12th Business Maths Weekly Test - 2 ( Numerical Methods )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Weekly Test - 2 ( Numerical Methods )-Aug 2020

Time : 2.00 Hours

Part - A

Generic 2 - Answer All Question

From the following data find y at x = 43 and x = 84

x 40 50 60 70 80 90

y 184 204 226 250 276 304

Evaluate ∆(log ax).

Using Newton’s forward interpolation formula find the cubic polynomial.

x 0 1 2 3

f(x) 1 2 1 10

Find f(0.5) if f(−1) = 202, f (0)= 175, f(1) = 82 and f(2) = 55

The following data gives the melting point of a alloy of lead and zinc where ‘t’ is the temperature in degree c and P is the percentage of lead in the alloy

P 40 50 60 70 80 90

T 180 204 226 250 276 304

Find the melting point of the alloy containing 84 percent lead.

If f(x) = x²+ 3x than show that Δf(x) = 2x + 4

If u₀ = 560, u₁ = 556, u₂ = 520, u₄ = 385, show that u₃= 465

Using interpolation, find the value of f(x) when x = 15

x 3 7 11 19

f(x) 42 43 47 60

Find the value of f (x) when x = 32 from the following table

x 30 35 40 45 50

f(x) 15.9 14.9 14.1 13.3 12.5

From the following table obtain a polynomial of degree y in x

x 1 2 3 4 5

y 1 -1 1 -1 1

Using interpolation estimate the business done in 1985 from the following data

Year 1982 1983 1984 1986

Business done (in lakhs) 150 235 365 525

If f (x) = e^ax then show that f(0), Δ(0), Δ² are in G.P

Using Lagrange’s interpolation formula find a polynomial which passes through the
points (0, –12), (1, 0), (3, 6) and (4,12).

Use Lagrange’s formula and estimate from the following data the number of workers
getting income not exceeding Rs. 26 per month

Income not exceeding (Rs) 15 25 30 35

No. of workers 36 40 45 48

If y = x³− x²+ x − 1 calculate the values of y for x = 0,1,2,3,4,5 and form the forward differences table.

Using graphic method, find the value of y when x = 48 from the following data:

x 40 50 60 70

y 6.2 7.2 9.1 12

In an examination the number of candidates who secured marks between certain interval were as follows

Marks 0-19 20-39 40-59 60-79 80-99

No.of.candidates 41 62 65 50 17

If h = 1 then prove that (E⁻¹Δ)x³= 3x²− 3x + 1.

Find the missing figures in the following table

x 0 5 10 15 20 25

y 7 11 - 18 - 32

Evaluate Δ\(\left[ \frac { 1 }{ (x+1)(x+2) } \right] \) by taking ‘1’ as the interval of differencing

Find the missing entries from the following

x 0 1 2 3 4 5

y = f(x) 0 - 8 15 - 35

The area A of circle of diameter ‘d’ is given for the following values

D 80 85 90 95 100

A 5026 5674 6362 7088 7854

Prove that
(1 + Δ)(1 - ∇) = 1

Using interpolation estimate the output of a factory in 1986 from the following data

Year 1974 1978 1982 1990

Output in 1000 tones 25 60 80 170

The following data relates to indirect labour expenses and the level of output

Months Jan Feb Mar Apr May June

Units of output 200 300 400 640 540 580

Indirect labour
expenses (Rs) 2500 2800 3100 3820 3220 3640

Estimate the expenses at a level of output of 350 units, by using graphic method

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Year	1982	1983	1984	1986
Business done (in lakhs)	150	235	365	525

Months	Jan	Feb	Mar	Apr	May	June
Units of output	200	300	400	640	540	580
Indirect labour expenses (Rs)	2500	2800	3100	3820	3220	3640

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12th Standard English Medium

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12th Business Maths Weekly Test - 2 ( Numerical Methods )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Weekly Test - 2 ( Numerical Methods )-Aug 2020

Part - A

Generic 2 - Answer All Question

From the following data find y at x = 43 and x = 84 x 40 50 60 70 80 90 y 184 204 226 250 276 304

Evaluate ∆(log ax).

Using Newton’s forward interpolation formula find the cubic polynomial. x 0 1 2 3 f(x) 1 2 1 10

Find f(0.5) if f(−1) = 202, f (0)= 175, f(1) = 82 and f(2) = 55

The following data gives the melting point of a alloy of lead and zinc where ‘t’ is the temperature in degree c and P is the percentage of lead in the alloy P 40 50 60 70 80 90 T 180 204 226 250 276 304 Find the melting point of the alloy containing 84 percent lead.

If f(x) = x2 + 3x than show that Δf(x) = 2x + 4

If u0 = 560, u1 = 556, u2 = 520, u4 = 385, show that u3 = 465

Using interpolation, find the value of f(x) when x = 15 x 3 7 11 19 f(x) 42 43 47 60

Find the value of f (x) when x = 32 from the following table x 30 35 40 45 50 f(x) 15.9 14.9 14.1 13.3 12.5

From the following table obtain a polynomial of degree y in x x 1 2 3 4 5 y 1 -1 1 -1 1

Using interpolation estimate the business done in 1985 from the following data Year 1982 1983 1984 1986 Business done (in lakhs) 150 235 365 525

If f (x) = eax then show that f(0), Δ(0), Δ2 are in G.P

Using Lagrange’s interpolation formula find a polynomial which passes through the points (0, –12), (1, 0), (3, 6) and (4,12).

