Kenya Certificate of Secondary Education (K.C.S.E.)

[Pages:13]Name: ................................................An...sw...e...rs............ Index no .............................................. School: .......................................a...n...d ....................... Candidate's sign ............................ MorehtD1MPJTFt2UArIaAp1MeLtP/:eTe1YE:E/H/.../R:KAwE2C...1wUMP?wEG....AHUfRT...rOSeIeTvCU...eiSRk2s...0ciS1po...1enKp...eaPns...atyspa...taCp...Peea...rrpstei....frcisc...oam...te ...of...S...ec...on...da...ry...E...ducation (K.C.S.E.) FoVrisit

Mathematics Paper 1

INSTRUCTIONS TO CANDIDATES: Write your name, index number , Signature and write date of examination in the spaces provided The paper contains two sections. Section I and Section II. Answer ALL the questions in section I and any five questions in section II. Answers and working must be written on the question paper in the spaces provided below each

question. Show all steps in your calculations below each question. Marks may be given for correct working even if the answer is wrong. Non programmable silent electronic calculators and KNEC mathematical table may be used, except

where stated otherwise.

FOR EXAMINERS USE ONLY

SECTION 1

Question

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 TOTAL

Marks

SECTION II Question 17 18 19 20 21 22 23 24 TOTAL

Marks

Grand Total

This paper consists of 12 printed pages. Candidates should check to ascertain that all papers are printed as indicated and that no questions are missing

? Nyamira ? 2011

Form Four 1

Mathematics 121/1

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SECTAInOsNweIrs(50 MARKS)

1.

Evaluate without using tables or caanlcdulators

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FoVrisit

3. Solve the equation ( logx)2 ? logx ? 2 = 0

(3mks) (3mks)

(3mks)

4. The interior angle of a regular polygon is 9 times the exterior angle. How many sides does the

polygon have?

(3mks)

? Nyamira ? 2011

Form Four 2

Mathematics 121/1

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5.

Simplify the expression

x2 + 3x +2

x2 - 1and

Answers

Moreht6Ft.rpe:e//KwFCwPinwEd.ftRhreeeveiqksuciapoteinopnaPsoatfsptthaepPteaarnpsge.ercnsot mto the curve y= 3x2 ? 2x + 5 at the point where x = 2

FoVrisit

(2mks) (4mks)

7. Find all solutions between 0o and 180o of the equation, 4 Cos 2 + 3 = 0

(4mks)

8. The diagram below shows an isosceles right-angle triangle. Construct the locus of P, for

which APB= 45o

(2mks)

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Form Four 3

Mathematics 121/1

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9. Let x = 8 )

Answers

3 - 5 Write x in the form a + b 5

whearneda and b are integers.

(2mks)

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are

given

to

the nearest (3mks)

FoVrisit

11. Find the equation of the image of the line y = 3x + 5 under reflection in the line x = y (3mks)

12. In the diagram below, O is the centre of the circle of radius 5.0cm. If the area of the shaded region is

26.5cm2, calculate the area of the major segment cut off by the chord AB.

(4mks)

5

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Form Four 4

Mathematics 121/1

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13.

If Tan A = ?, show that

Cos2 A + SiAnn2sAwe=rs1

and

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FoVrisit

(3mks) (3mks)

15. During a certain ceremony, goats and chicken were slaughtered. The number of heads for both goats

and chicken was 45. The total number of legs was 100. Determine the exact number of goats and

chicken slaughtered.

( 4mks)

16. Find all the intergral values of x which satisfy the inequalities x + 11 4x ? 9 2 ( 2 ? x)

(4mks)

? Nyamira ? 2011

Form Four 5

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SECATnsIOweNrsII (50MKS)

Answer oannlydfive questions from this section.

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in

size

and

shape.

Kemunto

selected 3 balls (2mks)

FoVrisit

(b) Calculate the probability that she chooses; (i) Two blue balls and one red ball.

(2mks)

(ii) Two red balls and one blue ball (iii) At least one blue ball

(2mks) (2mks)

(iv) Three balls of the same colour.

(2mks)

? Nyamira ? 2011

Form Four 6

Mathematics 121/1

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18.

(a) Complete the table below

x

0o

30o

Sin x

0 0.5

an6d0oAnsw91e0ros

120o

150o

180o 0

210o -0.5

240o

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= 3 sin

sin x =

3 ? x for 3 sin ?

0o x in

x 240o this range.

0 (2mks)

FoVrisit

(d) State the amplitude and period of 3 sins ? x (e) Describe the transformations which take y = sin x to y = 3 sin ? x.

(2mks)

? Nyamira ? 2011

Form Four 7

Mathematics 121/1

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19.

The table below shows the tax levied aAt ndisfwfeerresnt rates for different level of income.

Monthly taxabnlde pay (shs) Rate of tax

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a nominal rent of the rent

(2mks)

(4mks)

sh.

b) A man invests Ksh. 10,000 in an account which pays 16% interest p.a. The interest is compound

quarterly. Find the amount in the account after 1 ? years.

(4mks)

? Nyamira ? 2011

Form Four 8

Mathematics 121/1

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