Mathematic Mock Examination Questions 3 2019/2020 Session – Senior Secondary School Three( SSS 3)

              

 

EDUDELIGHT SECONDARY SCHOOL

                            1 Benson Avenue, Lekki Phase 1, Lagos.

MOCK EXAMINATION FOR 2019/2020 SESSION.

SUBJECT: MATHEMATICS               CLASS: S.S 3          TIME: 2HrS

                                             PAPER 1        

                        THEORY PART A             ( COMPULSARY).

1a.     Given that  () ( =  find  and .

1b.    If 

2a.A regular polygon of  n-sides is such that each interior angle is 120⁰ 
     greater than the exterior angle.Find i.the value of n ii.the sum of all the
     interior angles.                                                                                     

   (b)A boy walks 6km from a point P to a point Q on a bearing of  065⁰ .He
    then walks to a point R, a distance of 13km, on a bearing of 146⁰ . (i)
    Sketch the diagram of his movement. (ii)Calculate,correct to the nearest
    kilometer,the distance PR.

     3a. Out of 30 candidates applying for a post, 17 have degrees, 15 diplomas
            and 4 neither degree nor diploma. How many of them have both?                
       (b) A pentagon is such that one of its exterior angles is 60⁰. Two others are
           (90 – m) ⁰  each while the remaining angles are ( 30 + 2m)⁰ each . Find
            the value m.

4a. A rectangular field is  meters long  meters wide. Its perimeter is
      280meters. If the length is two and half times its breadth, find the value
      of .                                                                                                     

 (b) The base of a pyramid is 4.5m by 2.5 m. the height of the pyramid is 4
     m. calculate it volume.

5a. Solve the inequality: 

5b. Given that,  (i) Express p in it simplest form; (ii) find the value of p if .

                               SECTION B

        ANSWER ANY FIVE QUESTIONS FROM THIS SECTION.

6a. If and find the values of  and.

6b. P, Q and R are related in such a way that  When P = 36, Q = 3
      and R = 4. Calculate Q when P = 200 and R = 2.

7a. Solve, correct to two decimal places , the equation

7b. The area of a circle is 154cm².It is divided into three sectors such that
      two of the sectors are equal in size and the third sector is three times
      the size of the other two put together.calculate the perimeter of the third
      sector.

8. The ages, in years, of 50 teachers in a school are given below:

21   37   49   27   49   42   26   33   46   40

50   29   23   24   29   31   36   22   27   38

30   26   42   39   34   23   21   32   41   46

46   31  33   29   28   43   47   40    34   44

26   38   34   49   45   27   25   33   39   40

• From a frequency distribution of the data using the intervals: 21-25, 26-30, 31-35, etc.
• Draw the histogram of the distribution
• Use your histogram to estimate the mode.
• Calculate the mean age using 33 as the assume mean.

9a. The triangle ABC has sides AB = 17m, BC = 12m and AC = 10m.
      Calculate the:

•  Largest angle of the triangle;
• Area of the triangle.

9b. From a point T on a horizontal ground, the angle of elevation of the top
      R of the tower RS, 38m high, is 63⁰. Calculate correct to the nearest
      meter, the distance between T and S.

10a. show that the angle at center of a circle is twice the angle which is
        subtends at the circumference of the circle.

10b. A rope 60cm long is made to form a rectangle. If the length is 4 times
        its breadth, calculate, correct to one decimal, the:

• Length;
• Diagonal of the rectangle.

11(a). copy and complete the table of values for .

X	-3	-2	-1	o	1	2	3	4	5
y	35			-7	-9		5

           (b)Using scales of 2cm to 1unit on the x-axis and 2cm to 5units on the             
              y- axis, draw the graph of  y = 3x² – 5x – 7. 

           (c)From your graph: (i).find the roots of the equation 3x² – 5x – 7 = 0

               (ii).estimate the minimum value of of y.

12a.The distance between two points (6,1) and (r,-5) is 10units,where r is a
       constant.Find the possible values of r.

12b. A man sold 100 articles at 25 for #66.00 and made a gain of
        32%.Calculate his gain or loss percent if he sold them at 20 for #50.00      

13.(a)   

     (b) Find   if (i)  y = 2x + 5 . Using the first principle method.

                      (ii)  y =  4x⁵ + 5x⁴ – 2x – 6

                          EDUDELIGHT SECONDARY SCHOOL

                            1 Benson Avenue, Lekki Phase 1, Lagos.

MOCK EXAMINATION FOR 2019/2020 SESSION.

