Mathematics Paper 1 Questions - Mumias West Pre Mock Exams 2023

INSTRUCTIONS TO CANDIDATES

1. This paper consists of two sections: Section I and Section II.
2. Answer all questions in section I and any five questions in Section II.
3. Show all the steps in your calculations, giving your answers at each stage in the spaces below each question.
4. Marks may be given for correct working even if the answer is wrong.
5. KNEC Mathematical tables may be used.

For Examiner’s Use Only

QUESTIONS

Section I (50 marks)
Answer all the questions in this section in the spaces provided

1. Without using calculators evaluate 1/3 of (2³/₄ - 5¹/₂) x 3⁶/₇ ÷ ⁹/₄ {2 marks}
2. Use the method of completing the square to solve the quadratic equation
   2x² – 13x + 15 = 0 {3 marks}
3. Solve for θ in the equation 6 cos² θ - Sin θ - 4 = 0 in the range 0º ≤ θ ≤ 180º.  {3 marks}
4. The sides of a rectangle are x cm and (x + 1) cm. A circle has radius of (x + 2) cm. If the sum of the area of the rectangle and the circle is 184 cm². Using π as find the value of x. {4 marks}
5. In the figure below ABCD is a cyclic quadrilateral and BD is a diagonal .EADF is a straight line, <CDF = 68º, < BDC = 45º and < BAE = 98º
   
   Calculate the size of
   1. < ADB (2 marks)
   2. < ABD (2 marks)
6. A line L₁ passes through point (1, 2) and has a gradient of 5. Another line L₂ is perpendicular to L1 and meets it at a point where x = 4. Find the equation for L2 in the form y = mx + c. {4 marks}
7. Find the value of x in the following equation. {3 marks}
   9x + 3^2x – 1 = 53
8. The first and the last terms of an AP are 2 and 59 respectively. If the sum of the series is 610, find the number of terms in the series and the common difference.{4 mks}
9. All prime numbers less than ten are arranged in descending order to form a number.
   1.  Write the number formed (1 mark)
   2. State the total value of the second digit in the number formed in (a) above (1 mk)
10. Use reciprocals, square and square roots tables to evaluate, to 4 significant figures, (4 marks)
    
11. Solve the inequality 3 – 2x ≤ x ≤ 2x + 5  and show the solution on the number line.  {4 marks}
                                                            3
12. Kenyan bank buys and sells currencies at the exchange rates below
    

    Currency	Buying(Ksh)	Selling Ksh
    1 Euro	147.87	148.00
    1 US dollar	74.22	74.50

    An American tourist arrived in Kenya with 24,000 Euros He converted all the Euros to Kenya shillings at the bank .He spent a total of Sh. 200,000 while in Kenya and converted the rest to into US dollars at the bank. Find the amount in dollars that he received to the nearest whole number.
    (3 marks)
13. A salesman earns a basic salary of sh. 9,000 per month. In addition he is also paid a commission of 5% for sales above sh. 15,000. In a certain month he sold goods worth sh. 120,000 at a discount of 2½%. Calculate his total earnings that month. {3 marks}
14. A small cone of height 8 cm is cut off from a bigger cone to leave a frustum of height 16 cm. If the volume of the smaller cone is 160 cm³, find the volume of the frustum. {3 marks}
15. Vector OP = 6i + j and OQ = -2i + 5j. A point N divides PQ internally in the ratio 3:1.
    Find PN in terms of i and j. {3 marks}
16. Without using mathematical tables or calculators express in surd form and simplify  {3 marks}
    1 + Cos30º
    1 - Sin 60º

SECTION II (50 marks).
Answer only five questions in this section in the spaces provided.

17. The figure below shows a frustrum. The top and bottom radii are 5cm and 10cm respectively, while the vertical height of the frustrum is 12cm.
    
