POST-UTME PAST QUESTIONS AND ANSWERS

MATHEMTICS 
1. The sum of N140, 000 is shared between Abu, Kayode and Uche. Abut has twice as much a kayode, and  Kayode has twice as much as Uche. What is Kayode’s share? (A) N80,000 (B) N10,000 (C) N40,000 (D)  N20,000
2. I am x years and my brother is 3years older. How old was my brother last year (A) (x – 4) years (B) (x +2) years (C) (3x – 1) years (D) (3x +1) years
3. Divide the sum of 8,7,2,6,0,4,7,2,3 by their mean (A) 7 (B) 9 (C) 8 (D) 6
4. A chord of length 6cm is drawn in a circle of radius 5cm. find the distance of the chord from the centre of  the circle (A) 2.5cm (B) 3.0cm (C) 3.5cm (D) 4.0cm
5. A sector of a circle of radius 1cm containing an angle 60o is folded to form a cone. Calculate the radius of the base of the cone (A) 5 ½cm (B) 4 2/3cm (C) 3 ½ cm (D) 2 1/3cm
6. A rectangular picture 6cm by 8cm is enclosed by a frame ½ cm wide. Calculate the area of the frame (A)  20sq.cm (B) 15sq.cm (C) 13sq.cm (D) 16sq.cm
7. In a sector competition in one season, a club had scored the following goals:
2,0,3,3,2,1,4,0,0,5,1,0,2,2,1,3,1,4,1 and 1. The mean, median and mode are, respectively: (A) 1.8, 1 and 1.5 (B) 1.8, 1.5 and 1 (C) 1.5, 1 and 1.8 (D) 1, 1.8 and 1.5
8. Seven (7) pupils of average age 12years leave a class of 25 pupils of average age of 14 years. If 6 new pupils of average age 11 years join the class, what is average age of the pupils now in the class? (A) 13 years (B) 12 years 7 ½ months (C) 13 years 5month (D) 13 years 10 months
9. By selling an article for N45.00 a man makes a profit of 8%. For how much should he have sold it in order to make a profit of 32% (A) N180.00 (B) N58.00 (C) N55.00 (D) N63.00
10. A group of 14 children received the following scores in a reading test:
35,35,26,26,26,29,29,29,12,25,25,25,25,17. What was the median score? (A) 29 (B) 26 (C) 25 (D) 23 
SOLUTION
1. let my age be x
Since my brother is 3 years older, than we have
(x + 3) years
His age last years: (x+3) -1 years
(x +3 -1)years
  Ans = B
2. From the name, let Abu, Kayode and Uche,s
share A, K and U respectively.
Since Abu has twice as Kayode: A = 2k
= > K= -A/2
By putting the value of K in k, we have A/2
Therefore A/2 x ½ = A/4
Total share: A + A/2x = A/4 #140,000
4A + 2A +A = A #140,000
4
7A = _ # 140,000
7A  = _#560,000
A    x = A   #140,000
 A = #80,000 Abu’s share N80,000
REM: Abu has twice as Kayode: A = 2k; k = A
       2
We have 80,000 = #40,000
       2
Therefore Kayode’s share = # 40,000
 Ans = C
3. The sum of the set of no. gives
8+7+2+6+0+4+7+2+3 = 39
Their mean = total no. of the set = 39
   No. of the set           9
 = 4.33   Ans = B 
4 Using Pythagoras theorem
OA2= Ap2 + Op2
52 = 32 + d2
25 = 9 + d2
16 = d2 => d =4.0 Ans=D
5 Using ϴ= r = unknown,
1 = radius, ϴ = 60o
60 =  r
360  14
840= 360r
84= 36r
R= 2.5cm Ans= A 
6 Area of frame = External Area – Internal Area
= [8 + 1] [6 + 1] – 8[6]
= 9x 7 – 48
= 63- 48 => 15 sq. cm  Ans= A
7 [i] The mean =  total no. of the set
    No. of the set
Total no. of the set = 36 = 1 4/5
 No. of the set 20
[ii] To find the median, first arrange the set on nos.
in either ascending or descending order. By
arranging in ascending order it becomes
0,0,0,0,1,1,1,1,1,1,12,2,2,2,3,3,3,4,4,5. By
counting 10s on both sides of the set of nos 1
and is middle numbers in this case, we have to
add them and divide their sum by 2. i.e 1+1= 2
= 1      2
       [iii]
 Mode = the number with the highest
occurrence [Highest frequency]. From the set
of nos. the mode is 1, since it occurred 6 times
and 1.5 in the options. Therefore, from the
options Ans = A[1.8, 1 and 1.5] since it follows
the sequences.
 
8 Total sum of 7 pupils of average age 12 yrs. Total sum of 25 pupils of average age 14 yrs = 25
x 14 = 350. Total no. age remaining: 350 – 84 = 266. Total sum of 6 pupils of average age 11
yrs = 6x11= 66. Since they joined the class, then it gives = 266 + 66 = 332. No of pupils
remaining in the class: = 25 – 7 +6 = 24.
Average age of remaning pupils gives: = 332 = 13 Rem. 5 => 13 years 5 months  Ans = C
9. 8% profit = 100 + 108%, 32% profit = 100 + 32 = 132%
108% => N45.00
132% =>?
Therefore 132% x 45 = N55.00 Ans = C
   100
10. Frist arrange the set of nos. in either ascending or descending order:
12,17,25,25,25,25,26,26,26,29,29,29,35,35
By counting 6 on each side on the set of the nos. the median fall b/w 26 and 26
Median = 26+ 26/2 = 26 Ans = B