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MATHEMATICS 29

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ENGLISH LANGUAGE 29

Lecture3.1

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INTEGRATED SCIENCE 29

Lecture4.1

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SOCIAL STUDIES 29

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Bece Past Questions & Answers – 2018 (Maths)
1. Which of the following is arranged in ascending order?
A. 25, 64, 4, 17
B. 64, 25, 4, 17
C. 64, 25, 17, 4
D. 17, 4, 25, 64
B.64, 25, 4, 17 . Arranging numbers (or other items) in ascending order means to arrange them from smallest to largest.
2. If P = {x: x is an even number greater than two and less than or equal to twelve}, list the members of P.
A. {2, 4, 6, 8, 10, 12}
B. {3, 4, 6, 8, 10, 12}
C. {2, 4, 6, 8, 10}
D. {4, 6, 8, 10, 12}
D. This set satisfies the question is since 4 is an even number greater than 2 and all other even numbers before the number 13.
3. Which of the following is an infinite set?
A. {1, 2, …, 5, 6, 7}
B. {4, 6, 8, 10, 12}
C. {2, 3, 5, 7, 11, …}
D. {3, 6, …, 18, 21, …, 33, 36}
C. An infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable. This set has an ellipses at the end of the last number 11 which means it continues to no end.
4. Find the HCF of 18, 36 and 60.
A.
B.
C.
D.
D. 2 x 3 satisfies this question because 2 x 3 is the Highest Common Factor of 18,36 and 60. The HCF of a given set of numbers is the largest positive number that divides the given numbers without a remainder.
Solution Steps
Prime Factorization of 18 = 2 • 3 • 3
Prime Factorization of 36 = 2 • 2 • 3 • 3
Prime Factorization of 60 = 2 • 2 • 3 • 5
The prime factors common to both are 2 • 3
5. Write two hundred and two million, two thousand, two hundred and two in figures.
A. 202,002,202
B. 202,020,202
C. 202,022,202
D. 202,200,202
A. 202,000,000 + 2,000 + 200 + 2
6. Find the number that can be added to 207 to make the sum divisible by 17.
A. 3
B. 13
C. 14
D. 30
C. 14 is the number that when added to 207, gives 221 to make it divisible by 17.
10 x 17 = 170
so 12 x 17 = 204.
So the next multiple of 17 is 221.
therefore 221 – 207 = 14.
7. If P = {factors of 36} and Q = {multiples of 4 less than 40}, find the number of subsets in P ∩ Q.
A. 10
B. 8
C. 6
D. 4
D. 4
P={1,2,3,4,9,12,18,36} and Q={4,16}
The intersection(P∩Q) of two sets is a new set that contains all of the elements that are in both sets. Therefore P∩Q = {4}
8. Find the LCM of 10, 15 and 25.
A. 90
B. 120
C. 150
D. 300
C. 150
The LCM of a,b is the smallest positive number that is divisible by both a and b.
Solution Steps
Prime factorization of 10: 2 • 5
Prime factorization of 15: 3 • 5
Prime factorization of 25: 5 • 5
computer a number comprised of factors that appears in at least one of the following 10,15,25
= 2 • 5 • 5 • 3 = 150
9. Evaluate
A.
B.
C.
D.
A. 1/2 Apply BODMAS to solve this equation
Solution Steps
Step 1: Simplifying the expression in the bracket
finding the LCM of 3 & 4 which is 12 and adjusting the fractions based on the lcm
Since the denominators are equal, we can combine the fractions:
Simplifying the resulting expression by this rule
The expression therefore becomes
Cancelling out and simplifying for final expression
=
10. Arrange , and in ascending order.
A. , ,
B. , ,
C. , ,
D. , ,
D. 3/7, 4/9, 2/3
Order from Least to Greatest
3/7 < 4/9 < 2/3 Solution
Rewriting as fractions if necessary: 2/3, 4/9, 3/7 The least common denominator (LCD) is: 63. Rewriting as equivalent fractions with the LCD:
Ordering these fractions by the numerator in order from least to greatest:
Therefore, the order from least to greatest is:
11. Find the simple interest on GHC 600.00 saved for 2 years 8 months at 5% per annum.
A. GHC 64.00
B. GHC 80.00
C. GHC 84.00
D. GHC 92.00
B. GHC 80.00
Solution Steps
STEP 1: Convert 2 Years 8 months into fractions
STEP 2: Find an interest by using the formula I=P x i x t, where I is interest, P is total principal, i is rate of interest per year, and t is total time in years.
P = GHC 600, i = 5% and t = 2.6667 years, so
12. The number of girls in a mixed school is 420. If the ratio of boys to girls in the school is 3:2, how many students are in the school?
A. 1050
B. 1470
C. 1630
D. 1680
A. 1050
This is solved using simple ratio and proportion computations.
Ration of
Boys:Girs = 3:2 = x Boys:520 girls
Step 2:Convert to fractional form
If more, less divides
hence
Step 3: Solving For x
Step 4 Adding Number of Boys and Girls
630 + 420 = 1050
