Knowledge Check : Algebra
Knowledge Check – Algebra
Patterns and Introduction to Algebra
Q1: Which of the following is an algebraic expression?
A) 25
B) x + 5
C) 7%
D) 3.14
Q2: In the expression 7x, the coefficient of x is
A) 1
B) 7
C) x
D) 0
Q3: 3x²y is a
A) Monomial
B) Binomial
C) Trinomial
D) Polynomial with two terms
Q4: 5x − 3 is a
A) Monomial
B) Binomial
C) Trinomial
D) Constant
Q5: How many terms are there in 2x² − 3x + 4?
A) 1
B) 2
C) 3
D) 4
Q6: If x = 3, the value of 2x + 5 is
A) 8
B) 9
C) 11
D) 13
Q7: In the pattern 2, 5, 8, 11, … the rule is
A) Add 1
B) Add 2
C) Add 3
D) Multiply by 2
Q8: Which is the correct example of a variable?
A) 5
B) 10
C) x
D) 3.5
Q9: The constant term in 4x² − 7x + 9 is
A) 4
B) −7
C) 9
D) x²
Q10: In 5ab², the number of factors (including numbers and variables) is
A) 1
B) 2
C) 3
D) 4
Q11: Which of these is a trinomial?
A) x + 1
B) x² − 3x + 2
C) 7x
D) 9
Q12: If 3x − 4 = 11, the value of x is
A) 3
B) 4
C) 5
D) 6
Q13: 2x²y³ has degree
A) 2
B) 3
C) 5
D) 6
Q14: The like terms among the following are
A) 3x and 3y
B) 2x² and 5x²
C) 4x and 4x²
D) 7 and 7x
Q15: If x = 2 and y = 3, the value of xy + y is
A) 5
B) 7
C) 9
D) 11
Operations on Algebraic Expressions
Q16: (3x + 2x) simplifies to
A) 5x
B) 6x
C) x²
D) 3x²
Q17: 5x − 3x + 4 equals
A) 2x + 4
B) 8x
C) 5x + x
D) 5x − 3x − 4
Q18: (x + 4) + (2x − 1) simplifies to
A) 3x + 3
B) 3x + 5
C) x² + 3
D) 2x + 3
Q19: 3x × 4x is
A) 7x
B) 7x²
C) 12x
D) 12x²
Q20: 2x(3x + 5) equals
A) 6x + 10
B) 6x² + 10x
C) 5x² + 6x
D) 6x² + 5x
Q21: (x + 2)(x + 3) equals
A) x² + 5x + 6
B) x² + 6x + 5
C) x² + 2x + 3
D) x² + 3x + 2
Q22: Which is a correct expansion of (a + b)²?
A) a² + b²
B) a² + 2ab + b²
C) a² − 2ab + b²
D) 2a² + b²
Q23: (a − b)(a + b) equals
A) a² + b²
B) a² − b²
C) a² − 2ab + b²
D) a² + 2ab + b²
Q24: 4x² − 9 can be factorised as
A) (2x − 3)²
B) (2x + 3)²
C) (2x − 3)(2x + 3)
D) (x − 3)(x + 3)
Q25: Simplify (3x² + 2x) − (x² − 5x)
A) 2x² + 7x
B) 2x² − 3x
C) 4x² + 3x
D) 2x² + 3x
Q26: (2x − 1)(x − 3) equals
A) 2x² − 7x + 3
B) 2x² − 5x − 3
C) 2x² − x − 3
D) 2x² + 5x − 3
Q27: 0.5x + 1.5x simplifies to
A) 1x
B) 2x
C) 3x
D) 4x
Q28: If a shopkeeper uses (SP − CP) to find profit, this expression is
A) Numerical expression
B) Algebraic expression
C) Equation
D) Constant
Q29: 3(2x − 1) + 2(1 − x) simplifies to
A) 4x − 1
B) 2x − 1
C) 6x − 3 + 2 − 2x = 4x − 1
D) x − 1
Q30: (a + b)³ is equal to
A) a³ + b³
B) a³ + 3a²b + 3ab² + b³
C) a³ − 3a²b + 3ab² − b³
D) a³ + 3ab + b³
Exponents and Powers
Q31: 2³ × 2² equals
A) 2⁵
B) 2⁶
C) 2¹
D) 2⁴
Q32: a⁵ ÷ a² equals
A) a³
B) a⁷
C) a²
D) a⁴
Q33: (3²)³ equals
A) 3⁵
B) 3⁶
C) 3²
D) 3³
Q34: The value of 10⁰ is
A) 0
B) 1
C) 10
D) 100
Q35: 2⁻³ equals
A) −8
B) 1/8
C) 8
D) −1/8
Q36: Which is in standard form (scientific notation)?
