SS 1 THIRD TERM EXAMINATION MATHEMATICS

   THIRD TERM   

Examination malpractices may lead to a repeat of the subject or suspensions don’t be involved.   

Subject:  MATHEMATICS           

Class: SS 1      DURATION ; 2Hrs          

Part 1: OBJECTIVES

Time : 1HR

1. Simplify 2 –log255    A. 11/2      B. 21/2      C. 51/2     D. ½
2. Find x if log9x = 1.5    A. 72    B. 27     C.  36    D. 3.5  
3. The edge of a cube whose volume is equal to the volume of a cuboid of dimensions 63 cm ×    56 cm × 21 cm is (A) 21 cm (B) 28 cm (C) 36 cm (D) 42 cm 
4. If radius of a sphere is doubled, then its volume will become how many times of the original volume?  (A) 2 times (B) 3 times (C) 4 times (D) 8 times
5. Volume of a cylinder of the same base radius and the same height as that of a cone is  (A) the same as that of the cone (B) 2 times the volume of the cone (C) 3.1 times the volume of the cone (D) 3 times the volume of the cone.

Use the information below for questions 6 to 8:

A dice is thrown 14 times and the scores were:  1, 6, 6, 4, 3, 5, 5, 4, 4, 4, 5, 2, 1, 6.

1.  Find the range (A)4 (B)3 (C)5 (D)6
2.  Find the median score (A)4 (B)3 (C)5 (D)6
3.  Find the mode score. (A)4 (B)3 (C)5 (D)6
4.  Find the mode, median, and range of 50%, 55%, 60%, 70%, 65%.(A) 0.55 (B)0.6 (C)0.65 (D)0.70

Use the information below for questions 10 to 12:

Given that U ={all positive integers from 1 – 10}, A ={all odd numbers 10}, B ={all even numbers < 10} and C ={all prime numbers }

1.  Find n (A B) I. (A) 10 (B) 1 (C) 0 (D) .
2.  Find (AC) I B. (A) {3 – 8} (B) {3, 5, 7} (C) {1, 2, 3, 8, 9} (D) {2, 5, 7, 6, 10}.
3.  Find n (AI BI CI). (A) 2 (B) 0 (C) 1 (D) {0}.
4.  Evaluate x . (A) 20 (B) 5 (C) 1/20 (D) -20.
5.  Simplify; (216)-2/3 x (0.16)-3/2. (A) 2/125 (B) 125/288 (C) 4/225 (D) -2/225.
6.  Simplify; 2n-1 x 42n+1 83n where n = 1. (A) 1/8 (B) 1/16 (C) -8 (D) 16.
7.  Which of the following is the solution to the equation; 2x2 + 3x – 5? (A) 5 and -2 (B) -2 and -5 (C) 2 and 5 (D) -5 and 2. 
8.  Simplify 82/3 x 4-1/2 163/4. (A) 1/16 (B) 1/24 (C) 16 (D) 8.
9.  Given that 2x = 0.125, find the value of x. (A) -2 (B) 8 (C) 14 (D) -3
10.  Simplify Log1.5 2.25 = 2. (A) 1 (B) -1 (C) 2 (D) -3.
11.  Simplify 82/3 x 4-1/2 163/4. (A) 1/16 (B) 1/24 (C) 16 (D) 8.
12.  Given that 2x = 0.125, find the value of x. (A) -2 (B) 8 (C) 14 (D) -3.
13.  The curved surface area of a cylinder, 5cm high, is 110cm2. Find the radius of its base.( take =)       (A) 2.6cm    (B) 3.5cm    (C) 3.6cm    (D) 7cm
14.  The volume of a pyramid with height 5cm is 90cm3. If its base is a rectangle with dimensions  xcm by 6cm, find the value of x.    A. 3    B. 5    C. 6    D. 8
15.  Make “s” the subject of the relation: p = s +          

(A) s =         (B) s =         (C) s =       (D) s =

1.  Factorise: (2x + 3y)2 – (x – 4y)2         

(A)(3x – y)(x + 7y)   (B) (3x + y)(2x – 7y)  (C) (3x + y)(x – 7y)  (D) (3x – y)(2x + 7y)

              P                    Q                      R

                    480

              S                T                    U                  V

                          600

            W                X            Y

In the diagram, PR//SV//WY, TX//QY, <PQT = 480 and <TXW = 600. Find <TQU     

(A) 1200     (B) 1080     (C) 720     (D) 600

1. The ratio of the exterior angle to the interior angle of a regular polygon is 1:11. How many sides have the polygon?     A. 30      B. 24      C. 18     D. 12
2. Halima is n years old. Her brother’s age is 5 years more than half of her age. How old is her brother?         A. +     B. – 5  C.     D. + 5
3. An object is 6m away from the base of a mast. If the angle of depression of the object from the top of the mast is 500, find, correct to 2 decimal places, the height of the mast. A. 8.60m B. 7.83m C. 7.51m D. 7.15m
4. The coefficient of a2 in the expression 3a2 – 2a + 25 A. 25 B. -2  C. 2     D. 3    
5. Find the sum of 1001two and 111101two    A. 100001two     B. 100011two    C. 100110two      D. 1000110two
6. How many vertices have a cuboid?    A. 4    B. 6    C. 8     D. 12     

