The date for the 2023 Basic Education Certificate Examination (BECE) is drawing nearer. Candidates are therefore advised to make themselves prepared especially Mathematics before the due day. Master the following Mathematics questions with their answers which have been given in detailed manner. Students who want to pass the Basic Education Certificate Examination (BECE) should familiarize themselves with the following Mathematics questions and answers so as to get equiped with the concepts. Students cannot pass Mathematics without constant solving of questions.
(1) Given the L.C.M of two numbers to be 360 and H.C.F of 30 if one of the numbers is given to be 120, find the other number
A.390
B.90
C.330
D.150
Correct answer is B.
Explanation
Given the H.C.F of 30 and L.C.M of 360 and the other number as 120, let a variable represent the
other number say (y). Find the product of H.C.F and the L.C.M and equate it to the product of
the given number and the other number. Solve for the missing variable to get the other number. After going through the processes, you will realize that 90 is the correct answer which makes the correct option B.
Solution
H.C.F = 30, L.C.M =360, given number =120let x= the other number
=> H.C.F × L.C.M = given number × other no
=> 30 × 360 = 120x
=> multiply both sides
=> 10800=120x
=> Divide both sides by 120
=> 10800/120=120/120
=> 10800/120= x
=> 90= x
=> x = 90
Therefore the other number = 90; hence, the correct answer is B.
(2)Alice has been given an assignment by his home tutor to express 180 as the product of prime
factor. Her result will be written as…
A.3?2 x 4 x 5
B.2?3 x 3?3 x 5?2
C.2?2 x 3?2 x 5
D.2 x 3?2 x 5
Correct answer is C.
Explanation
To express 180 as a product of prime factors, find the product of the last prime numbers by
half of the given number. Note that, the two numbers should go directly into the number
given without any remainder.
Solution
180 = 2 x 90
It can further be expand as
2 x 2 x 45
2 x 2 x 3 x 15
Maintain each prime number at every step. Now expand 15 to get 3 x 5 making it;
2 x 2 x 3 x 3 x 5
2 x 2 =2?2, 3 x 3 = 3?2, 5 x 1 = 5
Product of prime factor now becomes;
2?2 x 3?2 x 5
Hence the correct answer is C.
(3)The product of primes of 10 and 15 are…..respectively
A.2 X 3, 3 X 5
B.2 X 5, 3 X 5
C.2 X 3, 5 X 5
D.2 X 3, 5 X 5
Correct answer is B.
Explanation
To solve this, find the product of primes of 10 and 15. Later, proceed to find two prime
factors of 10 and 15 which will sum up to 10 and 15 respectively when they are multiplied.
Solution
10 = 2 x 5; it cannot be reduced nor expanded any further
15 = 3 x 5; it cannot be reduced nor expanded any further
2 x 5, 3 x 5 is the correct answer which is option B.
(4)The number of elements of factors of 320 is given by…..
A.12
B.20
C.16
D.14
Correct answer is D.
Explanation
To begin, first find all the possible numbers which can go into 320 directly without any
remainder starting from 1 and ending at the same number given which is 320. When you are
done, count the number of element to find your answer.
Solution
Factors of 320= {1,2,4,5,8,10,16,20,32,40,64,80,160 and 320}
There are 14 element hence, the answer is option D.
It is my hope that these questions and solutions will be beneficial to BECE candidates who want to pass Mathematics.
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