A) 25 × 10⁵
B) 2.5 × 10⁶
C) 0.25 × 10⁷
D) 25.0 × 10⁴
Q37: 5² × 5³ × 5 equals
A) 5⁵
B) 5⁶
C) 5⁴
D) 5³
Q38: (ab)³ equals
A) a³ + b³
B) a³b³
C) a³b
D) ab³
Q39: a² × b³ / b equals
A) a²b²
B) ab²
C) a²b³
D) a²/b²
Q40: 10⁵ ÷ 10² equals
A) 10³
B) 10⁷
C) 10²
D) 10⁵
Q41: (2x³)² equals
A) 4x⁶
B) 2x⁶
C) 4x³
D) x⁶
Q42: a⁻²b equals
A) b/a²
B) a²/b
C) ab²
D) 1/a²b
Q43: The standard form of 0.00045 is
A) 4.5 × 10⁻⁵
B) 4.5 × 10⁻⁴
C) 45 × 10⁻⁵
D) 0.45 × 10⁻³
Q44: Which is equal to 9⁻¹?
A) −9
B) 1/9
C) 9
D) 1/81
Q45: 3² × 3⁻⁴ equals
A) 3⁻²
B) 3²
C) 3⁶
D) 3⁻⁶
Linear Equations
Q46: The solution of 2x + 3 = 11 is
A) x = 3
B) x = 4
C) x = 5
D) x = 2
Q47: The equation 3x − 7 = 2x + 5 has solution
A) x = 12
B) x = −12
C) x = 7
D) x = −7
Q48: 5(x − 2) = 15 gives
A) x = 1
B) x = 2
C) x = 3
D) x = 5
Q49: A linear equation in one variable has
A) No solution
B) Exactly one solution
C) Two solutions
D) Infinitely many solutions always
Q50: The equation 2x + 3y = 12 represents
A) A point
B) A line
C) A parabola
D) A circle
Q51: If 3x = 15, then x equals
A) 3
B) 4
C) 5
D) 6
Q52: The pair of equations x + y = 6 and x − y = 2 has solution
A) x = 4, y = 2
B) x = 3, y = 3
C) x = 2, y = 4
D) x = 5, y = 1
Q53: If 2x + 5 = 2x + 7, then
A) x = 1
B) x = 2
C) No solution
D) 5 = 7 is a contradiction
Q54: The graph of y = 3x + 1 passes through point
A) (0,0)
B) (1,3)
C) (0,1)
D) (1,4)
Q55: A student’s mark in Maths (x) and Science (y) satisfy x + y = 100. This represents
A) A line of possible marks
B) Only one pair of marks
C) A circle
D) No marks possible
Q56: The solution of 4(x − 1) = 3(x + 2) is
A) x = 10
B) x = −10
C) x = 2
D) x = −2
Q57: A linear equation in one variable can be written in the form
A) ax² + bx + c = 0
B) ax + b = 0
C) ax³ + b = 0
D) a/x + b = 0
Q58: The pair of equations representing two parallel lines is
A) x + y = 2, x + y = 5
B) x + y = 2, 2x + 2y = 4
C) x + y = 2, x − y = 0
D) 2x + y = 1, 4x + 2y = 2
Q59: 7x − 4 = 3x + 12 gives
A) x = 4
B) x = −4
C) x = 2
D) x = −2
Q60: The nature of graph of any linear equation in two variables is
A) Straight line
B) Curve
C) Circle
D) Parabola
Polynomials
Q61: 3x² − 5x + 2 is a polynomial of degree
A) 1
B) 2
C) 3
D) 0
Q62: A polynomial with degree 1 is called
A) Constant
B) Linear
C) Quadratic
D) Cubic
Q63: If p(x) = x² − 4, then p(2) equals
A) 0
B) 4
C) −4
D) 2
Q64: A polynomial with no variable term is called
A) Linear
B) Constant
C) Quadratic
D) Zero polynomial only
