Time: 1 hour
M.M. 30
Attempt all questions.
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 =, 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
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