T HE UN!TED FiEf>UBUCY>F TANZANIA THE Ul•·i!TED REPUBLIC OF TANZAN!A THE UN!TED REPUSUC OF TANZANiA THE. UNiTEDREPUBUG OF TANZAN!A THE UNlTED REPUBLIC OF TANZANIA TJ-1£ UNJiED REPUBLiC OF TANZAN:'A T}-fE UNJTEO REPUBUC QF TANZANIA THE .UNITED REPUBUC OF TANZANiA THE UNITED RE;;}UBUC OF T ANZAN!A THe VI'< I TIED RIEPUBLIC OF TANZANIA THE J!iiiTED flEPUfJUC OF TANZANIA 7"'ri£ UNITED RE PU8LIC Ol" TANZANIA THE UNITED REPUBLIC OF TANZANIA THE UNITED REPUBLIC OF TANZANIA THE UNiTED REPUBLiC OF TANZANIA THE UNffED REPUBLIC OF TANZANIA THE UNITED REPUBLIC OF TANZA/Ii!A THE UNITED HEPUBUC OF TANZANIA THE UNITED REPUBLiC o.c TANZANJA Tt-iE UNITED REPUBL!O OF TANZANIA THE UNITED REPUBUC OF TANZ4N!A !HE UNJTED REPUBUC OF iANZAIVIA THE UNITED REPUBLIC OF TANZANIA THE UNITED AEP' " "'7-FD REP' 'BLIC o ·-- '"NZ'. "A THC u·'·J ·I-"D· . su_ u:v.,_ , ._, l-' ..._ - IV. U '- -if r:c.�vu.�:e Or ;r, ,Q.2.A.1A ,}!e UiiJ' .;;,...>nl!f-Vti.t...> C DP ·PNZ ··HvlA I AI! Vl¥1 ·EDFJEP06 L

.

I V c,p 1AN?.AN1A THE UN!TE.O REPUBLiC OF" TANZANIA THE U!'-ln""ELl HEPUBUC OF TANZANIA THE UNITED REPUBLiC OF TANZANIA THE UNJTED RS�tJUBLiC OF r ANZANJA THE UNt!ED REPUBLIC OF TANZANiA THE JJNjfED REPUBLsC OF TANZANIA Ti-iE UNPEO REPUBUC OF TANZANiA THE UNITED FiEPtJBUC OF TANZ.4NIA 7'HE UNJTED P.EPUBUC OF TANZ4NIA T.YE UNtiED P€PUBL.iC OF TA'•iZAN!l! THE UN! TED REPUBLIC OF TANZANiA THE UN!TED REPUBLIC OF TANZANIA THE UNITED FlEPUBLIC OF TANzANIA THE UN!TED REPU8UC OI= TANZANIA THE UN!7ED REPUBLiC o.c TANZAN.tA THE UNITED FfEP!.JBUC OF TANZArVlA THE :..JNfTED HEPUBUC Qp· TANZANiA THE UNITED REPUBLIC OF. T.4NZANIA THE UN/TEO REPUBLIC OF TANZANIA THE I.JNrifnstF,UeU(JJIS' TANZANIA THE UNFED FIEPUBUC OF TANZANIA THE UNITED REPUBLIC OF. TANZANiA THE U!''I/!Tt;D f;!t;PUBUC OF TANZANiA T,'-i£ UNri'C:D PE!-'UBUC OF 7ANZAN!A T'HE UNiTED HEPUBUC OF 1P.NZANIA THE UNI TED F!ETOUBUC OF·; ANZANtA 1}iE UNi'r£.0 ii£PU8L!C Of-- T4NZANJA "i'H1: UNf'l"i:D !--·'E.PUBU(; OF T"4NZAt1JiA r/i£ tHVf''£0 !1iiP!..;'8UC OF" TANZANiA 7HE UNir'fiD HEPUBUC OF' TANZANIA THE UNITED HE_P:JBLjC OF TfNZAN!J'>'li� '�er ,IJ��.!i�r.; OlfW!Zt UNiTED REPUBLIC OF TANZANIA '1':-i£ UNl FlED ifEPUBUCOJ- rA!\·'LAN�A f HE UN11''ED PEPU8i..iC OP "tAf"iLAUBUC OF TANZ,..1/oJ!A THE UNfTED RE?UBL"iC

\_...-0!"! A NZA!'ii A !'!f? UN!(&WUI '\tlt-in � S fo'P-fl. "14i'ljifj.·,: �itlfn-ffi#t':it:_lt�"Ql�' f�W.:

SECTION A (60 Marks)

Answer ALL questions in this section

1. (a) Find the value of the expression

( 4.75 + 1.31 )2 3.13

giving your answer in three decimal places.