Q65: For polynomial p(x) = 2x + 3, the value of p(0) is
A) 0
B) 2
C) 3
D) 5
Q66: If (x − 2) is a factor of x² − 4, the other factor is
A) x − 2
B) x + 2
C) x² + 2
D) x² − 2
Q67: The number of zeroes of a quadratic polynomial is at most
A) 1
B) 2
C) 3
D) 4
Q68: The graph of a linear polynomial is a
A) Straight line
B) Parabola
C) Circle
D) Ellipse
Q69: The remainder when x² − 5x + 6 is divided by (x − 2) is
A) 0
B) 2
C) −2
D) 6
Q70: A cubic polynomial has degree
A) 1
B) 2
C) 3
D) 4
Q71: If p(x) = x² − 1, then its zeroes are
A) 0 only
B) 1 only
C) 1 and −1
D) 2 and −2
Q72: The value of polynomial 3x² − x at x = −1 is
A) 2
B) −2
C) 4
D) −4
Q73: The zero of linear polynomial 5x − 10 is
A) 0
B) 1
C) 2
D) −2
Q74: The constant term of polynomial x³ − 4x + 7 is
A) 3
B) −4
C) 7
D) 1
Q75: A polynomial of degree 0 has
A) No variable term
B) Only x term
C) Highest power 2
D) Highest power 3
Factorization and Division of Algebraic Expressions
Q76: The HCF (greatest common factor) of 6x and 9x² is
A) 3x
B) 6x
C) 9x
D) x²
Q77: Factorise 3x + 3y
A) 3(x + y)
B) (3x + 1)(3y + 1)
C) 3(x − y)
D) x(3 + y)
Q78: Factorise x² − 5x + 6
A) (x − 2)(x − 3)
B) (x + 2)(x + 3)
C) (x − 1)(x − 6)
D) (x + 1)(x + 6)
Q79: 12x² ÷ 3x equals
A) 4x
B) 4x²
C) 4
D) x/4
Q80: Factorise ax + ay
A) a(x − y)
B) a(x + y)
C) x(a + y)
D) y(a + x)
Q81: The factorised form of x² − 9y² is
A) (x − 3y)²
B) (x + 3y)²
C) (x − 3y)(x + 3y)
D) (x − y)(x + y)
Q82: 8a³b ÷ 4ab equals
A) 2a²b
B) 2a²
C) 2ab²
D) a²b
Q83: Quotient when x² − 1 is divided by (x − 1) is
A) x − 1
B) x + 1
C) x² + 1
D) x − 2
Q84: Factorise x² + 7x + 10
A) (x + 2)(x + 5)
B) (x − 2)(x − 5)
C) (x + 1)(x + 10)
D) (x − 1)(x − 10)
Q85: 15x²y ÷ 5xy equals
A) 3xy
B) 3x
C) 3y
D) 5x
Q86: Factorise x² − 4x
A) x(x − 4)
B) (x − 2)²
C) x(x + 4)
D) (x + 2)²
Q87: If (x − 5) is a factor of x² − 5x, the other factor is
A) x + 5
B) x
C) x − 1
D) x + 1
Q88: 21a²b ÷ 7ab equals
A) 3a
B) 3ab
C) 3a²b
D) a³
Q89: Factorisation helps mainly to
A) Increase degree
B) Solve equations easily
C) Make expression longer
D) Remove variables
Q90: Quotient when 4x² − 12x is divided by 4x is
A) x − 3
B) x + 3
C) x² − 3x
D) x² + 3x
Coordinate Geometry and Linear Graphs
Q91: The coordinates of origin are
A) (0, 1)
B) (1, 0)
C) (0, 0)
D) (1, 1)
Q92: In point (3, −2), 3 represents
A) x-coordinate
B) y-coordinate
C) Both coordinates
D) Distance from origin only
Q93: The point on y-axis has coordinates
A) (0, y)
B) (x, 0)
