## KNEC KCSE Mathematics Paper 2 Question Paper / 2015 KCSE Gem Sub-County Joint Evaluation

### MATHEMATICS PAPER 2 QUESTION PAPER

### 2015 KCSE Gem Sub-County Joint Evaluation

#### Mathematics Paper 2

### SECTION I: (50 Marks)

**Answer all the questions in this section**

A radius of a circle as 2.8cm to 2 significant figures. By taking 𝜋𝜋 to be 3.142, find to 4 significant figures, the limits between the area of the circle lie.

3 marks

Kamau sells a packet of type A of sugar for KSh. 63 and that of type B of Sugar for KSh. 36. He mixed the two types of sugar in the ratio 3:2. Find the price per packet of the mixture for which he will make the same profit as before

3 marks

Solve 2SSin2y + 3Cos y = 3 for 00 ≤ 3600.

4 marks

Use logarithm tables to evaluate:

� 1.67 𝑥𝑥 23.8

45.9 ÷ 73.26�

2

3

5. By expressing tan 300 as

1

√𝑎𝑎

, simply the expression tan 30

2−√2 , leaving your answer with a rationalized denominator.

4 marks

By expressing tan 300 as

1

√𝑎𝑎

, simply the expression tan 30

2−√2 , leaving your answer with a rationalized denominator.

3 marks

In the figure below DC is a tangent to the circle at point D. Given that ABC is a straight line where AB = 7cm and AC =

16.5cm, find the length of DC.

3 marks

Make P the subject of the formula in:-

L = 2

3 �𝑥𝑥2−𝑃𝑃𝑃𝑃

𝑦𝑦

3 marks

Given that Log 3 = 1.585 while Log2

36√5

5 without using mathematical tables or a calculator.

3 marks

Write down the equation of a circle (0,2) and radius 3 units, leaving your answer in the form (3 Marks)

a2 + by2 + cx + dy + e = 0

3 marks

A man invests KSh. 10,000 in an account which pays 16% interests p.a compounded quarterly. Fid the amount in the account after 1 ½ years.

3 marks

(a) Expand and simplify (1 – 5x)4 (1 Mark)

(b) Use the expansion in (a) above to estimate the value of 0.94 to 4 significant figures. (2 Marks)

3 marks

On the same side of AB as C, in the triangle below, construct the locus of points P such that triangle ABP has an areas of 24cm2.

3 marks

The position vectors of points P and Q are p =2i + 3j – k and q = 3i – 2j + 2k respectively. Find the magnitude of PQ correct to 4 significant figures.

3 marks

A two digit number is such that the sum of the digits is 11. When the digits are interchanged the new number formed is 45 less than the original number. Determine the original number.

2 marks

An unbiased coin with faces, head (H) and tail (T) and a fair die with faces marked 1, 2,3,4,5, 6 are each tossed once.

(a) Show all the possible outcomes. (1 Mark)

(b) Calculate the probability that a 4 of the die and a head (H) of the coin shows up. (1 Mark)

2 marks

Evaluate ∫ (−2𝑥𝑥 + 7) 3

−1 𝑑𝑑𝑑𝑑

3 marks

### SECTION II: (50 Marks)

**Answer only five questions in this section.**

A ship sailing at a speed of 200 knots left harbour A (300S, 320E) and sailed due north to harbour B (300N, 320E)

(a) Calculate the distance it covered in nautical miles. (2 Marks)

(b) After a 15 minutes stop over at B the ship due west to harbour C (300N, 150E) at the same speed.

(i) Calculate the total time taken by the ship from A to C through B. (5 Marks)

10 marks

A triangle PQR has co-ordinates P(-6,5), Q(-4,1) and R(3,2) and is mapped onto P1Q1R1 by a shear x-axis invariant where P1 is (-6,-4)

(a) On the grid provided draw both PQR and its image P1Q1R1 under the shear. (3 Marks)

(b) Determine the matrix representing the shear. (2 Marks)

(c) Triangle P1Q1R1 is mapped onto PIIQIIRII by the matrix � −1 0

−1.5 −1

�

(i) Draw PIIQIIRII on the same grid above. (3 Marks)

(ii) Describe a single transformation that maps PIIQIIRII onto PQR. (1 Mark)

(iii) State the single matrix of transformation that maps PIIQIIRII onto PQR. (1 Mark)

10 marks

The electricity bill E of school is partly fixed and partly varies inversely as the total number of students T.

(a) Write down an expression of E in terms of T. (1 Mark)

(b) When the school had 100 students the bill was KSh. 174 per student while for 35 students the bill was KSh. 200 per

student. Calculate the fixed charge. (4 Marks)

(c) Find the appropriate number of students for which the two parts of electricity bill are equal. (3 Marks)

(d) Find the electricity bill E when the students population is 1000. (2 Marks)

10 marks

A right pyramid VABCD below has a square base ABCD of side 4m. The slant edges VA, VB, VC and VD are 6m long.

Calculate

(i) the height of the pyramid. (4 Marks)

(ii) the angle between the plane VAB and the base ABCD. (3 Marks)

(iii) C1 and D1 are mid points of VC and VD respectively. Calculate the angle between the planes ABCD and ABC1D1.

(3 Marks)

10 marks

(a) The first term of an arithmetic progression is 3 and the sum of its 8 terms is 164.

(i) Find the common difference of the arithmetic progression. (2 Marks)

(ii) Given that the sum of the first terms of AP is 570, find n. (3 Marks)

(c) The first, the fifth and the seventh terms of another Arithmetic sequence forms a decreasing geometric progression. If

the first terms of the geometric progression is 64.

(i) find the values of the common differenced of AP. (3 Marks)

(ii) find the first sum of the first ten terms of the G.P. (2 Marks)

10 marks

(a) Complete the table given below by filling in the values correct to 2 decimal place. (2 Marks)

x0 00 300 600 900 1200 1500 1800 2100

3Sin x0-1 -1.00 0.50

Cosx0 1.00 0.87 0.50 0.00 -0.87 -1.00

(b) On the same axes draw the graph of y – 3Sinx0 – 1 and y = Cos x0 on the grid. (5 Marks)

(c) Use your graph to solve the equation, 3 Sinx0 – Cosx0 = 1 (2 Marks)

(d) Find the range of values of x for which 3 Sin x 0 – 1 > Cos x 0 (1 Mark)

10 marks