TANZANIA PARENTS ASSOCITAION (TAPA)

KASULU SECONDARY SCHOOL P.O.BOX 46, KASULU

FORM FIVE MID-TERM EXAMINATION

ADVANCED MATHEMATICS PAPER 1

TIME: 2.30 HOURS TUESDAY, 24th .03.2015

INSTRUCTION

1. This paper consists TEN (10) questions only.

2. Answer all questions clearly in the answer sheets provided.

3. Spent at most 15 minutes to every question attempted.

4. Scientific calculator or mathematical tables are allowed in the examination room.

5. Write your registered name on every answer sheet used

6. Whenever necessary use Л= 3.14.

2. a) Using basic properties of set operations, show that (A U B) ∩ A = Ø

b) Use Venn diagram to verify that (A∩ B) U (A U B ) = A U B

3. a) Given that a = 2RsinA; b = 2 RsinB; c = 2RsinC, prove that in any triangle ABC

b) Solve triangle XYZ given ∠X =90◦, ∠Y =23◦17 and YZ =20.0 mm. Determine also its area.

5. a)Find the area of parallelogram whose vertices are A(3,4), B(0,4), C(-2,-2), and D(-3,2).

b) Find the angle between the lines intersecting at a certain point P whose equations are given by

L1: 3x + 4y -5 = 0 and L2: 4x – 3y + 2 = 0.

6.The tensile strength in mega Pascal’s for 15 samples of tin were determined and found to be:

34.61, 34.57, 34.40, 34.63, 34.63, 34.51, 34.49, 34.61, 34.52, 34.55, 34.58, 34.53, 34.44, 34.48, 34.40

Calculate the mean, variance and standard deviation from the mean for these 15 values, correct to 4 significant

figures.

Advance mathemtics Mid-term examination Mr. Kibbi K.K

7. Show that the following argument is valid;If I study hard, then I will not fail Mathematics.

If I do not play truant, then I will study.

But I fail Mathematics. Therefore, I played truant.

8. a) Express in polar co-ordinates the position (−4, 3).

b) Determine the angle, in degrees and minutes, subtended at the centre of a circle of diameter 42mm

by an arc of length 36 mm. Calculate also the area of the minor sector formed.

9. a) Find the point that divides the line of segment internally and whose end coordinates are P(8,9) and

Q(-7,4) in the ratio 3:5.

10. a) Make the truth table for the contrapositive of the statement P → Q

b) Write down the statement corresponding to the following electrical network.

ALL THE BEST WISHES

BY MR. KIBBI K.K

Advance mathemtics Mid-term examination Mr. Kibbi K.K

TANZANIA PARENTS ASSOCITAION (TAPA)

KASULU SECONDARY SCHOOL P.O.BOX 46, KASULU

FORM FIVE MID-TERM EXAMINATION

ADVANCED MATHEMATICS PAPER 2

TIME: 2.30 HOURS TUESDAY, 26th .03.2015

INSTRUCTION

1. This paper consists only TEN (10) questions.

2. Answer all questions clearly in the answer sheets provided.

3. Spent at most 15 minutes to every question attempted.

4. Scientific calculator or mathematical tables are allowed in the examination room.

5. Any cheating in the examination room will not be tolerated

6. Whenever necessary use Л= 3.14.

1.a) The product of sets A and B is defined by M x N = {(a,b): mϵM and nϵN}. Find M x N when M = {x, 3, z}

and N= {s, t, y.}.

b) If A, B and C are any three sets, prove that their union is associative such that (A ᴗ B) ᴗC =Aᴗ(BᴗC)

2. a) If x and y are two distinct values of Ɵ when 00 ≤ Ɵ ˂ 900 satisfy the equation, 3sin2Ɵ + 6sin2Ɵ – 4 = 0.

Find the exactly value of tan(x + y).

3. Find the equations of the lines with equation 2x2 + 5xy - 12y2 = 0 intersect at point P ( x, y ) and then find

the angle between them.

4.The weights in kilogram of a sample of 700 males of a certain minor settlement are given in the table below.

Weight 62 63 64 65 66 67 69 70 71 72

Frequency 25 35 52 84 120 135 61 40 33 14

Calculate;

i. The mean weight of the males

ii. The standard deviation of the weights to two decimal places.

b) Using the principle of mathematical induction prove that 32n+2 – 8n -9 is divisible by 8.

Advance mathemtics Mid-term examination Mr. Kibbi K.K

6. a) If f(x) = x2 + 2x +2, find the two functions g(x) for which (fog)(x) = x2 – 4x + 5.

7. i) If g is a positive integer show that the sum of the series g + (3+g) + (6+g) − − − +4g is five times the sum

of the series 1 + 2 +3 +4 + − − − + g.

ii) Calculate the distance from point A(2, -3) to the line x- 2y – 4 =0.

8. a) Prove the following argument by using the law of algebra of propositions p → q, q |→ r

b) A sentence is formed from the statements A, B, and C. Write M in the most simplified form and use it to

draw an electric circuit which will allow current to flow when M is true.

A B C MT T T TT T F TT F T TT F F TF T T TF T F FF F T FF F F F

9. a) Solve the triangle PQR and find its area given that QR=36.5 cm, PR= 29.6cm and ∠Q=36◦.

b) Two aircraft leave an airfield at the same time. One travels due north at an average speed of 300 km/h and

the other due west at an average speed of 220 km/h. Calculate their distance apart after 4 hours.

10. The line 3x -4y +8 =0 meets the y axis at the point A, and the point C has the coordinates (2, 1). The line

through C perpendicular to the line 3x -4y +8 =0 meets it at B. Calculate the area of triangle ABC.

Best Wishes

By Mr. Kibbi K.K.

Advance mathemtics Mid-term examination Mr. Kibbi K.K

Advance mathemtics Mid-term examination Mr. Kibbi K.K