senior cycle

SECTION A: OBJECTIVES

1.               Express the product of 0.06 and 0.09 in standard form

[A] 5.4 × 10^-3                               [B ] 5.4 × 10^-1      [C ]5.4 × 10²        [D]  5.4 × 10³

          2             Simplify   36 ^½   ×   64 ^-1/2 ×  5 ⁰

                                   [A] 2               [B] ¾      [C] 2 ¾                  D 4

3                 Find the number whose logarithm to base 10 is 2.6025

[A] 0.404                      [B] 40                    [C] 400.4                              [D] 0.04

       4.            The angles of a pentagon are x⁰,  2x⁰,  (x+60)⁰,  (x+10)⁰,  (x-10)⁰ find x

                                 [A] 30                            [B] 800                  [C] 0.8                   [D] 80

      5.            The angles marked in this diagram are measured in degrees, find x.   

                                         

                       [A] 24⁰                   [B] 48⁰                   [C] 30⁰                   [D] 36⁰

    6.        Convert 101101_two to a number in base ten

                [A] 46                    [B] 45                    [C] 44                    [D] 61

     7.       In the diagram, PQRS is a parallelogram and <QRT=30⁰. Find x.

                [A] 95⁰                    [B] 100⁰                                [C] 150⁰                                         [D] 120⁰

     8.       Correct 0.04945 to two significant figures.

                [A] 0.49                [B] 0.050                              [C]0.040                               [D]0.049

     9.       Evaluate 7¹/₂ –( 2¹/₂ + 3) ÷ 33/2

                [A] 7                      [B] 8                       [C] 32                    [D]14

10.          In the diagram below, IQRI= 5cm, PQR =60 and PSR =45⁰. Find IPSI.

                [A] 24                    [B] 12.25              [C] 13                    [D] 43   

        

11.   Each interior angle of a regular polygon is 162⁰. How many sides has the polygon?

         [A]    8       [B]    12      [c]      20       [d]      16

12.  From the diagram above, find the value of x.

                               

  [A]   25    [B]     40       [C]     20       [D]      30

13.   Which of the following is not true

  [A]   A parallelogram is a quadrilateral

  [B]   A rhombus is a parallelogram

  [C]   A square is a rhombus

  [D}   A square is a polygon

14.  Simplify ( 1⁵/₈ + 1 ³/₅₎ ÷ 5³/₅

       [A]    ⁴/₅     [B]      ²/₃     [C]     ³/₅   [D]     ¹/₂

15.   186 is the result of increasing a number by 20%. Find the number.

     [A]    40     [B]     130    [C]   155    [D]   85

16.  Find the value of   4(3d - e) -2f when d=2, e=4 and f=3

    [A]   -3    [B]    6    [C]    2    [D]    4

17.  If  N = {  odd numbers greater than 11 }, which one of the following is an element of N?

    [A]    9      [B]     10        [C]       13       [D]    14

18.    In the diagram below, ABP = 110⁰ and DCP = 163⁰, calculate BPC

   [A]    47⁰      [B]    63⁰    [C]    93⁰     [D]    180⁰                                                                      

19.  Which of the following statements is false?                                                

   [A]    12 є {2, 4, 6, 8…}

   [B]     {a, b } C { f, a, c, e }

   [C]     {1,2} U { 2, 3} == {2}

  [d]   If Z = {10}, n(Z) = 0

20.  Express 40cm as a percentage of 8m

    [A]   32%    [B]   20%     [C]   5%    [D]    8%

21.  Simplify  (¹/₄)^-1.5

   [A]   21     [B]    8    [C]    2      [D]     4

22.  If a=1, b=2, and n=5,

    Find the value of 

  [A]   7    [B]    6     [C]     3      [D]     2

The table below shows the frequency distribution of a number of choirs in each of 40 rooms of various houses.

Use the table to answer Question 23- 25

23. Find the mean of the distribution.

  [A]     5.7      [B]      4.4       [C]      5.0      [D]   3.5

24.  Find the mode of the distribution.

   [A]    40      [B]     5       [C]      9    [D]    7

25. Find the median of the distribution

   [A]    3     [B]     5       [C]     4      [D]     4.5

26.  In the diagram, EF//QR, PE = 2cm, EQ= 4cm and FR = 6cm. Find x

         

