Mathematics Part 2

Triangles Question 1.State which pairs of triangle in the figures, are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form : Solution:(i) In ∆s ABC and PQR, we observe that∠A = ∠P = 60°, ∠B = ∠Q = 80° and […]

Triangles Question 1.In figures, (i) and (ii), DE || BC. Find EC in (i) and AD in (ii). Solution:(i) In Fig. (i),since DE || BC, thereforeAD/DB = AE/EC or 1.5/3 = 1/ECor EC = 3/1.5 or EC = (3×10)/15 cm ∴ EC = 2 cm (ii) In Fig. (ii),since DE || BC, thereforeAD/DB =AE/EC or AD/7.2 = 1.8/5.4or AD = 18/54 x 72/10 cm ∴ AD = 2.4 cm. Question 2.E and F are

Triangles Question 1.Fill in the blanks using the correct word given in brackets : Solution: Question 2.Give two different examples of pair of(i) similar figures(ii) non-similar figures. Solution:(i) Two different examples of pair of similar figures are : (ii) Two different examples of pair of non-similar figures are : Question 3.State whether the following quadrilaterals

Arithmetic Progressions Question 1.Which term of the AP : 121, 117, 113, …, is its first negative term? Solution:121, 117, 113, …a = 121, d = 117 – 121 = – 4an = a + (n – 1 )d= 121 + in – 1) x (- 4)= 121 – 4n + 4 = 125 – 4nFor

Arithmetic Progressions Question 1.Find the sum of the following APs:(i) 2, 7, 12, … , to 10 terms.(ii) – 37, – 33, – 29, … , to 12 terms.(iii) 0.6, 1.7, 2.8, … , to 100 terms. Solution:(i) Let a be the first term and d be the common difference of the given AP. Then,

Arithmetic Progressions Question 1.Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the AP: Solution:Blanks may be filled as under:(i) an = a + (n – 1)d or an = 7 + (8 – 1)3or an = 7 + 7 × 3

Arithmetic Progressions Question 1.In which of the following situations, does the list of numbers involved make an arithmetic progression, and why?(i) The taxi fare after each km when the fare is Rs 15 for the first km and Rs 8 for each additional km.(ii) The amount of air present in the cylinder when a vacuum

Quadratic Equations Question 1.Find the nature of the roots of the following quadratic equations. If the real roots exist, find them:(i) 2×2 – 3x + 5 = 0(ii) 3×2 – 4√3x + 4 = 0(iii) 2×2 – 6x + 3 = 0 Solution:(i) The given equation is 2×2 – 3x + 5 = 0.Here, a = 2, b =

Quadratic Equations Question 1.Find the roots of the following quadratic equations, if they exist by, the method of completing the square:(i) 2×2 – 7x + 3 = 0(ii) 2×2 + x – 4 = 0(iii) 4×2 + 4√3x + 3 = 0(iv) 2×2 + x + 4 = 0 Solution:(i) The equation 2×2 – 7x + 3 is the same

Quadratic Equations Question 1.Find the roots of the following quadratic equations by factorisation:(i) x3 – 3x – 10 = 0(ii) 2×2 + x – 6 = 0(iii) √2×2 + 7x + 5√2 = 0(iv) 2×2 – x + 1/8 = 0(v) 100×2 – 20x + 1 = 0 Solution:(i) We have:x2 – 3x – 10 = 0or x2 – 5x + 2x – 10 = 0or