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JAMB PAST QUESTION AND ANSWER on polygon, set, bearing, permutation and combination

Mathematics questions with solutions

1. A regular polygon has each of its angles as 160⁰. What is the number of sides of the polygon?

a) 36
b) 9
c) 18
d) 20
Solution
Number of sides of the polygon » n
»180(n-2)/n
160 »180(n-2)/n
Cross multiply
160n » 180n-360
Collect like terms
360 »180n-160n
360 » 20n
Divide both sides by 20
n » 18 (C)

2. A girl walks 30m from a point p on a bearing of 040⁰ to a point Q. She then walks 30m on a bearing of 140⁰ to a point R. The bearing of R from P is?

2. A girl walks 30m from a point p on a bearing of 040⁰ to a point Q. She then walks 30m on a bearing of 140⁰ to a point R. The bearing of R from P is?

a) 90⁰
b) 50⁰
c) 45⁰
d) 40⁰
Solution
From the figure above, the bearing of R from P » 40⁰ + ø
Triangle PQR In isosceles,
Therefore, angle P = angle R = ø
Ø » (180-80)/2 » 50⁰
The bearing of R from P
Ø » 40⁰ + 50⁰
» 90⁰ [A]

3. How many different three digits number can be formed using the integers 1 to 6 if no integer occurs twice in a number?

a) 24
b) 120
c) 60
d) 48

Solution

The number of three digit number from integer 1 to 6

6P3 » n!/(n-r)!
6!/(6-3)! 
6!/3!
6×5×4×3!/3!
120 [b]

4. In how many different ways can the letters of the word GEOLOGY be arranged in order?

a) 720

b) 1260

c) 2620

d) 5040

Solution

The word GEOLOGY has 7 letters » 7!
‘0’ occurs twice  (2!)
‘G’ occurs twice = (2!)

The rest appears only ‘once’

In how many different ways can the letters be arranged in order

7!/(2!2!) 
7×6×5×4×3×2!/(2!2!)
» 7×6×5×2×3 
1260 [b]

5. A cyclist rode for 30 minutes at xkm/hr and due to a breakdown he had to push the bike for 2hrs at x-5km/hr. If the total distance covered is less than 60km, what is the range of the value of x?

a) X<14

b) X<20

c) X<29

d) X<28

Solution

Distance covered in the first part » speed × timetaken
X × 30/60
½xkm
Distance covered in the second part » 2(x-5)km

When distance covered is less than 60km

Therefore, 2(x-5)2 + ½x < 60

4x-20 + ½x < 60 
4x-20 + x < 120

5x<140

X<28 [d]

Oluwamuyide Peter

My name is seyi, the main aim of creating this platform is to help users get information like school updates, electrical engineering topics, school project and many more for free

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