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MATHEMATICS 29

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ENGLISH LANGUAGE 29

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INTEGRATED SCIENCE 29

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SOCIAL STUDIES 29

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2019 BECE Mathematics (Maths) Past Questions Paper Two
1. (a) Given that x = {whole numbers from 4 to 13} and y = {multiples of 3 between 2 and 20},
find .
(b) Find the Least Common Multiple (L.C.M) of the following numbers: 3, 5, and 9.
(c) If , find the value of .
1. (a)
x = { 4,5,6,7,8,9,10,11,12,13}
y= {3,6,9,12,15,18}
= {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
C.
2. (a) Solve:
(b) The ratio of boys to girls in a school is 12:25. If there are 120 boys.
(i) how many girls are in the school?
(ii) what is the total number of boys and girls in the school?
(c) Simplify:
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. (a) In an examination, 60 candidates passed Integrated Science or Mathematics. If 15 passed both
subjects and 9 more passed Mathematics than Integrated Science, find the:
(i) number of candidates who passed each subject
(ii) probability that a candidate passed exactly one subject.
(b) Factorize: xy+6x+3y+18.
(a) Let U be the universal set
X – Number of students who passed integrated science
Y – Number of students who passed Mathematics
Solving this question requires the use of venn diagrams.
From the informationtion given
X n Y = 15
9 more students passed mathematics than integrated science
Hence Y = x+9
Solving for x
x+915+15+x15=60
2x6=60
2x=66
X = 33
Number of students who passed math only = x+915 = 27
Number of students who passed science = 3315 = 18
Probability of passing only one subject = (18+27)/60 = 3/4
(b) Factorize: xy+6x+3y+18.
xy+6x+3y+18
x(y+6)+3(y+6)
(x+3)(y+6)
4. (a) Express 250% as a fraction in its lowest term.
(b)
Use the diagram to find the value of x.
(c) Simplify:
(d) if find (q + r )
a. 250% =
b. Using the knowledge that angles on a straightline sum to 180, write an equation for the missing internal angles
we solve this question by using a least known property of triangles shown in the image below.
Hence
C.
D.
5. (a)
The mapping shows the relationship between x and y.
using a scale of 2cm to 1unit on the xaxis and 2 cm to 2 units on the yaxis, draw two perpendicular axes 0x and 0y on a graph sheet for
plot the point for each ordered pair, .
Join the points with a straight line;
Using the graph, find the gradient of the line in 5 (a)(iii);
Use the graph to find the equation of the line in 5 (a)(iii).
The relation is plotted on a graph sheet as shown below.
(iv) gradient
the gradient can be found from the graph using the formula below, choosing any 2 points on the line
Equation of a line is given as
Y = mx+Cw
Where m is the gradient
C is y intercept
From the graph the y intercept is 3
So the equation of the line
Y=3x3
(b) Simplify: , leaving your answer in the form 2^n.
6. The marks obtained by students in a class test were
4 8 7 6 7
2 1 7 4 7
3 7 8 4 3
7 5 2 7 2
5 4 8 3 2
(a) construct a frequency distribution table for the data.
(b) Find the:
(i) mode of the distribution;
(ii) median mark of the test;
(iii) mean mark.
(a).
Marks  frequency  cumulative frequency 
1  1  1 
2  4  5 
3  3  8 
4  4  12 
5  2  14 
6  1  15 
7  7  22 
8  3  25 
(b) Find the:
(i) mode of the distribution = 7
(ii) median mark of the test = 5
(iii) mean mark = 4.92