BECE 2020 Mathematics Past Questions and Answers

Answer: B. ½
Step 1

Find the least common multiple (LCM)

LCM for 4, 3 and 12 is 12, thus

Multiples of 4

4,8,12,16,20,24,28,32,36,40,44,48
Multiples of 3

3,6,9,12,15,18,21,24,27,30,33,36

Multiples of 12

Multiples of 12 are numbers 12 can divide without a remainder (Simply the multiplication of 12). If you don't know the recitation of the multiples, simply add 12 to the preceding numbers to get the subsequent numbers starting from 12.

12,12+12=24,24+12 = 36,36+12 = 48,48+12 = 60,60+12 = 72,72+12 = 84,84+12 = 96,96+12 = 108,108+12 = 120,120+12 = 132,132+12 = 144,...

⇒ 12,24,36,48,60,72,84,96,108,120,132,144,...

From the above you can see that the least number which appeared in all the above multiples is 12, hence the LCM for 3,4 and 12 is 12

Step 2

Divide by the LCM and find out how many times the denominator goes into the LCM and multiply that by the numerator and maintain the signs

Thus for ¾ , the numerator is 3 and the denominator is 4 and 4(denominator) goes into 12(the LCM),3 times, hence 3 x 3 (numerator)

Thus for -⅓ , the numerator is 1 and the denominator is 3 and 3(denominator) goes into 12(the LCM),4 times, hence 4 x 1 (numerator) and maintain the negative sign.

Thus for +1⁄12 , the numerator is 1 and the denominator is 12 and 12(denominator) goes into 12(the LCM),1 time, hence 1 x 1 (numerator) and maintain the positive sign.

Now simplify the numerator first and afterward simplify the new fraction

As shown below

Answer: D. {}
x:x is read as x is such that x is ...

N contains the list of factors of 18. A factor is a number or algebraic expression that divides another number or expression evenly, thus no remainder.

Factors of 18 are 1,2,3,6,9 and 18 itself

Thus

1x18 = 18

2x9 = 18

3x6 = 18

Hence 1,2,3,6,9 and 18 are factors of 18

⇒ N = {1,2,3,6,9,18}

Multiples of 12 are numbers 12 can divide without a remainder (Simply the multiplication of 12). If you don't know the recitation of the multiples, simply add 12 to the preceding numbers to get the subsequent numbers starting from 12.

Multiples of 12

12,12+12=24,24+12 = 36,36+12 = 48,48+12 = 60,60+12 = 72,72+12 = 84,84+12 = 96,96+12 = 108,108+12 = 120,120+12 = 132,132+12 = 144,...

⇒ multiples of 12 are 12,24,36,48,60,72,84,96,108,120,132,144,...

⇒ M = {12,24,36,48,60,72,84,96,108,120,132,144,...}

∩ means intersection. The element(s) which you can find in both sets.

Hence N ∩ M should contain element(s) which can be found in both set N and M.

From the above, you can see that there is no element that can be found in N,{1,2,3,6,9,18} and at the same time be found in M,{12,24,36,48,60,72,84,96,108,120,132,144,...}. Hence the intersection of N and M is an empty set {}

Answer: D. 4.38293 x 10$^{3}$
Standard form, or standard index form, is a system of writing numbers which can be particularly useful for working with very large or very small numbers.

It is based on using powers of 10 to express how big or small a number is.

Standard form is written in the form of a x 10$^{n}$, where a is a number bigger than or equal to 1 and less than 10.

n can be any positive or negative whole number.

For example 1.2 x 10$^{3}$, 3.14 x 10$^{-5}$

The rules when writing a number in standard form is that first you write down a number between 1 and 10, then you write × 10(to the power of a number).

Thus the decimal point must be behind the first non-zero digit

If you move the decimal point to the left, the power (number of times of movement) of 10 will be positive and if to the right, negative

The first non-zero digit in 4382.93 is 4, hence we have to move the decimal point (.) 3 times to the left before placing it behind the 4. Since the movement is to the left, the power (3) of 10 is positive.

Answer: C. Distributive
Associative Property

This property states that when three or more are added (or multiplied), the sum (or the ) is the same regardless of the grouping of the (or the multiplicands).

Associative property gets its name from the word "Associate" and it refers to grouping of numbers.

Grouping means the use of parentheses or brackets to group numbers.

Associative property involves 3 or more numbers.

The numbers that are grouped within a parenthesis or bracket become one unit.

Associative property can only be used with addition and multiplication and not with subtraction or division.

Example of Associative Property for Addition





Examples of Associative Property for Multiplication:





The above examples indicate that changing the grouping doesn't make any changes to the answer.

The associative property is helpful while adding or multiplying multiple numbers. By grouping, we can create smaller components to solve. It makes the calculations of addition or multiplication of multiple numbers easier and faster.

Example Addition:

17 + 5 + 3 = (17 + 3) + 5
= 20 + 5
= 25

Here, adding 17 and 3 gives 20. Then, adding 5 to 20 gives 25. The grouping helped to find the answer easily and quickly.

Example Multiplication:
3 × 4 × 25 = (25 × 4) × 3
= 100 × 3
= 300

Here, multiplying 25 by 4 gives 100. Then, 3 can be easily multiplied by 100 to get 300.

However, we cannot apply the associative property to subtraction or division. When we change the grouping of numbers in subtraction or division, it changes the answer and hence, this property is not applicable.

Example Subtraction:

10 – (5 – 2) = 10 - 3 = 7
(10 – 5) – 2 = 5 – 2 = 3
So, 10 – (5 – 2) ≠ (10 – 5) – 2

Example Division:

(24 ÷ 4) ÷ 2 = 6 ÷ 2 = 3
24 ÷ (4 ÷ 2) = 24 ÷ 2 = 12
So, (24 ÷ 4) ÷ 2 ≠ 24 ÷ (4 ÷ 2)

Commutative Property

The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. The property holds for Addition and Multiplication, but not for subtraction and division.



The above examples clearly show that we can apply the commutative property on addition and multiplication. However, we cannot apply commutative property on subtraction and division. If you move the position of numbers in subtraction or division, it changes the entire problem.

Therefore, if a and b are two non-zero numbers, then:

The commutative property of addition is:
a + b = b + a

The commutative property of multiplication is:
a × b = b × a

In short, in commutative property, the numbers can be added or multiplied to each other in any order without changing the answer.

Distributive Property

To "distribute" means to divide something or give a share or part of something. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.



Example

( 5 + 7 + 3 ) x 4 = 15 x 4
= 60

This can be solved using the distributive property as:
( 5 + 7 + 3 ) x 4 = 5x4 + 7x4 + 3x4
= 20+28+12
= 60

Answer: C. 8-10*x*
Subtract (7*x*-3) from (5-3*x*) ⇒ (5-3*x*) - (7*x*-3)

(5-3*x*) - (7*x*-3) = (5-3*x*) - 1(7*x*-3)

NOTE: Every number is multiplied by 1 which is the same number or has no effect, thus - (7*x*-3) = - 1(7*x*-3)

Applying the distributive property, a(x+y) = a*x*x+a*x*y

⇒ - 1(7*x*-3) = -1x7*x*-1x(-3) = -7*x*+3

NOTE: - x - = +

(5-3*x*) - 1(7*x*-3) = 5-3*x* -7*x*+3

Grouping like terms ⇒ 5-3*x* -7*x*+3 = 5+3 -3*x*-7*x*

⇒ 5-3*x* -7*x*+3 = 8 -10*x*