# WUC 116 Mathematics

## Question:

Given the sets  and
(i)     List the first 10 elements of set A.

(ii)    List the first 10 elements of set B.

(iii)   List the elements of set C.

(iii)   Draw a Venn diagram to illustrate .
(iv)   Insert any common elements in the Venn diagram  of part (iii).

[Note: elements in a Venn diagram has to be indicated by a dot, together with the element, as shown, " ]

Question 2

• Draw an equilateral triangle of sides about 4 cm, naming the vertices as A, B and C.[You may use MS Word to 'draw', no need to be exactly equilateral, but close to one.]

• Copy and paste triangle in (i) and draw an inverted equilateral triangle inside it using the mid-points of AB, BC and CA as vertices. Name this triangle PQR.

• Copy and paste the result shape in (ii) and draw another equilateral triangle inside triangle PQR, naming this triangle LMN where L, M and N are the mid-points of the sides of triangle PQR.

• Now, count the number of triangles in each of the diagrams in (i), (ii) and (iii) and write down the answers next to the diagrams.

• Can you predict the number of triangles in the next 2 diagrams if you were to continue the process of drawing equilateral triangle within the inner most triangle.
• List the five numbers in a horizontal manner; what type of sequence does the 5 numbers above constitute

Use the information to find the number of triangles after adding the 10th triangle.

Question 3

(a)   (i)   A geometric sequence is given as 2, 6, 18 ….... Use the symbols, ‘a’ for first  term and ‘r’ for common ratio, state the values of 'a' and 'r'.

(ii)   Find the 11 term,  , of the sequence.

(iii)  Find the sum of the first 11 terms of the sequence.

(b)   The scores of 60 students in a test are:

61     49     42     63     50     76     61     84     66     72

75     35     58     54     82     66     53     48     36     55

82     55     68     32     62     58     48     70     80     49

58     67     70     46     40     70     69     57     52     60

47     50     48     68     59     60     62     71     72     68

46     55     36     70     36     82     60     42     55     50

• Find the mean score using the data above.
• Find the mode of the scores.
• Complete the grouped frequency table below:
 Class Tally for Counting Frequency 30 – 39 40 – 49 50 – 59 60 – 69 70 – 79 80 - 89

[Use '/' for the counting purposes.]

• Complete the table below and find the mean and median of the data.
 Class Mid-point (m) Frequency (f) Cumulative Frequency mf 30 – 39 40 – 49 50 – 59 60 – 69 70 – 79 80 - 89

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