(b) By rounding each term of the expression in (a) above to one significant figure, obtain a rough estimate of the expression.

(c) Express 1.21:3 as a rational number.

2. (a) How many even numbers greater than 2000 can be formed with digits 1, 2, 4 and 8 if each digit may be used only once?

(b) If n (A) = 8, n (B)= 12 and (AnB) = 5, fmd n (AU B).

'3. (a) Solve the equation tan 9 = 2 sinS for values of 9 from oo to 180°.

(b) If .il = 4i + 5j, h = 6i + 9i determine the magnitude and direction of the

vectorY = Yz.i! + .!...h. 6

4. (a) Solveforx if Vex -1) + 3 = 0.

(b) Using mathematical tables, evaluate

{36.12)3 X 750.9 (113.2ix·h2.5

S. (a) PXQ and RXS are straight lines and PR is parallel to SQ. Calculate PX and RX if PR=XQ = 18 em, XS = 9 em and SQ = 12 em.

X 18 em Q p

9� s

(b) An exterior angle of a regular polygon has degree measure of22Yz. Find the sum of degree measure of all the interior angles.

6. (a) A variable a varies directly as b and inversely as the square root of c.

0141

If a= 0.2 when b = 4 and c = 100, fmd the value of a when b = 16 and c = 64.

(b) John wants to invest a certain sum of money so that its value after 3 years will be sh. 1 00,000/=. How much should he invest at 5 % p.a. compound interest?

2

7. Both lines rand s pass through point (k, 9). Liner has a gradient of -4/ and passes through . /3 point (5, -3). Find

(a) the value ofk

(b) the equation of line s if it crosses the x axis at (-14, 0)

(c) the equation of a line t perpendicular to line r and passes through point (k, 9).

8. (a) Find the perimeter of a sector of a circle of radius 3.5 em if the angle of the sector is 144°.

(b) Find the area of triangle ABC if AB = 4 em, BC = 7 em and m (ABC)= 30°.

9. (a) Make t the subject of the expression 3rx - 2xy = 3ry.

(b) Find the remainder when 2x3 + 3x2 - 5x - 6 is divided by x + 1 and hence solve the equation 2x3 + 3x2 - 5 x - 6 = 0.

10. Below is the velocity- time graph for a certain car journey.

0141

0 20

(a) Calculate the acceleration of the car during the first 20 seconds.

(b) Find the value ofT if the final retardation is 0.5 m/s2.

(c) Calculate the total distance travelled by the car.

3

T 240 t

(s)

SECTION B (40 marks)

Answer FOUR (4) questions from this section.

11. (a) IfB1 = { (x, y):x + y < 6, x, y e R} and B2 = { (x, y): x- y < 2, x, y e R} draw the graphs ofB1 and B2 and shade the area represented by B1 n B2•

(b) Write down three inequalities which deflne the shaded area labelled A in the diagram below.

12. The following table represents age distribution of members of a school choir.

Age 14 15

Frequency 2 1

{a) How many students are in the school choir?

{b) What is the modal age?

16 17

3 6

(c) Calculate the mean age of the members of the school choir.

18

5

(d) What is the probability that a member chosen at random from the choir is

{i) 17 years old?

(ii) over or equal to 17 years?

19

3

(e) Draw a pie chart to show the age distribution of the members of the school choir.

0141 4

)

13. (a) Find the capacity in litres of a bucket 24 em in diameter at the top, 16 em in diameter at the bottom and 18 em deep.

·

(b) Given that the radius of the earth is 6400 k:m, fmd

(i) the length of the parallel latitude 30°N

(ii) the shortest distance along the surface of the earth from town Q whose position is (30° N, 10° E) to town P whose position is (30° N, 50° W).

14. (a) Find the image of the point (2, 4) when it is

(i) reflected about the line y + x = 0

(ii) rotated through 180° about the origin

(iii) translated by the vector� = (2, 4).

(b) A triangle with vertices 0(0, 0), B(2, 0) and C(2, 3) is enlarged by the matrix

to a triangle with vertices 0', B' and C'. Draw on the same set of axes the triangles

OBC and O'B'C'.

15. Given that f(x) ={ 1 x2+1

whenx