Use Lagrange’s formula and estimate from the following data the number of workers getting income not exceeding Rs. 26 per month Income not exceeding (Rs) 15 25 30 35 No. of workers 36 40 45 48

If y = x3 − x2 + x − 1 calculate the values of y for x = 0,1,2,3,4,5 and form the forward differences table.

Using graphic method, find the value of y when x = 48 from the following data: x 40 50 60 70 y 6.2 7.2 9.1 12

In an examination the number of candidates who secured marks between certain interval were as follows Marks 0-19 20-39 40-59 60-79 80-99 No.of.candidates 41 62 65 50 17

If h = 1 then prove that (E−1Δ)x3 = 3x2 − 3x + 1.

Find the missing figures in the following table x 0 5 10 15 20 25 y 7 11 - 18 - 32

Evaluate Δ\(\left[ \frac { 1 }{ (x+1)(x+2) } \right] \) by taking ‘1’ as the interval of differencing

Find the missing entries from the following x 0 1 2 3 4 5 y = f(x) 0 - 8 15 - 35

The area A of circle of diameter ‘d’ is given for the following values D 80 85 90 95 100 A 5026 5674 6362 7088 7854

Prove that (1 + Δ)(1 - ∇) = 1

Using interpolation estimate the output of a factory in 1986 from the following data Year 1974 1978 1982 1990 Output in 1000 tones 25 60 80 170

The following data relates to indirect labour expenses and the level of output Months Jan Feb Mar Apr May June Units of output 200 300 400 640 540 580 Indirect labour expenses (Rs) 2500 2800 3100 3820 3220 3640 Estimate the expenses at a level of output of 350 units, by using graphic method

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From the following data find y at x = 43 and x = 84

x 40 50 60 70 80 90

y 184 204 226 250 276 304

Using Newton’s forward interpolation formula find the cubic polynomial.

x 0 1 2 3

f(x) 1 2 1 10

The following data gives the melting point of a alloy of lead and zinc where ‘t’ is the temperature in degree c and P is the percentage of lead in the alloy

P 40 50 60 70 80 90

T 180 204 226 250 276 304

Find the melting point of the alloy containing 84 percent lead.

If f(x) = x²+ 3x than show that Δf(x) = 2x + 4

If u₀ = 560, u₁ = 556, u₂ = 520, u₄ = 385, show that u₃= 465

Using interpolation, find the value of f(x) when x = 15

x 3 7 11 19

f(x) 42 43 47 60

Find the value of f (x) when x = 32 from the following table

x 30 35 40 45 50

f(x) 15.9 14.9 14.1 13.3 12.5

From the following table obtain a polynomial of degree y in x

x 1 2 3 4 5

y 1 -1 1 -1 1

Using interpolation estimate the business done in 1985 from the following data

Year 1982 1983 1984 1986

Business done (in lakhs) 150 235 365 525

If f (x) = e^ax then show that f(0), Δ(0), Δ² are in G.P

Using Lagrange’s interpolation formula find a polynomial which passes through the
points (0, –12), (1, 0), (3, 6) and (4,12).

Use Lagrange’s formula and estimate from the following data the number of workers
getting income not exceeding Rs. 26 per month

Income not exceeding (Rs) 15 25 30 35

No. of workers 36 40 45 48

If y = x³− x²+ x − 1 calculate the values of y for x = 0,1,2,3,4,5 and form the forward differences table.

Using graphic method, find the value of y when x = 48 from the following data:

x 40 50 60 70

y 6.2 7.2 9.1 12

In an examination the number of candidates who secured marks between certain interval were as follows

Marks 0-19 20-39 40-59 60-79 80-99

No.of.candidates 41 62 65 50 17

If h = 1 then prove that (E⁻¹Δ)x³= 3x²− 3x + 1.

Find the missing figures in the following table

x 0 5 10 15 20 25

y 7 11 - 18 - 32

Find the missing entries from the following

x 0 1 2 3 4 5

y = f(x) 0 - 8 15 - 35

The area A of circle of diameter ‘d’ is given for the following values

D 80 85 90 95 100

A 5026 5674 6362 7088 7854

Prove that
(1 + Δ)(1 - ∇) = 1

Using interpolation estimate the output of a factory in 1986 from the following data

Year 1974 1978 1982 1990

Output in 1000 tones 25 60 80 170

The following data relates to indirect labour expenses and the level of output

Months Jan Feb Mar Apr May June

Units of output 200 300 400 640 540 580

Indirect labour
expenses (Rs) 2500 2800 3100 3820 3220 3640

Estimate the expenses at a level of output of 350 units, by using graphic method