Mathematics Questions and Answers - Form 2 End Term 1 Exams 2023

SECTION 1

1. Evaluate 5 ½ - 1¹/₇ (1¹/₅ + ⁹/₁₀ ) + ¹/₃ of (²/₃ ÷ ⁵/₆) (3mks)
2. The interior angles of hexagon are (4x -5 )⁰, (4x + 5)⁰, 3x⁰,(4x +26) ⁰, 2x⁰ and (2x + 5)⁰ Find the value of x (3mks)
3. Use the exchange rates below to answer this question
                                Buying                   Selling
   1 US dollar            63.00                     63.20
   ! UK £                   125.30                  125.95
   A tourist arriving in Kenya from Britain had 9600 UK sterling pounds (£). He converted the pounds to Kenya shillings at a commission of 5%. While in Kenya he spent ¾ of this money. He changed the balance to US dollars after his stay. If he was not charged any commission for this last transaction, calculate to the nearest US dollars the amount he received. (4mks)
4. Use logarithm tables to evaluate the following (3mks)
   
5. A square based brass plate is 2mm high and has a mass of 10.5kg.The density of the brass is 8.4g/cm ^₃ . Calculate the length of the plate in centimeters.(3mks)
6. Find the equation of a line through point (5, -1) and perpendicular to line 4x + 2y–3=0. (4 marks)
7. Solve the simultaneous equations.
   2x + 5y = 34
   x + 2y = 21
8. Convert0.12^•3^• into a fraction.(2marks)
9. Find the value of M in the following equation.(3mks)
   (¹/₂₇)^M × 81⁻¹ = 243
10. The ratio of the area of two circles is¹⁶/₉
    1. Find the ratio of their radii (2mks)
    2. If the larger circle has a radius of 20cm, find the radius of the smaller one (2mks)
11. Find the area of a triangle ABC in which AB=5cm, BC=6cm, and AC = 7cm.(3mks)
    
12. Without using tables evaluate Sin30°Cos30° (2mks)
13. An electric pole is supported to stand vertically by a tight wire as shown below. Find the height of the pole.(3mks)
    

SECTION II
INSTRUCTION: ANSWER ONLY THREE QUESTION

14.  
    1. Plot on the graph provided a triangle with vertices A(-5,6), B(-3,3) and C(-5,3) (2mks)
    2.  
       1. Draw the image A’B’C’ under a reflection in the line x=0 (2mks)
       2. Write the coordinates of A’B’C’ (1mk)
    3.  
       1. Draw the image A’’B’’C’’ of ABC under a reflection in the line y-x=0 (2mks)
       2. Write the coordinates of A’’B’’C’’ (1mk)
    4.  
       1. Using triangle ABC and A’B’C’, show if the two triangles are congruent.(1mk)
       2. If they are congruent, state the type of congruence (1mk)
15.  
    1. Using a ruler and compasses only, construct triangle ABC in which BC=8cm, angle ABC=30^o and angle ACB=45^o (3 marks)
    2. Measure AB and AC. (2 marks)
    3. At A drop a perpendicular to meet BC at D. (2marks)
    4. Measure AD and hence calculate the area of the triangle ABC. (3marks)
16. A salesman is paid a commission of 2% on goods worth over Ksh.100000. He is also paid a monthly salary of Ksh.12000. In a certain month, he sold360 pairs of shoes at Ksh.500 each pair.
    1. Calculate the salesman’s earning that month. (3marks)
    2. The following month, his monthly salary was increased by 10%. His total earnings that month were Ksh.17600. Calculate
       1. The total amount of money received from the sales of the shoes that month. (5marks)
       2. The number of pairs of shoes sold that month. (2marks)
17.  
    1. Plot the points A(3,-3), B(6,-3), C(3,-6) and D(6,-6) and join to form a square.(2mks)
    2. A’B’C’D’ is the image of ABCD under a rotation of +90⁰ about the origin. On the same axes draw A’B’C’D’. (6mks)
    3. Calculate the area of the object ABCD. (2mks)