C) (0, 0) only
D) (x, y)
Q94: The graph of y = 2 is
A) Vertical line
B) Horizontal line
C) Diagonal line
D) Circle
Q95: The point (−4, 0) lies on
A) x-axis
B) y-axis
C) Neither axis
D) Both axes
Q96: The line x = 3 is
A) Horizontal
B) Vertical
C) Slanting
D) Curved
Q97: The coordinates of a point in II quadrant are of the form
A) (+, +)
B) (−, +)
C) (+, −)
D) (−, −)
Q98: If a point is on both axes, it is
A) (1, 1)
B) (0, 0)
C) (−1, 1)
D) (1, −1)
Q99: The solution of equation x + y = 4 can be represented as
A) A point
B) A line
C) A circle
D) A parabola
Q100: The distance of point (0, 5) from origin is
A) 0
B) 5
C) √5
D) 10
Q101: The coordinates of a point 3 units to the right of origin on x-axis are
A) (0, 3)
B) (3, 0)
C) (−3, 0)
D) (0, −3)
Q102: A point in IV quadrant has signs
A) (+, +)
B) (−, +)
C) (−, −)
D) (+, −)
Q103: The line passing through (0, 2) and (0, 5) is
A) Horizontal
B) Vertical
C) Diagonal
D) Curve
Q104: The point (−2, −3) lies in
A) I quadrant
B) II quadrant
C) III quadrant
D) IV quadrant
Q105: A linear graph representing constant speed of a bus shows
A) Curved line
B) Zig-zag line
C) Straight line
D) Circle
Arithmetic and Geometric Progressions (AP & GP)
Q106: In AP 2, 5, 8, 11, … the common difference d is
A) 1
B) 2
C) 3
D) 4
Q107: The nth term of an AP is given by
A) aₙ = a + nd
B) aₙ = a + (n − 1)d
C) aₙ = nd
D) aₙ = a − nd
Q108: In AP 4, 7, 10, 13, the 5th term is
A) 16
B) 17
C) 18
D) 19
Q109: The sum of first n terms of AP is
A) Sₙ = n/2 [2a + (n − 1)d]
B) Sₙ = a + (n − 1)d
C) Sₙ = nd
D) Sₙ = a/d
Q110: In AP with a = 5, d = 2, the 10th term is
A) 23
B) 24
C) 25
D) 26
Q111: In GP 2, 6, 18, 54, the common ratio r is
A) 2
B) 3
C) 4
D) 6
Q112: nth term of a GP is
A) aₙ = a + (n − 1)r
B) aₙ = a·rⁿ
C) aₙ = a·rⁿ⁻¹
D) aₙ = ar/n
Q113: If AP has 7, 10, 13, … then common difference d is
A) 2
B) 3
C) 4
D) 5
Q114: An AP is 5, 5, 5, 5, … here d is
A) 0
B) 1
C) 5
D) Not defined
Q115: In a GP, if a = 4 and r = 2, then 4th term is
A) 16
B) 32
C) 64
D) 8
Q116: An example of increasing GP is
A) 1, 1, 1, …
B) 8, 4, 2, …
C) 2, 4, 8, 16, …
D) 5, 5, 5, …
Q117: The 1st term of AP is 3 and 4th term is 12. The common difference d is
A) 2
B) 3
C) 4
D) 5
Q118: In an AP, if a = 10 and d = −2, then 3rd term is
A) 6
B) 8
C) 10
D) 12
Q119: In GP, if a = 9 and r = 1/3, the 2nd term is
A) 3
B) 1
C) 9
D) 27
Q120: A sequence 5, 10, 20, 40, … is
A) AP with d = 5
B) AP with d = 10
C) GP with r = 2
D) GP with r = 5