Free Printable Interpolation

1.

Estimate f(1.5) using Lagrange interpolation.

a)

−0.8673

b)

-0.7214

c)

−0.9773

d)

-0.9113

2.

Find f(2) for the data f(0) = 1, f(1) = 3 and f(3) = 55 using Newton's divided difference formula.

a)

25

b)

21

c)

23

d)

32

3.

Find f(0.25) using Newton's divided difference formula

a)

3.826

b)

3.2567

c)

3.2113

d)

3.912

4.

a)

3.125

b)

3.327

c)

3.542

d)

3.837

5.

The methods to find the polynomials approximation are ..

a)

Lagrange interpolation

b)

Newton's Divided Difference

c)

Natural Cubic Spline

d)

Clamped Cubic Spline

6.

f(x)-f(x-h)=

a)

$\Delta f\left(x\right)$

b)

$\nabla f\left(x\right)$

c)

E(x)

d)

none

7.

Backward difference operator pronounced as

a)

delta

b)

lamda

c)

nabla

d)

alpha

8.

$\Delta^2y_0=$

a)

$\Delta y_1-\Delta y_0$

b)

$\Delta y_0-\Delta y_1$

c)

$\Delta^2y_1-\Delta^2y_0$

d)

$\Delta y_1+\Delta y_0$

9.

∆2^x=…………….

a)

2^(x+h)-2^x

b)

2^(x+h)

c)

2^(x-h)-2^x

d)

2^(x-h)

10.

Predicting the number of days to finish when you read 40 pages is an example of:

a)

Interpolation

b)

Extrapolation

c)

An outlier

11.

Predicting the band grade after 3.5 hours of practice is an example of:

a)

Interpolation

b)

Extrapolation

c)

An outlier

12.

This means to predict a value inside the known values on a graph.

a)

trend line

b)

interpolation

c)

extrapolation

d)

causation

13.

This means to predict a value outside the known values on a graph.

a)

trend line

b)

interpolation

c)

extrapolation

d)

causation

14.

What is the approximate volume of 300 g according to the graph above?

a)

200 mL

b)

250 mL

c)

300 mL

d)

350 mL

15.

A student used the graph below to determine that the maximum heart rate of a person should be 45 beats per minute when a person is 80 years old. Was this point determined by extrapolation or interpolation?

a)

extrapolation

b)

interpolation

16.

About how many male math teachers were there in 2006?

a)

15

b)

30

c)

35

d)

45

17.

$1+x+x^2+x^3+...$

a)

$e^x$

b)

$\sin x$

c)

$\cos x$

d)

$\frac{1}{1-x}$

18.

$1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+...$

a)

$e^x$

b)

$\sin x$

c)

$\cos x$

d)

$\frac{1}{1-x}$

19.

Given $\frac{\text{d}y}{\text{d}x}=1-y,\ y\left(0\right)=0$ using a step size of h=0.1 , the value of y(0.2) using Euler’s method is most nearly

a)

0.1

b)

0.119

c)

0.19

d)

0.01

20.

Which of the following are single step techniques?

a)

Taylor's

b)

Euler's

c)

RK Mehod

d)

Milne's

21.

Modified Euler's method gives more _______results

a)

accurate

b)

moderate

c)

inconclusive

d)

none

22.

The error in Taylors series is given by

a)

$\frac{h^n}{n!}f^n\left(\theta\right)$

b)

$\frac{h^n}{n}f^n\left(\theta\right)$

c)

$\frac{h^n}{n!}f'\left(\theta\right)$

d)

$\frac{h^n}{n!}f^"\left(\theta\right)$

23.

$\frac{dy}{dx}=x-y$ and $f(3)=1$ Use Euler’s method with two steps of equal size to approximate $f(6)$

4 lines

24.

$\frac{dy}{dx}=2x+y$ and $y(1)=k$ Using Euler’s method, starting at $x=1$ with a step-size of 0.5, gives the approximation $y(1.5)\approx4$ . Find k.

4 lines

25.

$\frac{dy}{dx}=x-2y+2$ and $f(0)=2$ Use Euler’s method with two steps of equal size to approximate $f(2.4)$

4 lines

26.

$\frac{dy}{dx}=2x-2y+3$ and $y(3)=k$ Using Euler’s method, starting at x=3 with a step-size of 1, gives the approximation $y(4)\approx-6$ Find k.

4 lines

27.

$\frac{dy}{dx}=x+y+1$ and $f(2)=-1$ Use Euler’s method with two steps of equal size to approximate $f(2.6)$

4 lines

28.

$\frac{dy}{dx}=3x-2y$ and $y(0)=k$ Using Euler’s method, starting at x=0 with a step-size of 1, gives the approximation $y(2)\approx4.5$ Find k.

4 lines

29.

$\frac{dy}{dx}=x-y-2$ and $f(-1)=3$ Use Euler’s method with three steps of equal size to approximate $f(2)$ .

4 lines

30.

$\frac{dy}{dx}=x+2y-1$ and $y(-1)=k$ Using Euler’s method, starting at x=−1 with a step-size of 1, gives the approximation $y(1)\approx11$

4 lines

31.

$\frac{dy}{dx}=x+y$ and $f(1)=2$ Use Euler’s method with two steps of equal size to approximate $f(3)$

4 lines

32.

$\frac{dy}{dx}=3x+2y+1$ and $y(0)=k$ Using Euler’s method, starting at x=0 with a step-size of 2, gives the approximation $y(2)\approx1$

4 lines

Interpolation

Total questions: 32

Worksheet time: 1hrs 27mins

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