MARKING SCHEME

1. Evaluate;5¹/₂-1¹/₇(1¹/₅+⁹/₁₀)+¹/₃ of (²/₃÷⁵/₈) =
   ¹¹/₂-⁸/₇(⁶/₅+⁹/₁₀)+¹/₃of(²/₃×⁶/₅)
   ¹¹/₂-⁸/₇(²¹/₁₀)+¹/₃×⁴/₅
   ¹¹/₂-⁸/₇ײ¹/₁₀+⁴/₁₅=¹¹/₂+⁴/₁₅-¹²/₅
   =¹⁰¹/₃₀
   =3¹¹/₃₀
2. The interior angles of hexagon are (4_x-5)⁰,(4_x+5)⁰,3_x^o,(4_x+26)⁰,2_x⁰ and (2_x+5)⁰ find the value of x (3mks)
   (4x+5)+4x-5)+3x+(4x+26)+2x+(2x+5)
   720°
   19_x+31=720
   19_x=689
   x=⁶⁸⁹/₁₉
   =36.26°
3. Use the exchange rates below to answer the question 
   
   A tourist arriving in kenya  from Britain had 9600UK sterling pounds (£). if converted the pounds to kenya shillings at a commission of 5%.While in kenya he spent ³/₄ of this money. He changed  the balance to US dollars after his stay. If he was nit charged any commisiion for this transaction , calculate to the nearest  US dollars the amount he received  (4mks)
         1UK£ = Ksh 125.30
   9600UK£ =  ?
   9600 × 125.30 = Kssh 1,202,880
   95/100 × 1202880 = 1,142,736
   ¼ Spending 3/4 remainis
   ¼ × 1,142,732 = 255,634
   Changing to US dollars
   1US  = 63.20
    ?      = 285684
   285684 × 1
          63.20
   = 4,520.32
   = 4,520 US dolars
4. Use logarithm tables to evalute the following (3mks)
   
    
   9.378×10^-1
   =0.9378
5. A square bassed brass plate is 2mm high and has a mass of 10.5_kg .The density of the  brass is 8.4_g/cm³.Calculate the length of the plate in centimeters (3mks)
   .
6. Find the equation of ta line through point (5,− 1) and perpendicular ti line 4x + 2y − 3 = 0 (4mks)
   4x + 2y −  3 = 0
   4x + 2y = 3
   2y/2= 4x /2 + 3/2
   y = −  2x + 3/2
   Grad = − 2
   for perpendicular lines
   M₁M₂ = − 1
   −1M₂ = − 1
   M₂ = ½
   (x, y) (51− 1)
   y + 1 = ½
   x −  5  
   2y + 2 = 2.5
    2y −  x = − 7
   OR
   2y −  x + 7 =0
7. Solve  the simultaneous equations (3mks)
   2x + 5y = 34
   x + 2y = 21
   By elimination
   2x + 5y = 34   ....1
   x + 2y = 21       ..2
   2x + 5y = 34
   2x + 4y  = 42  −   
              y = −8
   x + 2y = 21
   x + 2(−8) = 21
   x − 16 = 21
   x = 21 + 16
   x = 37, y = −8
8. Convert 0.123^• into a fraction  (2mks)
   x=0.123123
   10x=1.23123
   100x=12.3123
   1000x=123.123123
   x        =o.123123
   ^999x/₉₉₉=¹²³/₉₉₉
   x=⁴¹/₃₃₃
9. Find the value of M in the following equation (3mks)
   (¹/₂₇)^m×81^-1=243
   (27)^-m×81^-1=243.......m₁
   3^-3×3^-4=3⁵
   3^-3-4=3⁵..........m₁
   -3m-4=5
   m=-3........A₁
10. The ratio of the area of two circles is ¹⁶/₉
    