[A]    4cm       [B]      3cm     [C]    5cm      [D]    6cm

27.  In the diagram, QRS is a Straight line, QP//RT, < PQR = 56⁰ , <QPR = 48⁰

        And <TRS = x⁰ Find x

   [A]   84⁰    [B]     76⁰   [C]     21⁰     [D]   33⁰

28. In isosceles ∆ ABC, ІABІ= ІACІ. If  B = 55⁰  calculate A

   [A]    125⁰       [B]     70⁰      [C]     81⁰      [D]     35⁰

29.  ABC is an equilateral triangle. P is a point on IACI such that PBC=46⁰

        Calculate <APB 

 [A]   100⁰      [B]   106⁰        [C]    41⁰      [D]     28⁰

30.  Find the interior angles of a regular polygon which has 6 sides.

  [A]    70⁰    [B]     120⁰       [C]      60⁰      [D]     140⁰

31.  One of the following is not a polygon.

   [A]   Triangle   [B]   Rectangle    [C]     Square     [D]    cube

32.  How many pieces of string each 8¹/₂ cm long can be cut from a string 42¹/₂ cm long

     [A]   50      [B]    35      [C]     ¹/₅    [D]    500

33.  A man gets a 10% pay rise. If his present wage is N 6000 per week, calculate his new weekly wage.

     [A]   N 250 [B]    N 700    [C]    N 300    [D]   N 6, 600

34.  Calculate the principal which earns N 75 075

       Simple interest in 11years at 7% p.a

     [A]   N 500     [B]   N 4 000   [C]     N 23 000     [D]    N 97, 500

35.  Remove the bracket and simplify 2a-(4a – 5a-7)

      [A]   2+a    [B]    -3 +4a    [C]    9a-2    [D]   3a-7

36.  Which of the following is incorrect?

     [A]   U = union   [B]  є = element   [C]  Ф = empty set  [D]  С = infinite set

37. Solve for the value of x in 22= 7 + 2⅟₂x

       [A]  18    [B]   7     [C]  4     [D]   6

38.  t= ^3p/_r  +  S    make r the subject of formular.

      [A]   r= ^t-p/_s       [B]  r= ^t/_p+t        [C]   r= t²/p+s        [D]  r= ^3p/_t-s

39. The square of  111_two  is

      [A]   10001   [B]    11101    [C]    10111    [D]  110001

40. ABCDEF is a regular hexagon with O at its centre. What kind of quadrilateral is ABCO

       [A] Rectangle   [B] Square   [C]   parallelogram   [D]   Rhombus

41. In the diagram below, IPRI = IPQI, IOSI = IQRI and RPQ = 40⁰ , calculate PQS.

     

       [A]   30⁰    [B]    70⁰     [C]    40⁰     [D]    85⁰  

Use the diagrams below to answer question 42 to 44

42. Which of the following triangles are congruent?

 [A]  ii   and iii     [B]   I and iv    [C]    iii and iv      [D]   I and iii

43.  Which of the following is/ are embedded angle?

  [A]  I   and ii    [B]   ii   and iii   [C]    I and iv   [D]    iii and iv

44. Which of the following is (AAS)

   [A]   i    [B]   ii      [C]    iv    [D]    iii

45.  Simplify    5x – 8x + x + 3y

   [A]   3y-2x     [B]    2-y       [C]   y-3x       [D]    3y+3x

46. Find the sum of angles in a regular heptagon.

   [A] 320⁰    [B]   900⁰    [C]   700⁰    [D]    540⁰

47. In the diagram below IXYI = IYZI, IXZI = IZHI and XYZ = 52⁰ calculate ZHX

   

48. The perimeter of a rectangle is 20m and the length is Xm. Find the area of     

   the rectangle in terms of x.

   [A]  2x+10   [B]  x-5    [C]    2x-20     [D]     10x-x²

49. If 8x-4 = 6x-10, find the value of 5x

   [A]   -15       [B]    6      [C]     7      [d]     3

50. Which of the following is not necessarily true of a rectangle?

    [A]   The diagonals are equal.

    [B]   Each diagonal divides the rectangle into

    [C]   The diagonals are perpendicular

    [D] Each diagonal divides the area of the rectangle equally.

SECTION B: THEORY

PART1: ANSWER ALL THE QUESTION IN THIS PART

1a. Simplify 125^-⅟₃ × 49^-½ × 10⁰

  b. list  (i)  four basic laws of indices.

              (ii) Two fractional indices.

1                     Use mathematical tables to evaluate

(a)         

(b)       

 

3a.    The sum of the interior angles of a regular polygon is 900⁰.      

         Calculate (i) The   number of sides   (ii)   The size of one   

         Exterior angle of the polygon.

  b.   Prove that the exterior angle of a triangle is equal to sum 

         of the opposite interior angles.                                                                         

4a.    Simplify 7¹/₂ – ( 2¹/₂ + 3 ) ÷ ³³/₂

  b.    Solve for the value of x in  3x-[3 (1+x) – 2x] =3

PART II:  ANSWER FOUR QUESTIONS ONLY FROM THIS PART

5a. The result of taking 3 from x and multiplying the answer by   

        4 is the same as

       Taking 3 from the x

b. 4m/₃ – ¹⁷/₂₁ = ^6m-1/₇  solve for m.

6a. Convert (i)    57_ten to binary

                       (ii)  1101_two to base Ten.

  b.  (i)   find ( 101₂ )² expressing the answer in base 2

        (ii)   Convert 1.101 from bicimals to decimals.

7a. Isosceles triangle ABC and ABD are drawn on opposite sides   

      of a common base AB. If ABC = 50⁰ and ADB = 110⁰,  

      Calculate ACB and CBD.

                            

    b.   List 2 properties each of the following:

        (i)  Parallelogram      (ii)    A rhombus

        (iii) A rectangle          (iv)   A square.

8a.     S = { 1,2,3,4,5,6 } ,  T = { 2,4,5,7 } and R = { 1,4,5 } , find

(i)                                 { S n T } U R

(ii)                               { S U T } n R

    b. Define the following:

           (i)    Ф     (ii)   є   (iii)    n    (iv)    С

9a.  Remove the brackets and simplify.

(i)                               y( 2y-3) -  3(2y-3)

(ii)                            3( 3a-b) – 5(a-4b)

  b.   factorise

       (i)    -18pq – 12                                           (ii) 100 – 49x²

10a.  The following give the summary for congruency of two

         triangles. Draw the diagrams to represent each of the

         following.

(i)                                 SAS   (ii)   ASA     (iii)   SSS     (iv)   RHS

   b.   In a given parallelogram ABCD, simply show that the

          opposite sides are equal.