    Find the:-
    1. Slant height of the frustum. (3marks)
    2. Curved area of the frustum.(3marks)
    3. Volume of the frustum.(4marks)
18. Bumala is a market centre 600km from Kisumu town. A bus starts from Kisumu for Bumala at 7.00am at an average speed of 80 km/h. At 8.30 am a car started from Kisumu to Bumala and moved at an average speed of 120 km/hr. Calculate
    1. The distance bus covered before the car started moving.(3marks)
    2. The relative speed for the two vehicles. (2marks)
    3. The time the car overtook the bus. (1 mark)
    4. Distance covered by the car before overtaking the bus. (2marks)
    5. Distance from Bumala to the car at the time the car was overtaking the bus. (2marks)
19. The height of 36 students in a class was recorded to the nearest centimeter as follows:-
    148 159 158 163 166 155 155 179 158
    161 160 157 165 165 175 173 172 178
    147 168 157 172 165 154 170 157 167
    155 159 173 171 168 160 172 156 167
    1. Make a frequency distribution table using a class interval of 5 and starting with the class
       145 – 149.        (2marks)
    2. From the table above
       1. Calculate the mean mark (3marks)
       2. Calculate the median (3marks)
          1. Draw a frequency polygon using the table in (a) above. (2 marks)
             
20. Bujumba Boys Secondary School. Intends to buy a certain number of chairs For Ksh. 16,200. The supplier agreed to offer a discount of Ksh. 60 per chair which will enable the school to get 3 chairs more.
    Taking y as the originally intended number of chairs:-
    1. Write an expression in terms of y for
       1. Original price per chair.(1mark)
       2. Price per chair after discount.(1mark)
    2. Determine
       
       1. The number of chair the school originally intended to buy.(4marks)
       2. Price per chair after discount. (2marks)
       3. The amount of money the school would have saved per chair of it got the intended number of chairs at a discount of 15%.(2marks)
21.                        
    1. Without using a protractor, construct triangle ABC such that angle ABC = 600, BC = 8cm and AC = 9cm.Measure AB.(3marks)
    2. Drop a perpendicular from A to BC and measure its length.(2marks)
    3. Hence calculate the area of triangle ABC.(2marks)
    4. Locate a point D on BC such that the area of triangle ABC is three times that of triangle ABD.(3marks)
22. In triangle ABC, shown below, AB = a AC = b point M lies on AB such that AM: MB = 2:3 and point N lies on AC such that AN: NC = 5:1 line BN intersects line MC at X.
    
    
    1. Express the following in terms of a and b
       1. BN (1 mark)
       2. CM (1 mark)
    2. Given that BX = kBN and CX = rCM where k and r are scalars
       1. Write two different expressions for AX in term of a, b, k and r (4marks)
       2. Find the values of k and r (4 marks)
23. A triangle ABC has vertices A(2,1), B(5,2) and C(0,4).
    1. On the grid provided plot the triangle ABC. (2 marks)
       
    2. A1B1C1 is the image of ABC under a translation . Plot A¹B¹C¹ and state its coordinates. (2 marks)
    3. Plot A¹¹B¹¹C¹¹ the image of A¹B¹C¹ after a rotation about the origin through a negative quarter turn.
       State its coordinates. (3 marks)
    4. A¹¹¹B¹¹¹C¹¹¹ is the image of A¹¹B¹¹C¹¹ after a reflection on the line y = 0. Plot A¹¹¹B¹¹¹C¹¹¹ and state its coordinates. (3 marks
24. Three business partners Abila, Bwire and Chirchir contributed Ksh 120,000, Ksh 180,000 and Ksh 240,000 respectively to boost their business. They agreed to put 20% of the profit accrued back into the business and to use 35% of the profits for running the business. The remainder was to be shared among the business partners in the ratio of their contribution. At the end of the year, a gross profit of Ksh 225,000 was realised.
    1. Calculate the amount.
       1. Put back into the business.(2mks)
       2. Used for official operations.(1mk)
    2. Calculate the amount of profit each partner got.(4mks)
    3. If the amount put back into the business was added to individual’s shares proportionately of their initial contributions, find the amount of Chirchir’s new shares. (3mks)