    1. Find  the ratio of their radii (2mks)
       A.S.F=(l.s.f)²
       L.S.F=√¹⁶/₇
       =⁴/₃
       ratio of radii=⁴/₃.....A₁
    2.  if the larger circle  has a radius  of 20cm , find the radius of  the smaller one (2mks)
       ⁴/₃ × 20 = 26.67cm
11. Find  the area of a triangle ABC in which AB=5cm,BC=6cm,and AC=7cm (3mks)
    
    using heroes formulae
    A = √{[s(s − a)(s− b)(s− c)]
    S = 5 + 7 + 6
                 2
       = 9
    A = √[9(9− 7)(9− 6)(9− 5)]
        = √(9 × 2 × 3 × 4)
       = √216
       = 14.6969 ≅ 14.70cm²
12. Without using tables evaluate sin30ºCos30º (2mks)
    sin30º=¹/₂
    Cos30º=√³/₂
    Sin30ºCos30º
    ¹/₂×√³/₂....A₁
13. An electric pole is suppoted to stand vertically by a tight wire as shown below . Find the height of the pole (3mks)
    using pytheogorus theory
    lenge of  the  pole is found as
    8.5² − 3² = h²
    h = √8.5² − 3²
    h = √72.25-9
    h = √63.25
    h = 7.95m
    total length = 1 + 7.95
    =8.95m
    SECTION 2
    INSTRUCTION :ANSWER ONLY THREE QUESTIONS
14.  
    1.  Plot on the graph provided a triangle with  vertices A(-5,6),B(-3,3),and C(-5,3) (2mks)
       
    2.  
       1. Draw the image A'B'C' under  a reflection in the line x=0 (2mks)
       2. Write the coordinates of A'B'C' (1mk)
          A¹(5,6),B¹(3,3)and C¹(5,3)
    3.  
       1. Draw the image A"B"C" of ABC under areflection in the line y-x=0 (2mks)
       2. Write the coordinates of A"B"C" (1mk)
          A"(6,-5),B"(3,-3) and C"(3,-5)
    4.  
       1. Using triangle ABC and A'B'C' show if the two triangles are congruent (1mks)
          • the  two triangles are  congruent
       2. if they are congruence ,state the type of congruence (1mks)
          • Opposite congruence
15.  
    1. Using  a ruler and  compasses only ,construct triangle ABC in which BC=8cm,angleABC=30º and angle ACB=45° (3mks)
       
    2. Measure AB and AC (2mks)
       AB=5.9cm
       AC=4.2cm
    3. At A drop a  perpendicullar to meet BC at D  (2mks)
       AD = 3cm
    4. Measure AD and  hence calculate the area of the triangle ABC  (3mks)
       AO = 3cm 
       A = ½bh
          = ½ × 8  × 3
         = 12cm²
16. A  salessman is paid  a commission of 2%  on goods worth ksh.100000.He is also paid a monthly salary  of  ksh,12000 , In a certain month, he sold 360 pairs of shoes  at ksh.500 each pair.Calculate  the salesman's earning that month(3mks)
    Sales = 360 × 500
             = Ksh 180,000
    Commission = ²/₁₀₀  × 180,000
                         = Ksh 3600
    Total pay = 12,000 + 3600
                    = Sh. 15,600
    
    1. The following month , his monthly salary was increased by 10%. His total earnings that month were ksh.17600. calculate 
       1.  the amount of money received from the sales if the shoes that month (5mks)
          ¹¹⁰/₁₀₀×12000=13200
          17,600-13,200=4,400
          ²/₁₀₀x=4,400
          x=4,400×¹⁰⁰/₂
          222000
       2. The number of pairs of shoes sold that month.(2mks)
          222,000 = 440 pairs
             500
17.  
    1. Plot the points A(3,-3),B(6,-3),C(3,-6) and D(6,-6) and join to form a square (2mks)
       
    2. A'B'C'D' is the image of ABCD under a rotation of +90° about the origin . on the same axes draw A'B'C'D'  (6mks)
    3. Calculate the area of the object ABCD. (2MKS
       A = 3cm × 3cm
          =9cm²