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NATIONAL TEST IN MATHEMATICS COURSE B

SPRING 2002

Directions

Test time 240 minutes for Part I and Part II together. We recommend that you spend no more than60 minutes on Part I.

Resources Part I: Formulas for the National Test in Mathematics Course BPlease note calculators are not allowed in this part.

Part II: Calculators, and Formulas for the National Test in Mathematics Course B.

Test material The test material should be handed in together with your solutions.

Write your name, the name of your education programme / adult education on all sheets

of paper you hand in.Solutions to Part I should be handed in before you retrieve your calculator. You should

therefore present your work on Part I on a separate sheet of paper. Please note that you

may start your work on Part II without a calculator.

The test The test consists of a total of 17 problems. Part I consists of 9 problems and Part IIconsists of 8 problems.

To some problems (where it says Only answer is required) it is enough to give short an-swers. For the other problems short answers are not enough. They require that you writedown what you do, that you explain your train of thought, that you, when necessary,draw figures. When you solve problems graphically/numerically please indicate howyou have used your resources.

Problem 17 is a larger problem which may take up to an hour to solve completely. It isimportant that you try to solve this problem. A description of what your teacher willconsider when evaluating your work, is attached to the problem.

Try all of the problems. It can be relatively easy, even towards the end of the test, toreceive some points for partial solutions. A positive evaluation can be given even forunfinished solutions.

Score and The maximum score is 44 points.mark levels

The maximum number of points you can receive for each solution is indicated aftereach problem. If a problem can give 2 Pass-points and 1 Pass with distinction-pointthis is written (2/1). Some problems are marked with , which means that they morethan other problems offer opportunities to show knowledge that can be related to thecriteria for Pass with Special Distinction.

Lower limit for the mark on the testPass: 12 pointsPass with distinction: 26 points of which at least 6 Pass with distinction points.Pass with special distinction: The requirements for Pass with distinction must be wellsatisfied. Your teacher will also consider how well you solve the -problems.

Name: School:

Education programme/adult education:

Concerning test material in general, the Swedish Board of Education refers to the Official

Secrets Act, the regulation about secrecy, 4th chapter 3rd paragraph. For this material, the

secrecy is valid until the expiration of June 2002.

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Part I

1. a) In a co-ordinate system, draw a straight line whose gradient is 3.Only answer is required (1/0)

b) Write down the equation to the line you have drawn.Only answer is required (1/0)

2. a) Expand 2)3( +x Only answer is required (1/0)

b) Simplify the expression )4(2252 ++ xx as far as possible.

Only answer is required (1/0)

3. Solve the equations

a) 04062 =+ xx (2/0)

b) 0)3( =xx (1/0)

4. In the figure below, you can see the graph to the function axy += 2

What is the value ofa? Only answer is required (1/0)

This part consists of 9 problems that should be solved without the aid of a calcula-

tor. Your solutions to the problems in this part should be presented on separate

sheets of paper that must be handed in before you retrieve your calculator. Please

note that you may begin working on Part II without the aid of a calculator.

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5. The point (2, 5) is on the line 4+= kxy . Calculate the value ofk. (2/0)

6. In a statistical survey, the nonresponse was rather high.How can this nonresponse affect the interpretation of the results? (1/0)

7. The pointsA,B and Care on a circle.O is the centre of the circle.

Calculate the angles of the triangleABC.

Calculations based on measurements of

the figure are not accepted

(1/1)

8. sa is going to bake a sponge cake and takes two eggs from a package of sixeggs. What she does not know is that her son has played a trick on her and ex-changed two of the eggs for boiled eggs.

a) What is the probability that the first egg sa picks is unboiled?Only answer is required (1/0)

b) What is the probability that both the eggs sa picks are unboiled? (0/1)

9. The figure below can be used for solving simultaneous equations graphically.

a) What are the solutions to the simultaneous equations?

Only answer is required (1/0)

b) What are the simultaneous equations? Only answer is required (0/2)

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Part II

10. Johanna and Michael buy CD-records in London. The CD-records are colourcoded according to price. Johanna pays 32 for two red and one blue CD-record.Michael pays 36 for one red and three blue CD-records. Johannas purchase can

be described by the equation 322 =+yx .

a) Describe Michaels purchase with a similar equation. (1/0)

b) Use the equations to calculate the priceof a red and blue CD-record respectively. (2/0)

11. Hugo, Ludvig and Fredrik have all solved the same ineguality, but they have re-cieved different answers.

1:Answer1

1010

102818

628418

>

+>

+>

xx

x

x

xx

1:A1

1010

281018

628418

>

>

>

>

+>

xnswerx

x

x

xx

1:Answer1

1010

102818

628418

>

+>

+>

xx

x

x

xx

Hugo Ludvig Fredrik

a) Which solution is correct? Only answer is required (1/0)

b) What mistakes do the others make? (1/1)

12. In a co-ordinate system three points have beenpointed out. Wilma believes that these threepoints are on a straight line. Madeleine claimsthat the points are not on a straight line, they

just appear to be.

Find out who is right.

(1/1)

This part consists of 8 problems and you may use a calculator when solving them.

Please note that you may begin working on Part II without a calculator

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13. Per offers his classmates a chance to win money.

Play my game! Bet $1 and then roll the six-sided dice. Not more than three eyes alto-gether will give you $10 back.

a) What is the probability of getting not more than three eyes when two diceare rolled? (1/0)

b) Who gains from the game, Per or his classmates?

Justify your answer (0/2/)

14. The figure to the right can be used to showthat the sum of all angles in a triangle is180.

The lineL is parallel to sideAB. Then , forexample, the alternate angles u andx are ofequal size.

Use the text and the figure above to show how it can be concluded that the sum ofall angles in a triangle is 180. (1/2)

15. When Stinas teacher reports the results of a test in mathematics, the teacher wri-

tes on the board:

Maximum score: 40pAverage score: 25pMedian: 21pNumber of participating students: 29

Stinas test score is 25. She claims that the number of classmates who have higherscores than she is equal to the number of classmates who have lower scores thanshe.

Decide whether Stinas statement is true or false. Explain why. (0/2)

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16. Pelle is standing on a rock next to a lake and throws a stone out over the lake.Aftertseconds the height of the stone above the surface of the water is h(t) metres

where 29.48.95.8)( ttth +=

a) When is the stone at the height 10 metres above the surface of the water? (1/1)

b) Calculate the stones maximum height above the surface of the water. (0/1)

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17.

The lines 13+= kxy and 1+=xy intersect at a point

in the first quadrant ifkis chosen in a suitable way.Then the co-ordinates of the intersection are positive.

Let 0=k and draw the both lines.Determine the point of intersection between the two lines.

The lines 13+= kxy , 1+=xy and they-axis form a triangle when 0=k .

The lines 13+= kxy , 1+=xy and the y-axis form another triangle when1=k .

Calculate and compare the areas of the triangles.

The area enclosed by the lines 13+= kxy , 1+=xy and they-axis depends

on the value ofk. Investigate and describe how the area depends on k, oncondition that the lines intersect in the first quadrant.

(3/4/)

When assessing your work with problem 17 the teacher will consider the fol-

lowing:

How well you calculate and compare the areas of the triangles How well you justify your conclusions How well you describe how the area depends on k

How well you present your work How well you use the mathematical language