# BECE 2019 Mathematics (Maths) Past Question Paper Two

1

## (c) If $\frac{p+2q}{p}=\frac{7}{5}$, find the value of $\frac{q}{p} ,\ where\ p\neq0 .$

1. (a)
x = { 4,5,6,7,8,9,10,11,12,13}
y= {3,6,9,12,15,18}

$X\ \cap Y$ = {6,9,12}

(b) The LCM is the smallest positive number that all of the numbers divide into evenly.
We solve this question by;

1. List the prime factors of each number.
2. Multiply each factor the greatest number of times it occurs in either number.

Since 3 has no factors besides 1 and 3. 3 is a prime number
Since 5 has no factors besides 1 and 5. 5 is a prime number
9 has factors of 1,3 and .

The LCM of 3,5,9 is the result of multiplying all prime factors the greatest number of times they occur in either number.

The LCM of 3,5,9 is $3^2 \times 5 =45.$

$\\ \frac{p+2q}{p}=\frac{7}{5}, \\ \text{simplifying }\\\ p+2q= \frac{7p}{5}, \\ \ 5p+10q= 7p,\\ \ 10q= 7p-5p \\ \ 10q = 2p \\ \frac{q}{p} = \frac{2}{10}\\ \frac{q}{p} = \frac{1}{5}\\$

2

## (c) Simplify:$\left(8x^2y^3\right)\left(\frac{3}{8}xy^4\right)$

2. (a)
Find the LCM of 5 and 4 which is 20.
Multiply all terms by 20 and simplify

(b) (i)
Boys : Girls = 12:25,
If there are 120 boys,let x be the number of girls
120 boys : x girls
12:25 = 120: x

If more, less divides
Therefore

Hence there are 250 girls in the class

(ii) the total number of people in the school = Number of boys + number of girls
=250 + 120
=370

(c) Simplify:

To solve, start by grouping exponential terms

Simplifying..

3

## (b) Factorize: xy+6x+3y+18.

2. (a)
Find the LCM of 5 and 4 which is 20.
Multiply all terms by 20 and simplify

(b) (i)
Boys : Girls = 12:25,
If there are 120 boys,let x be the number of girls
120 boys : x girls
12:25 = 120: x

If more, less divides
Therefore

Hence there are 250 girls in the class

(ii) the total number of people in the school = Number of boys + number of girls
=250 + 120
=370

(c) Simplify:

To solve, start by grouping exponential terms

Simplifying..

# End Of Paper

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