SUBJECT: MATHEMATICS               CLASS: S.S 3          TIME: 1Hr 30Min

PAPER 2

1. Correct 0.005854 to 2 significant figures (a) 0.0058 (b) 0.0059 (c) 0.0060
           (d) 0.0100
2. Simplify: 3½ – 1¹/₃ x 2⁵/₈ (a) 0 (b) ½ (c) 1 (d) 2
3. Find the sum of 303₅ and 104₅. (a) 412₅ (b) 402₅ (c) 244₅ (d) 144₅
4. If 2√5 + √125 – √45 + 4 = a + b√c, evaluate (2a-b). (a) 8 (b) 4 (c) 2 (d) 0
5. A petrol tank will take a factory 30 week when it uses 150 litres per day. How many weeks will it take the factory if it decides to use 500 litres per day? (a) 30 (b) 25 (c) 15 (d) 100
6. The nth term of the sequence 5, 8, 11 _________ is 383. Find n. (a) 125 (b) 126 (c) 127 (d) 194
7. A quantity z varies directly as the square root of x and inversely as the cube of s. if z = 8. When x = 4 and s = ½, express z in term of x and s (a) z = 2√x/S³ (b) z = √x/S³ (c) z = 2s³/√x (d) z = √x/2s³. 2√x/S³ (b) z = √x/S³ (c) z = 2s³/√x (d) z = √x/2s³
8. If 3x – y = 5 and 2x + y = 15, evaluate x² + 2y (a) 29 (b) 30 (c) 42 (d) 35
9. What is gradient of the line joining point [2, 5] and [5, 14]? (a) 5 (b) 4 (c) 3 (d) 2.
10. A car covers 180m in

[t-1]

seconds and 324m in [t + 3] seconds. If it is travelling at a constant speed, calculate the value of t. (a) 8 (b) 6 (c) 5 (d) 4

In the diagram PR is a diameter, |PQ| = 15cm and |QR| = 8cm. Use the information to answer question 11 and 12.

1. Calculate the area of triangle PQR. (a) 23cm² (b) 60cm² (c)  68cm² (d) 120cm²
2. Calculate the perimeter of the semi circle of radius 21cm  [Take  = ²²/₇] (a) 66cm (b) 47cm (c) 60cm d.35cm
3. A bicycle wheel covers 100cm in one revolution. Find in terms of , the radius of the wheel. (a) 50/cm (b) 100/cm (c) 50cm (d) 100cmm

       In the diagram, TP is a tangent to the circle PQRS and <RPT = 73⁰.
       Find <PQR. (a) 146⁰ (b) 134⁰ (c) 113⁰ (d) 107⁰.

1. If sin x = ¹/₃, 0⁰< x < 90⁰, calculate the value of cos x.
    (a) ¹/₈ (b) ²/₅ (c) ^√2/₃ (d) ^2√2/₃
2. A ship sails 5km due west and them 77m due south. Find, correct to the nearest degree, its bearing from the original position.
    (a) 055⁰ (b) 056⁰ (c) 215⁰ (d) 216⁰
3. The semi-interquartile range of a distribution is 20. If the upper quartile is 96, find the lower quartile. (a) 56 (b) 50 (c) 46 (d) 40

1. The sum of the interior angles of an n-sided polygon is 1620⁰. Find n.
    (a) 9 (b) 10 (c) 11 (d) 12
2.  

	130o

In the diagram, 0 is the centre of the circle, LM is a tangent and angle MON is 130⁰. Find the size of angle OLM. (a) 65⁰ (b) 50⁰ (c) 45⁰ (d) 40⁰.

