MTH100 Final Term Past Papers by Iqra Azhar

Q1. Write Pythagorean identity (2) marks

.Q 2 Find the value of cos(75) by trigonometric table. 5 marks

Cos(45+30)=cos[a]cos[b]-sin[a]sin[b] Cos75=cos45cos30-sin45sin30 Cos75=1/srt2 [srt3/2]-1/srt2[1/2] Cos75=1/srt2[st3-1]/2 Cos75=[srt3-1]/2srt2

Q3. Find the standard deviation 36,45,14,18,20,24,28,33,47,55,51.. 5 marks

Numbers: 36, 45, 14, 18, 20, 24, 28, 33, 47, 55, 51 Step 1: Mean (μ) = (36 + 45 + 14 + 18 + 20 + 24 + 28 + 33 + 47 + 55 + 51) / 11 ≈ 32.09 Step 2: Squared differences: (36 - 32.09)^2 ≈ 15.14 (45 - 32.09)^2 ≈ 166.24 (14 - 32.09)^2 ≈ 328.79 (18 - 32.09)^2 ≈

198. 05

(20 - 32.09)^2 ≈ 146.74 (24 - 32.09)^2 ≈ 65.64 (28 - 32.09)^2 ≈ 16.82 (33 - 32.09)^2 ≈

1. 83

(47 - 32.09)^2 ≈ 221.42 (55 - 32.09)^2 ≈ 525.94 (51 - 32.09)^2 ≈ 357.28 Step 3: Mean of squared differences = (15.14 + 166.24 + 328.79 + 198.05 + 146.74 + 65.64 +

16. 82 + 0.83 + 221.42 + 525.94 + 357.28) / 11 ≈ 193.62

Step 4: Standard Deviation = √193.62 ≈ 13.91

Q5. Find the slop of the (4,6)(2,1)

m=y2-y1/x2-x1

m=1-6/2-4 m=-5/-2 m=5/2

Q6. tanx/sinx=secx

[Sinx/cosx]*[1/sinx] 1/cosx

Sec x proved

Q7. sin2A=2Sin Acos A

sin(2A) = 2 * sin(A) * cos(A) To prove this identity, we'll use the sum-to-product trigonometric identities: sin(A + B) = sin(A) * cos(B) + cos(A) * sin(B) sin(2A) = sin(A + A) sin(A + A) = sin(A) * cos(A) + cos(A) * sin(A) sin(A + A) = sin(A) * cos(A) [1+ 1] sin(A + A) = 2 * sin(A) * cos(A)

Q8. if multiple of 4 is set of A and B is set of 2 multiples then set A is subset of B or B is subset of A???

A is the set of all multiples of 4: A = {4, 8, 12, 16, ...} B is the set of all multiples of 2: B = {2, 4, 6, 8, 10, 12, ...} Now, we need to check whether A is a subset of B or B is a subset of A. A set A is a subset of another set B if every element of A is also an element of B. To determine whether A is a subset of B, we need to check if every element of A is also in B. Looking at the sets, we can see that every element of A is also an element of B. Therefore, A is a subset of B. To check whether B is a subset of A, we need to see if every element of B is also in A. A = {4, 8, 12, 16, ...} B = {2, 4, 6, 8, 10, 12, ...} In this case, B contains elements that are not in A (e.g., 2, 6, 10, ...). Therefore, B is not a subset of A. In conclusion A is a subset of B. B is not a subset of A.

Q9. Frequency density find out if width is 5 and frequency is 23

Frequency Density = Frequency / Width Frequency Density = 23 / 5 Frequency Density ≈ 4.6 So, the frequency density in this case is approximately 4.6.

Q10. mode is 30 then and median 38 then find the mean..?

3median=mode +2mean 3[38]=30+2mean 114=30+2mean 114-30=2mean 86=2mean Mean=86/2 Mean= 43

Q11. if frequency=12 n freqnucy dencity=0.6 then find t he class width..?

Class Width = Frequency / Frequency Density Frequency = 12 Frequency Density = 0.6 Class Width = 12 / 0.6 Class Width = 20 So, the class width in this case is 20.

Q12. find the slope of the line through the (3,-1) and (-4,2)

Slope= m=y2-y1/x2-x1 m=2+1/-4-3 m=3/-7

Q13. the 3rd and the 4th terms of a geometric progression are 12 and 8 respectively. Find the sum to infinity of the progression.

. Let's assume that the first term is 'a' and the common ratio is 'r'.