a) 𝑎² + 𝑏² = 𝑐²
(b) 𝑎² + 𝑐² = 𝑏² ✓
(c) 𝑏² + 𝑐² = 𝑎²
(d) 𝑎² − 𝑐² = 𝑏²

16. In an isosceles right angled triangle two acute angles are equal to:
(a) 30°
(b) 45° ✓
(c) 60°
(d) 90°


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Sides And Angles Of A Triangle - Chapter No. 12 -Math Class IX - Prepared By Team Of Ustani G, Free Educational Team, KARACHI

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Chapter No. 12: Sides And Angles Of A Triangle
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(a) greater ✓
b) smaller
(c) equal 
(d) none

9. The distance between a line and a point on it is _________.
(a) zero ✓
(b) one
(c) equal
(d) none

10. The difference of two sides of a triangle is ________ the third side.
(a) greater than
(b) smaller than ✓
(c) equal to
(d) congruent to

11. In a triangle, the side opposite to greater angle is __________.
(a) smaller
(b) greater ✓
(c) equal
(d) congruent

12. In a triangle the angles opposite to congruent sides are ________.
(a) congruent ✓
(b) concurrent
(c) unequal
(d) none

13. In a triangle, the side opposite to smaller angle is ________.
(a) smaller ✓
(b) greater
(c) congruent
(d) concurrent

14. An exterior angle of a triangle is ________ non-adjacent interior angle.
(a) equal to
(b) smaller than
(c) greater than ✓
(d) congruent to

15. For a ΔABC, which of the following is true? (a) 𝑚AB + 𝑚BC < 𝑚CA
(b) 𝑚AB − 𝑚BC > 𝑚CA
(c) 𝑚AB + 𝑚BC > 𝑚CA ✓
(d) 𝑚AB + 𝑚BC >/ 𝑚CA  (>/  is greater or not equal to sign)

16. What is the supplement of a right angle?
(a) 60°
(b) 90° ✓
(c) 120°
(d) 180°

17. The sum of the measures of two sides of a triangle is greater than ________ the measure of the median which bisects the third side.
(a) twice ✓
(b) thrice
(c) hypotenuse
(d) angles

18. In an obtuse angled triangle, the side opposite to the obtuse angle is ________ than each of the other two sides.
(a) smaller
(b) longer ✓
(c) twice
(d) thrice


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Line Bisectors And Angle Bisectors - Chapter No. 11 -Math Class IX - Prepared By Team Of Ustani G, Free Educational Team, KARACHI

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Chapter No. 11: Line Bisectors And Angle Bisectors
MCQs Preparation Of IX Math

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8. If CD is right bisector of line segment AB then 𝑚AQ = ________
(a) 𝑚OA
(b) 𝑚OB
(c) 𝑚BQ ✓
(d) 𝑚OD

9. The right bisectors of the sides of an acute triangle intersects each other ________ the triangle.
(a) inside ✓
(b) outside
(c) midpoint
(d) none

10. The right bisectors of the sides of a right triangle intersect each other on the ________.
(a) vertex
(b) midpoint
(c) hypotenuse ✓
(d) none

11. The right bisectors of the sides of an obtuse triangle intersect each other ________ the triangle.
(a) outside ✓
(b) inside
(c) midpoint
(d) none

12. The point of line segment through which the right bisector passes is called its _________ point.
(a) end
(b) mid ✓
(c) non-collinear
(d) trisection

13. The point of intersection of right bisectors of sides of a triangle is equidistant from the ________ of triangle.
(a) sides
(b) vertices
(c) centre ✓
(d) angles

14. The altitudes of a triangle are _________.
(a) congruent
(b) concurrent ✓
(c) equal
(d) parallel


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Parallelograms And Triangles - Chapter No. 10 -Math Class IX - Prepared By Team Of Ustani G, Free Educational Team, KARACHI

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Chapter No. 10: Parallelograms And Triangles
MCQs Preparation Of IX Math

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Free Educational Team, KARACHI

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Congruent Triangles - Chapter No. 09 -Math Class IX - Prepared By Team Of Ustani G, Free Educational Team, KARACHI

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Chapter No. 09: Congruent Triangles
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(a) congruent ✓
(b) non- congruent
(c) unequal
(d) supplementary

21. Any two medians of an _______ triangle equal in measure.
(a) isosceles
(b) equilateral ✓
(c) acute
(d) obtuse

22. Sum of all the interior angles of a triangle is:
(a) 90°
(b) 150°
(c) 180° ✓
(d) 360°


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Quardatic Equations - Chapter No. 08 -Math Class IX - Prepared By Team Of Ustani G, Free Educational Team, KARACHI

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Chapter No. 08: Quardatic Equations
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Linear Graphs And Their Applications - Chapter No. 07 -Math Class IX - Prepared By Team Of Ustani G, Free Educational Team, KARACHI

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Chapter No. 07: Linear Graphs And Their Applications
MCQs Preparation Of IX Math

