Exam;2023 WAEC

Subject; Further Maths(OBJ&ESSAY)

Password;1980

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MATHS OBJ;-ExamgrandComNg
01-10 BBCCCDDCAB
11-20 BBBBBADDBA
21-30: CCCDCBDBAA
31-40: ACDDADDDBD

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(1)

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(2&3)

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4(a) We can use the formula for the sum of an arithmetic progression:

S = (n/2)(a1 + an)
where S is the sum of the terms, n is the number of terms, a1 is the first term, and an is the last term.
Plugging in the given values, we get:
286 = (n/2)(-8 + 52)
Simplifying:
286 = (n/2)(44)
Multiplying both sides by 2/44:
286(2/44) = n
n = 13
So there are 13 terms in the series.

(b) We can use the formula for the nth term of an arithmetic progression:
an = a1 + (n-1)d
where d is the common difference.
Plugging in the given values for a1, an, and n, we get:
52 = -8 + (13-1)d
Simplifying:
60 = 12d
d = 5

So the common difference is 5.
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(5)
TABULATE

Mass (kg): 31-40| 41-50| 51-60| 61-70| 71-80| 81-90

F: 3| 10| 15| 12| 6| 4

x: 35.5| 45.5| 55.5| 65.5| 75.5| 85.5

Fx: 106.5| 455| 832.5| 786| 453| 342

Class boundaries: 30.5-40.5| 40.5-50.5| 59.5-60.5| 60.5-70.5| 70.5-80.5| 80.5-90.5

(i) Mean (x-bar) = ∑fx/∑f = 2975/50 = 59.5
:. Mean = 60kg

(ii) Mode = L¹ + ( fm-fa/2fm-fa-fb) c
= 50.5. + (15-10/2*15-10-12)10
= 50.5 +(5/8)10
= 50.5+6.25
:. Mode = 56.75
Mode = 57kg(approx)
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(7)