1. Given that logx 64 = 3, evaluate x log2 8     (A) 6  (B) 9 (C) 12 (D) 24 
2. If 2n = y, find 2(2 + n/3)     (A) 4y1/3     (B) 4y-3    (C) 2y1/3    (D) 2y-3
3. If m = 4, r = 16 and n = 9, evaluate m/n – 17/9 + n/r        (A) 15/16    (B) 11/16      (C) 5/16       (D) –37/48

    p

                   m                  n

From the diagram, which of the following is true?    (A) m + n + p = 1800     (B) m + n = 1800     (C) m = p + n     (D) n +p= m +180

1. In the diagram below,  is a chord of a circle KMN centre O and radius 10cm. if <MON = 1400, find, correct to the nearest cm, the length of the chord MN.      A. 19cm     B. 18cm      C. 17cm       D. 12cm

                                                                                                                                                                                                                              K

            O

          1400

                                 M            N

1.  If 23x + 101x = 130x, find the value of x.    A. 7   B. 6    C. 5     D. 4
2.  Simplify: ( – ) x 1.      A.   B.   D.1
3. A motorcycle is paid for in twelve equal installments. Each payment is 5,500. How much does the motorcycle cost?  A.66,000   B.15,000    C.32,000    D.60,000    
4. Solve 1 + 2m > 3m + 5         A. m > 4      B. m > -4        C. m < 4        D. m < -4        
5. Express – as a single fraction     A.     B.       C.     D.      
6. Express 526000 in standard form:   A. 5.26 x 104    B. 5.26 x 10-4       C. 5.26 x 103        D. 5.26 x 105  
7. If 5 people can do a piece of work in 6 days, how many days should 10 people take to do it? (Assume that the rate of work is the same)    A. 4   B. 5    C. 7    D. 3
8.  0.5046 correct to 3 decimal places     A. 0.5050   B. 0.504    C. 0.50     D. 0.505    
9. The square root of 12 is   A. 1    B. 3       C. 3      D. 6     E. 6

Use the figure below for questions 45-47

Below is a chart of favourite colours of selected people.

1.  Which is the most popular colour?  A. blue    B. yellow    C. green    D. red   
2. Which is the least popular colour?   A. blue    B. yellow    C. green    D. red   
3. How many people were asked to name their favourite colours?    A. 5    B. 10     C. 12     D. 15    
4.                                            T

                               cm

              W                    cm          X    1cm      U

In the diagram, TX is perpendicular to UW,/UX/ 1cm and /TX/ = /WX/ = cm. find <UTW                            A. 1350     B. 1050       C. 750     D. 600

THIRD TERM

Examination malpractices may lead to a repeat of the subject or suspensions don’t be involved.   

SUBJECT   MATHEMATICS 

 CLASS: S. S. S ONE

DURATION 2HR

Theory

PAPER 2   

              Answer only four questions in this section. (50 marks)

1.  (a)A survey carried out recently to find the number of applicants that applied for jobs in three newspaper establishments revealed that 70 applied to the Daily Times, 65 applied to the Daily Graphics and 85 applied to the Punch. 40 applied to the Daily Times only, 20 applied to the Daily Graphic only, while 45 applied to the Punch only. If 5 applied to all the three newspaper establishments, find:

1. The number that applied to both the Daily Times and the Daily Graphics.
2. The number that applied to the Daily Times and the Punch.
3. The number that applied to both the Daily Graphic and the Punch.
4. The number that applied to at least one newspaper establishment.

(b)An operation * is defined on the set R, of real numbers by x*y = x + y + 3xy. If the operation * is commutative, 

1. Find the identity element e of R under the operation *
2. Determine the inverse of the element x R, under the operation *
3. Find the value of x R, which has no inverse.

1. (a)Solve for x if 22x+1 – 5(2x) + 2 = 0.

(b) Find the values of x which satisfy the equation; log10 (x2 + 4) = 2 + log10 x – log10 20.

 (3) (a) Find the gradient of the line whose equation is given by: (a – b)x + (c – d)y = e + f

 (b) Given that p = (4i – 3j) and q=(-1 + 5j), find (i) /p+q/  (ii) /q/

(4) (a) find the acute angles between the pairs of line: 4y + 3x = 2 and x – 2y = 3

(b) Find the equation of the line which is parallel to the line 5x + 4y = 18 and makes an intercept of 2 units on the x-axis

(5)(a)The function f over the set of real number is defined by f(x) = 12x-3. Find f-1(5)

(b) Find without using logarithms tables, the value of:      log327 – log1/464 

                                                          log3 1/81

(6) (a) A binary operation *is defined over R (the set of real numbers) by                                   x * y = xy + x2 + y2 for all x, y € R.    i.    determine whether or not * is commutative    

1. If x*(x+2) = 49, find x 

(b) Solve the equation: log10(4P2 + 1) – 2log10P – log102 = 1

(7)  (a) Consider the mapping below:                        X                f          G   

                                                          p                          1

                                                                                                        q                                         

 Find the range and determine the type of mapping above

(b) 52x+1 – 26(5x) + 5= 0