Prepared By Team Of Ustani G,
Free Educational Team, KARACHI

9. The point of intersection of two coordinate axes is called:
(a) origin ✓
(b) centre
(c) 𝑥-coordinate
(d) ordinate

10. The 𝑥-coordinate of a point is called _______.
(a) origin
(b) abscissa ✓
(c) 𝑦-coordinate
(d) ordinate

11. The 𝑦-coordinate of a point is called _______.
(a) origin
(b) 𝑥-coordinate
(c) 𝑦-coordinate
(d) ordinate ✓

12. The set of points which lie on the same line are called _______ points.
(a) collinear ✓
(b) similar
(c) common
(d) none of these

13. The plane formed by two straight lines perpendicular to each other is called:
(a) cartesian plane ✓
(b) coordinate axes
(c) plane
(d) none of these

14. An ordered pair is a pair of elements in which elements are written in specific:
(a) order ✓
(b) array
(c) point
(d) none

15. Point (−1, 2) lies in quadrant.
(a) I
(b) II ✓
(c) III
(d) IV

16. Point (1, 1) lies in quadrant.
(a) I ✓
(b) II
(c) III
(d) IV

17. Point (1, −3) lies in quadrant.
(a) I
(b) II
(c) III
(d) IV ✓

18. Which of the following points is one the origin?
(a) (0, 0)
(b) (−2, −3)
(c) (0, 2) ✓
(d) (4, 0)

19. Which of the following lines is parallel to 𝑥-axis?
(a) 𝑥 = 0
(b) 𝑥 = −3
(c) 𝑥 = 3
(d) 𝑦 = −3 ✓

20. Which of the following lines is parallel to 𝑦-axis?
(a) 𝑦 = 2𝑥
(b) 𝑥 = −3 ✓
(c) 𝑦 = 3
(d) 𝑦 = 4𝑥 + 1


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Linear Equation Ans Linear Inequalities - Chapter No. 06 -Math Class IX - Prepared By Team Of Ustani G, Free Educational Team, KARACHI

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Chapter No. 06: Linear Equation Ans Linear Inequalities
MCQs Preparation Of IX Math

Prepared By Team Of Ustani G,
Free Educational Team, KARACHI

18. |𝑥| = 0 has only _______ solution:
(a) one ✓
(b) two
(c) three
(d) none of these

19. The equation |𝑥| = 2 is equivalent to:
(a) 𝑥 = 2 or 𝑥 = −2 ✓
(b) 𝑥 = −2 or 𝑥 = −2
(c) 𝑥 = 2 or 𝑥 = 12
(d) 𝑥 = 2 or 𝑥 = −12

20. A/an ________ is equation that is satisfied by every number for which both sides are defined:
(a) identity ✓
(b) conditional
(c) inconsistent
(d) inequation

21. A/an ________ equation is an equation whose solution set is the empty set:
(a) identity
(b) conditional
(c) inconsistent ✓
(d) none

22. A/an ________ equation is an equation that is satisfied by at least one number but is not an identity:
(a) identity
(b) conditional
(c) inconsistent ✓
(d) none

23. 𝑥 + 4 = 4 + 𝑥 is __________ equation:
(a) identity ✓
(b) conditional
(c) inconsistent
(d) none

24. 2𝑥 + 1 = 9 is __________ equation:
(a) identity
(b) conditional ✓
(c) inconsistent
(d) none

25. 𝑥 = 𝑥 + 5 is __________ equation:
(a) identity
(b) conditional
(c) inconsistent ✓
(d) none

26. Equations having exactly the same solution are called _____ solution.
(a) equivalent ✓
(b) linear
(c) inconsistent
(d) inequation

27. A solution that does not satisfy the original equation is called ______ solution.
(a) extraneous ✓
(b) root
(c) general
(d) proper


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Algebraic Manipulation - Chapter No. 05 -Math Class IX - Prepared By Team Of Ustani G, Free Educational Team, KARACHI

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Chapter No. 05: Algebraic Manipulation
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a) Square
b) Square root ✓
c) L.C.M
d) H.C.F

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Factorization - Chapter No. 04 -Math Class IX - Prepared By Team Of Ustani G, Free Educational Team, KARACHI

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Chapter No. 04: Factorization
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Algebraic Expression And Formulas - Chapter No. 03 -Math Class IX - Prepared By Team Of Ustani G, Free Educational Team, KARACHI

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Chapter No. 03: Algebraic Expression And Formulas
MCQs Preparation Of IX Math

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19. Which of the following is not surd?
(a) √2
(b) √3
(c) √2 + 5
(d) √𝜋 ✓

20. In the polynomial with the variable 𝑥, all the powers of 𝑥 are _____ integers.
(a) non-negative ✓
(b) negative
(c) non-positive
(d) none of these

21. Polynomial means an expression with:
(a) one term
(b) two terms
(c) three terms
(d) many terms ✓


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Logarithms - Chapter No. 02 -Math Class IX - Prepared By Team Of Ustani G, Free Educational Team, KARACHI

