Mathematics Questions and Answers - Form 3 Term 1 Opener Exams 2021 ^Featured

1. Simplify:                                           ( 4marks )
   
2. Solve for x in the equation.
   27^x x 3^(2x−2) = 9^{(x +2)}                       (3marks)
3. The size of each interior angle of a regular polygon is five times the size of the exterior angle. Find the number of sides of the polygon.                       ( 3 marks )
4. The dimensions of a brick are 2cm x 3.4cm x 6.42cm. Find the percentage error in the calculation of its area.                  (3marks)
5. Masses of three babies was stated as a=12.7kg, b=9.8 kg and c=3.20kg. find the relative error in the following expressions:
   1. a+b−c                 (3mks)
   2. c÷ab             (3mks)
6. Find the relative error in using 0.3 as the estimate of ¹/₃.     (2mks)
7. Find the length of AC of triangle ABC in which AB=5cm, <ABC=151° and <BCA=13°. (3mks)
8. In a triangle LMN, <L=81°, n=4.3cm and m=3.5cm. Calculate
   1. Length l                   (2marks)
   2. Angles M and N                (3marks)
      
9. In triangle ABC, <B=61º, and b = 5.3cm. find the radius of the circle passing through the vertices A,B and C       (3marks)
10. The table below shows height of 50 students
    

    Height (cm)	Frequency
    140 – 144  145 – 149  150 – 154  155 – 159  160 – 164	3  16  20  10  1

    
    
    1. State the modal class        ( 1 mark)
    2. Calculate the median height.         ( 3 marks )
11. Use completing square method to solve for X in.      (3marks)
    ½ x² – ⁵/_2x + 1 =0 
12.  
    1. Complete the table below for the function y = 6 + x – x².         ( 2 marks )
       

       x	−4	−3	−2	−1	0	1	2	3	4	5
       y	−14				6		4		−6

    2. On the grid provided below, draw the graph of y = 6 + x – x² for −4 ≤ x ≤ 5.      (3marks )
    3. On the same axes draw the graph of y = 2 – 2x.       (2marks )
    4. From the graphs, find the values of x which satisfy the simultaneous equations.
       y = 6 + x – x²
       y = 2 – 2x.                          ( 1 marks )
    5. Write down and simplify a quadratic equation in the form ax² + bx + c = 0 which is satisfied by the values of x where the two graphs intersect.               (2 marks )

Marking Scheme

1. ³/₅ x 60 – ⁸/₃ x ³/₂                              M1 simplification of numerator
   ⁴⁵/₈ x ¹⁶/₉ – ⁵/₄ x ²⁴/₅ + ¹⁴/₅ x ¹⁰/₇ 
      36 – 4                                            M1 simplification of denominator
   10 – 6 + 4
   ³²/₈ = 4
                   
2. 3^3x x 3^{(2x – 2)} = 3^{2(x + 2 )}         M1 expressing in index form
   3x + 2x – 2 = 2x + 4                M1 relating index
   3x = 6
     x = 2
3. Exterior < = 360
                          n
   Interior < = 180 - 360
                                   n
   180 – 360 = 5 ( ³⁶⁰/_n )             M1
              n
   180n – 360 = 1800
                 n          n              M1
   180n = 2160
         n = 12             A1
4. The dimensions of a brick are 2cm x 3.4cm x 6.42cm. Find the percentage error in the calculation of its area.      (3 mks)
   Relative error = ^0.5/₂ + ^0.05/_3.4 + ^0.005/_6.42 = 0.26548 .......m1
   Working Product = 2 x 3.4 x 6.42 =43.656.............m1
   Percentage error = 0.26548 x 100 = 0.608%............A1
                                    43.656
5. Masses of three babies was stated as a=12.7kg, b=9.8 kg and c=3.20kg. find the relative error in the following expressions:
   1. a+b-c (3mks)
      Absolute error = 0.05 + 0.05 + 0.005 = 0.105.......m1
      Working (a+b-c)= 12.7+9.8 −3.2 = 19.3.............m1
      Relative error = 0.105 = 0.005440..............A1
                                  19.3
   2. c÷ab (3mks)
      Relative error = 0.05 + 0.05 + 0.005 = 0.01060
                                 12.7      9.8       3.2
6. Find the relative error in using 0.3 as the estimate of ¹/₃.      (2mks)
   Absolute error = ¹/₃ – ³/₁₀ =¹/₃₀..................m1
   Relative error = ¹/₃₀ ÷ ¹/₃ = ¹/₁₀...................m1
7. Find the length of AC of triangle ABC in which AB=5cm, <ABC=151° and <BCA=13°. (3mks)
   
       5     =     AC   
   Sin 13      Sin 151      m1
   AC =5Sin 151
            Sin 13              m1
        =10.78cm             A1
8. In a triangle LMN, <L=81°, n=4.3cm and m=3.5cm. Calculate
   1. Length l       (2marks)
      
      L² = 4.3² + 3.5² – 2 x 4.3 x 3.5Cos 81°         M2
      L = 5.10 cm
   2. Angles M and N    (3marks)
         5.1   =   4.3 
      Sin 81     Sin N
      Sin N = 4.3Sin81
                     5.1
      Sin N = 0.8328               M2
      N = 56.38°
      M = 180 – (81+56.38) = 42.62°          A1
9. In triangle ABC, <B=61°, and b = 5.3cm. find the radius of the circle passing through the vertices A,B and C      (3marks)
     5.3    =2R
   Sin 61
   R =     5.3     
          2 Sin 61°
   R = 3.03 cm
10.  
    1. Modal class 150 – 154                    B1
    2. 
       

       Class	f	cf
       140 – 144   145 – 149  150 – 154  155 - 159  160 - 164	3  16  20  10  1	3  19  39  49  50

                                           B1 C.F
       M =
            
       =149.5 + (25 – 19) x 5
                            20                  M1 
       = 151
11. Use completing square method to solve for X in.
    ½ x² – ⁵/_2x + 1 =0       (   3marks)
    x² – 5x + 2 =0
    x² – 5x + C = −2 + C
    x² – 5x + (⁵/₂)² = −2 + 6.25
    (x – ⁵/₂)² = 4.25
    X – 2.5 = ±2.061
    X = ±2.061 + 2.5
    X= 2.561 or 0.439
12.  
    1. 
       

       x	−4	−3	−2	−1	0	1	2	3	4	5
       y	−14	−6	0	4	6	6	4	0	−6	−14

       B2 b1 for 4 ✓values
    2. Graph
    3. 
       
    4. x = −1 or x = 4            B1
    5. (x + 1 ) ( x – 4) = 0             M1
       x² – 4x + x – 4 = 0
       x² – 3x – 4 =0                       A1