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CBSE Class 10  >  Class 10 Notes  >  Mathematics (Maths)   >  Unit Test: Quadratic Equations

Unit Test: Quadratic Equations

Time: 1 hour

M.M. 30

Attempt all questions.

  • Question numbers 1 to 5 carry 1 mark each.
  • Question numbers 6 to 8 carry 2 marks each.
  • Question numbers 9 to 11 carry 3 marks each.
  • Question number 12 & 13 carry 5 marks each.

Q1: Equation of (x+1)2-x2=0 has a number of real roots equal to: (1 Mark)
(a) 1
(b) 2
(c) 3
(d) 4

Q2: The sum of two numbers is 27, and the product is 182. The numbers are: (1 Mark)
(a) 12 and 13
(b) 13 and 14
(c) 12 and 15
(d) 13 and 24

Q3: A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train. (1 Mark)
(a) 30 km/hr
(b) 40 km/hr
(c) 50 km/hr
(d) 60 km/hr

Q4: A quadratic equation ax2 + bx + c = 0 has no real roots if _______________________________. (1 Mark)

Q5: The maximum number of roots for a quadratic equation is equal to (1 Mark)
(a) 1
(b) 2
(c) 3
(d) 4

Q6: The sum of the areas of two squares is 468 m2. If the difference of their perimeters is 24cm, find the sides of the two squares. (2 Marks)

Q7: If x =Unit Test: Quadratic Equations​, is a solution of the quadratic equation 3x2 + 2kx - 3 = 0, find the value of k. (2 Marks)

Q8: The product of two consecutive positive integers is 132. Find the integers. (2 Marks)

Q9: Solve the quadratic equation 2x2 - 7x + 3 = 0 by using the quadratic formula. (3 Marks)

Q10: Find two numbers whose sum is 30 and product is 200. (3 Marks)

Q11: Find the roots of the following quadratic equations by factorization: (3 Marks)
(i) x2 + 7x + 10 = 0
(ii) 3x2 - 5x - 2 = 0

Q.12: A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced and the cost of each article. (5 Marks)

Q13: The diagonal of a rectangular field is 60 meters more than the shorter side. If the longer side is 30 meters more than the shorter side, find the sides of the field. (5 Marks)


You can find the solutions to this Unit Test here: Unit Test (Solutions): Quadratic Equations​

The document Unit Test: Quadratic Equations is a part of the Class 10 Course Mathematics (Maths) Class 10.
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FAQs on Unit Test: Quadratic Equations

1. What are the standard forms of a quadratic equation?
Ans. The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants, and a ≠ 0. The values of a, b, and c determine the shape and position of the parabola represented by the equation.
2. How can I solve a quadratic equation?
Ans. A quadratic equation can be solved using several methods: factoring, completing the square, and applying the quadratic formula. The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), which can be used when factoring is difficult.
3. What is the discriminant, and how does it affect the solutions of a quadratic equation?
Ans. The discriminant is the part of the quadratic formula under the square root, given by b^2 - 4ac. It determines the nature of the roots: if it's positive, there are two distinct real roots; if it's zero, there's one real root; and if it's negative, there are two complex roots.
4. Can a quadratic equation have no real solutions?
Ans. Yes, a quadratic equation can have no real solutions if the discriminant (b^2 - 4ac) is less than zero. In this case, the solutions will be complex numbers.
5. What are some real-life applications of quadratic equations?
Ans. Quadratic equations are used in various real-life applications, such as calculating projectile motion in physics, determining profit maximization in business, and modeling certain types of growth in biology. They help in analyzing situations where relationships between variables are parabolic.
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