• IF ½p + q = 1 and p – ½q = 7, Find (p + q). (a) -8 (b) -4 (c) 4 (d) 8.
• Simplify: 1/x + 5 – 2(x + 2)/x² – 25 (a) x + 9/x² – 25 (b) x – 9/x² – 25
   (c) –x + 9/x² – 25 (d) –x – 9/x² – 25.
• The ratio of the area of the base of a cylinder to the curved surface area of the cylinder is 1:4. If the radius of the cylinder is 4cm, find the height of the cylinder. (a) 1cm  (b) 2cm (c) 4cm (d) 8cm
• Find the common factors of (9r² – 16s²) and (12r + 16s).            (a) 4(3r + 4s) (b) 4(3r – 4s) (c) 3r – 4s) (d) (3r + 4s).
• The height of a triangular prism is 6cm. if the cross section of the prison is an equilateral triangle of side 8cm, find its volume. (a) 96√3cm³ (b) 64√3cm³ (c) 32√3cm³(d) 16√3cm³.
• The interior angles on the same side of a transversal on two parallel lines are (a) equal (b) obtuse (c) complementary (d) supplementary.
• The average of 5 numbers is 40_six. Find the sum of the numbers in base six. (a) 200_six (b) 260_six (c) 300_six (d) 320_six.
• What is the value of x if the gradient of the joining (- 2, x) and (x, 3) is ¼? (a)  – 3 (b) – 2 (c) 1 (d) 2
• Simplify: m² – n²/n – m (a) m + n (b) –m – n (c) –m + n (d) m – n.
• Find the dimensions of a rectangle whose perimeter and area are 46cm and 112cm², respectively. (a) 16cm by 7cm (b) 17cm by 6cm (c) 14cm by 9cm (d) 12cm by 11cm.
• Given that p = {2, 4, 6, 7} and Q = {1, 2, 4, 8}. If a number is selected at random from PUQ, find the probability that it is only in set p. (a) ²/₃ (b) ½ (c) ¹/₃ (d) ¹/₆.
• If {x: 2 ≤ x ≤ 18; x  integer} and 7 + x = 4 (mod 9), find the highest value of x. (a) 2 (b) 5 (c) 15 (d) 18.
• Find the midpoint of a line joining the points M (4, 0) and N (3 , p) (a) (p/2, 7/2) (b) (7/2, p/2) (c) (1/2, p/2) (d) (p/2, 1/2)
• A trader bought an engine for $15,000.00 outside Nigeria. If the exchange rate is $0.075 to N1.00, how much did the engine cost in naira? (a) N250,000.00 (b) N200,000.00 (c) N150,000.00 (d) N100,000.00.
• Find the 7th term of the sequence: 2, 5, 10, 17, 26, _________ (a) 37 (b) 48 (c) 50 (d) 63.
• Given that log_x 64 = 3, evaluate x log₂8. (a) 6 (b) 9 (c) 12 (d) 24.
• If 2ⁿ = y, find 2 ^{(2 + n/3)} (a) 4y^1/3 (b) 4y^-3 (c) 2y^1/3 (d) 2y^-3.
• Factorize completely : 6ax – 12by – 9ay + 8bx. (a) (2a – 3b)(4x + 3y) (b) (3a + 4b)(2x – 3y) (c) (3a – 4b)(2x + 3y) (d) (2a + 3b)(4x – 3y).
• Find the equation whose roots are ¾ and -4. (a) 4x² – 13x + 12 = 0    
   (b) 4x² – 13x – 12 = 0 (c) 4x² + 13x – 12 = 0 (d) 4x² + 13x + 12 = 0.
• If m = 4, n = 9 and r = 16, evaluate ^m/_n – 1⁷/₉ + ⁿ/_r. (a) 1⁵/₁₆ (b) 1¹/₁₆
  (c) ⁵/₁₆ (d) –³⁷/₄₈.
• Adding 42 to a given positive number gives the same result as squaring the number. Find the number. (a) 14 (b) 13 (c) 7 (d) 6.
• Ada draws the graphs of y = x² – x – 2 and y = 2x – 1 on the same axes. Which of these equations is she solving? (a) x² – x – 3 = 0 (b) x² – 3x – 1 = 0 (c) x² – 3x – 3 = 0 (d) x² + 3x – 1 = 0.
• The volume of a cone of height 3cm is 38½cm³. Find the radius of its base. [Take  = ²²/₇] (a) 3.0cm (b) 3.5cm (c) 4.0cm (d) 4.5cm.
• A sector of a circle with radius 6cm subtends an angle of 60⁰ at the centre. Calculate its perimeter in terms of . (a) 2( + 6)cm (b) 2( + 3)cm (c) 2( + 2)cm (d) ( + 12)cm.
• The dimensions of rectangular tank are 2m by 7m by 11m. If its volume is equal to that of a cylindrical tank of height 4cm, calculate the base radius of the cylindrical tank. [Take  = ²²/₇]. (a) 14m (b) 7m (c) 3½m
   (d) 1¾m.
• Given that tan x = ²/₃, where 0⁰ ≤ x ≤ 90⁰, find the value of 2 sin x.
  (a) ^2√13/₁₃ (b) ^3√13/₁₃ (c) ^4√13/₁₃ (d) ^6√13/₁₃.
• PQRS is a square. If X is the midpoint of PQ, calculate, correct to the nearest degree, <PXS. (a) 53⁰ (b) 55⁰ (c) 63⁰ (d) 65⁰.
• The angle of elevation of an aircraft from a point K on the horizontal ground is 30⁰. If the aircraft is 800m above the ground, how far is it from K? (a) 400.00m (b) 692.82m (c) 923.76m (d) 1,600.00m.
• The population of students in a school is 810. If this is represented on a pie chart, calculate the sectoral angle for a class of 72 students.
   (a) 30⁰ (b) 45⁰ (c) 60⁰ (d) 75⁰.
• The scores of twenty students in a test are as follows: 44, 47, 48, 49, 50, 51, 52, 53, 53, 54, 58, 59, 60, 61, 63, 65, 67, 70, 73, 75. Find the third quartile. (a) 62 (b) 63 (c) 64 (d) 65.

• Find the distance between the points C(3,3) and D(- 1, 5).
          (a)        (b)3      (c)    (d)2