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Chapter No. 02: Logarithms
MCQs Preparation Of IX Math

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Real And Complex Numbers - Chapter No. 01 -Math Class IX - Prepared By Team Of Ustani G, Free Educational Team, KARACHI

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Chapter No. 01: Real And Complex Numbers
MCQs Preparation Of IX Math

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Mathematics For Class IX Science - Unit 03: LOGARITHMS - Fill In The Blanks And Multiple Choice Questions (MCQs)

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Unit 03: LOGARITHMS
Fill In The Blanks And Multiple Choice Questions (MCQs)

1. The characteristics of log 0.00226 is 3.
2. If log_x81 = 4, then x = 3.
3. The natural logarithm has the base e.
4. The characteristics of log 0.08595 is 2.
5. The characteristics of log 8595 is 3.
6. If log₇x = 2, the value of x is 7² = x.
7. The scientific notation of 756837 is 7.56837 x 10⁵.
8. If log_a16 = 4, a = 2.
9. The logarithm from of 2⁵ = 32 is log₂32 = 5.
10. The characteristics of log 6.67 x 10^-11 is 11.
11. log_a ^x3y/_z² = 3log_ax + log_ay - 2log_az.
12. If log₁₀1000 = y, the value of y will be 3.
13. The characteristics of log 0.00234 is 3.
14. If log₄x = -³/₂ = ¹/₈.
15. If log_x32 = 5, x = 2.
16. Logarithms were introduced by Abu Muhammad Musa Al-Khwarizmi.

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Mathematics For Class IX Science - Unit 04: ALGEBRAIC EXPRESSION - Fill In The Blanks And Multiple Choice Questions (MCQs)

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Unit 04: ALGEBRAIC EXPRESSION
Fill In The Blanks And Multiple Choice Questions (MCQs)

1. (7a + 5) (7a - 5) = 49a² - 25. [Hint: (a² - b² = (a-b)(a+b)]
2.(a + 3b)² = a² + 6ab + 9b².
3. (3a - 2b)² = 9a² - 12ab + 4b².
4. (3a³ + b³)³ = 27a⁹ + 27a⁶b³ + 9a³b⁶ + 9b⁹
5. (p - q)³ = p³ - 3p²q + 3pq² - q³.
6.(2a² - 5y² - 3z²)² = 4a⁴ + 25y⁴ + 9z⁴ - 20a²y² + 30y²z² - 12z²a².
7. (x + 2) (x + 5) = x² + 7x + 10.
8. (2l + 3m²) - (2l - 3m²)² = 24lm².
9. The polynomial expression x² + 7x + 3 w.r.t the term is called trinomial.
10. The degree of polynomial x² + xy² + y is 3.
11. The algebraic expression 2a³y + 4ay² -5a² y³ in descending order w.r.t y is -5a² y³ + 4ay² + 2a³y.
12. The value of x - y - xy , if x = 1, y = 1 is 1.
13. (a + b)² + (a - b)² = 2a² + 2b²,
14. if x + y = 8, xy = 15. Find x² +y² = 34.
15. x⁴ + 64 can made a perfect square 16x².
16. if x³ + 4x² - 7x + 3 is divided by x - 1 then remainder is 1.
17. (a - b + c)² = a² - b² + c² - 2ab - 2bc + 2ca
18. (x - 6) (x - 4) = x² - 10x + 24.
19. If a + b = 2 and a - b = 2 then value of a² + b² is 4.

20. (√ x + √ y) (√ x - √ y) = (x - y)
21. (x - y)³ = x³ - y³ + 3x²y - 3xy².

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Mathematics For Class IX Science - Unit 07 - MATRICES - Fill In The Blanks And Multiple Choice Questions (MCQs)

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Unit 07: MATRICES
Fill In The Blanks And Multiple Choice Questions (MCQs)

Fill In The Blanks

UNIT 7: Matrices

1. The arrangement of matrix R x C (Row x Column).
2. The matrix were introduced by Arther Kelly in 1858.
3. The number of row and column are not equal in matrix is called rectangular matrix. (R ≠ C ).
4. If a matrix has only one column is called column matrix.
5. If a matrix has only one row is called row matrix.
6. The number of row and column are equal is called square matrix.
7. If the matrix has all zero elements is called zero matrix or null matrix.

29. (A x B)^t = B^t x A^t
30. (A^t)^t = A
31. By distributive property of multiplication matrix over subtraction A(B-C) = AB - AC
32. If the value of determinant of matrix is 0 (zero), the matrix is called a /an singular matrix.
33. If the value of determinant of matrix is 1 or greater than 1 or less than 1, the matrix is called non - singular matrix.
34. The multiplicative inverse of a - b is ¹/_{a -b}
35. The multiplicative inverse of ¹/_a+b is a+b.
36. The multiplicative inverse of  ¹/_-2 = -2.
37. If rows and columns are equal the matrix is singular matrix.
38. If rows and column are not equal, the matrix is non singular matrix.

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