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Worksheet
1) The roots of 3x²-7x+4 = 0 are ___, ___.
2) The discriminant of the equation bx²+ax+c = 0, b≠0 is _____.
3) If the roots of ax²+bx+c = 0 are equal, then the value of c is _____.
4) The sum of the ages of a son and his father is 35 years and the product is 150(years²). Their ages are ___, ___.
5) If (x/2) +(6/x) = 4, then the values of x are _____.
6) The nature of the quadratic equation x²-8x+12 = 0 is _____.
7) The value of k for which x = -2 is a root of the equation kx²+x-6 = 0 is _____.
8) The value of k for which the equation 2x²+8kx+8 = 0 has equal roots is _____.
9) The LCM of the smallest two-digit composite number and the smallest composite number is _____.
10) The greatest number, which divides 1251, 9377, and 15628 leaving remainders 1, 2, and 3, respectively is _____.
11) (2+√5)/3 is (a/an) _____ number.
12) The HCF of two numbers is 27 and their LCM is 162. If one of the numbers is 54, the other number is _____.
13) Ravi has a field with a total area of 1260m². He uses it to grow mango and orange. The land used to grow mango(mango-land) is in the shape of rectangular in shape while the orange-land is in the shape of square as shown in the following figure. The length of the mango-land is 3 meters more than twice the length of the orange-land.
Based on the above information, answer the following questions:
If the length of the orange-land is x meters, then the length of the mango-land of the field is _____.
The perimeter of the field is _____.
If the total area of the field is 1260m², then the value of x is _____.
The area of the mango-land is _____.
The area of orange-land is _____.
The ratio of the areas of the mango and the orange lands is _____.
14) Express 156 as the product of primes.
15) If xy=180 and HCF(x,y) = 3, then find the LCM(x,y).
16) Prove that √5 is an irrational number.
17) Given that √3 is an irrational, prove the 5+2√3 is an irrational.
18) _____ is the HCF of two consecutive even numbers.
19) (Wait, it is not given, maybe it was a numbering issue by the teacher, go to the next question)
20) The sum of four numbers in an AP is 20 and the sum of their squares is 120. Find the numbers.
[Hint: Take the numbers as a-3d, a-d, a+d, a+3d]
21) Which term of the AP: 27, 24, 21, ... is zero?
22) Find the values of k for which the quadratic equation 9x²-3kx+k = 0 has equal roots.
23) The discriminant of the quadratic equation (x-5)² = 0.
24) When Sₙ is given in an AP, then the nᵗʰ term of the AP is: tₙ = _____.
25) In an AP, if a=3.5, d=0 and n=101, then tₙ = _____.
26) If the numbers a, b, c, d, e form an AP, then the value of a-4b+6c-4d+e will be _____.
27) If 18, a, b, -3 are in an AP, then a+b = _____.
28) The 10ᵗʰ term of the sequence √3, √12, √27, ... is _____.
29) The next term of the AP: √7, √28, √63, ... is _____.
30) Find the 10ᵗʰ term from the last of the AP: 8, 10, 12, ..., 126.
31) Determine k so that k+2, 4k-6, and 3k-2 are the tree consecutive terms of an AP.
32) The sum of the first ten multiples of 5 is _____.
33) The numbers are in an AP and their sum is 24. Then, the value of the middle term is _____.
34) How many terms of the AP: 45, 39, 33, ..., must be taken, so that, their sum is 180? Explain the double answer.
35) The sum of 5th and 7th terms of an AP is 52 & the 10th term is 46. Find the AP.
36) The sum of 5th and 9th terms of an AP is 72 & the sum of 7th and 12th terms is 97. Find the AP.
37) A train travels a distance of 480km at a uniform speed. If the speed had been 8km/hr less, then it would have taken 4hrs more to cover the same distance. Find the speed of the train.
38) A train travels a distance of 300km at a uniform speed. If the speed of the train is increased by 5km/hr, the journey would have taken two hours less. Find the original speed of the train.
39) If the sum of the first n terms of an AP is given by Sₙ = 4n²-3n, find the nᵗʰ term of the AP.
40) Which term of the progression 65, 61, 57, 53, ..., is the first negative term?
Answer Key
1, 4/3
a²-4bc
b²/4a
5, 30
2, and 6
Different real roots
2
1, -1
20
625
An irrational
81
i) 2x+3 or 43m
ii) 8x+6 or 166m
iii) 20m
iv) 860m²
v) 400m²
vi) 43:202*2*3*13
60
(Do it yourself)
(Do it yourself)
2
(Numbering problem)
2, 4, 6, 8
10th
4, 0
0
(2Sₙ/n) - a
3.5
0
15
√300
√112
108
3
275
8
6 and 10, -ve and +ve terms cancel out each other
1, 6, 11, ...
6, 11, 16, ...
40km/hr
25km/hr
8n-7
18
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