13. Mary had a chance to select a number from 1 to 20 randomly. What is the probability that the number is divisible by 3?
A.
B.
C.
D.
C. 3/10
14. Ama bought a pair of sandals for GHC 20.00 and sold it at GHC 24.00. Find her percentage profit.
A. 4%
B. 17%
C. 20%
D. 44%
C. 20%
15. Eight men can do a piece of work in 12 days. How long will 6 men take to do the same work if they work at the same rate?
A. 14 days
B. 16 days
C. 18 days
D. 20 days
B. 16 days
This question is solved using simple ratio and proportion
6 men would take more days, hence if more less divides
In the diagram QP is parallel to ST, angle QPR = 68° and angle SRT = 40°
16. Find the value of angle PQR.
A. 40°
B. 68°
C. 72°
D. 108°
C. 72
PQR form a triangle and the internal angles sum up to 180. Also note that opposite angles are equal hence
PQR = 180 – 40 – 68 = 72
17. Find the value of angle TSR.
A. 40°
B. 68°
C. 72°
D. 112°
B. 68
Alternate angles are equal. The lines make a Z shape which can also be back to front.
18. A train is travelling at a speed of 60 km/h. What distance would it cover from 10:45 am to 12:15 pm?
A. 75 km
B. 87 km
C. 90 km
D. 150 km
C. 90 km
To solve this we first convert the period from 10:45 am to 12:15 pm into hours which is 1 hr 30 minutes (1.5 in decimal)
distance covered = speed x tome = 60 x 1.5 = 90 km
19. The perimeter of a rectangle is 26 cm. If its length is 10 cm, find its area.
A. 30
B. 60
C. 130
D. 160
A. 30
l = 10
p = 26
b = ?
The formula for perimeter of a rectangle: p = 2(l + b)
where, p stands for perimeter of a rectangle
l stands for length of a rectangle
b stands for breadth of a rectangle
p = 2(l + b)
26 = 2(10 + b)
26 = 20 + 2b
2b = 26 – 20 = 6
b = 6/2
b = 3cm
Area = Length x Breadth = 10 x 3 = 30
20. Find the slope of the line 3x – 6y = 33.
A. 3
B. –
C.
D. 3
C.
solve using y = mx+c by making y the subject of the equation.
21. If y = c + b, find y when c = , b=45 c=145, b=and x = 2.
A. 3
B. 4
C. 6
D. 7
C. 6
22. The volume of a cylinder is 20. If the height of the cylinder is 5 cm, find the base radius.
A. 1 cm
B. 2 cm
C. 3 cm
D. 4 cm
B. 2 cm
23.
In the diagram, PQR is a rightangled triangle with PR = 15 cm and QR = 12 cm. Find the length PQ.
A. 3.0 cm
B. 8.0 cm
C. 9.0 cm
D. 19.2 cm
C. 9.0 cm
24. How many edges has a triangular prism?
A. 3
B. 5
C. 6
D. 9
25. Make m the subject of the relation q=
A. m=
B. m= 3qhn
C. m= 3q+hn
D. m=
26. Simplify:
A.
B.
C.
D.
B.
27. Simplify: 4a – 9b – 2(2a – 3b).
A. 8a + 3b
B. 8a – 3b
C. 15b
D. 3b
28. If u=and v= evaluate 6v+2u.
A.
B.
C.
D.
29. Find the image of the point (2, 5) under the transformation:
A. (2, –3)
B. (2, 2)
C. (2, 3)
D. (2, 7)
30. Find the image of Q(–4, 5) when rotated anticlockwise through 90° about the origin.
A. Q(5, 4)
B. Q(5, 4)
C. (4, 5)
D. (4, 5)
The following data show the marks of students in a test:
10, 4, 1, 4, 3, 3, 2, 1, 1, 7, 8
Use the information to answer questions 31 and 32.
31. If the pass mark is 4, find the number of students who scored more than the pass mark.
A. 1
B. 2
C. 3
D. 4
32. Find the mean mark.
A. 3
B. 4
C. 7
D. 8
B. 4
33. How many lines of symmetry has a rhombus?
A. 2
B. 3
C. 4
D. 5
34. In an enlargement length AB = 3 cm and the length of its image = 15 cm. Calculate the scale factor.
A.
B.
C. 5
D. 12
35. Find the rule of the mapping:
A.
B.
C.
D.
36. Solve the inequality:
A.
B.
C.
D.
37. If 4 – x = 3(4x + 5), find the value of x.
A.
B.
C. 1
D. –
38. In class, there are 12 girls and 48 boys. Find the percentage of boys in the class.
A. 20%
B. 40%
C. 60%
D. 80%
39. The bearing of P from Q is 060°. Find the bearing of Q from P.
A. 120°
B. 150°
C. 210°
D. 240°
40. Which of the following statements best describes the construction below?
A. construction of line AB from P.
B. construction of perpendicular from P to meet line AB.
C. construction of an arc of a circle with centre P.
D. construction of the bisector of line AB.
2018 BECE Mathematics (Maths) Past Questions Paper Two
1(a) Solve the inequality:
(1b)
(1c) The sides of a triangle are in the ratio 6 : 8 : 10. If the perimeter of the triangle is 288 cm, find the:
(i) longest side
(ii) Shortest side
(iii) difference between the longest and the shortest sides.
longest side
shortest side
difference between the longest and the shortest sides.
=120 – 72
= 48 cm
2. (a) An English textbook costs GHc 25.00. The author of the book agreed to take 20% of the cost of each book sold. If 1,702 copies were sold, calculate the author’s share.
(2b)
(2c)
In the diagram, MN = 13 cm, MP = 15 cm, MN  = 12 cm and is perpendicular to NP . Calculate length NP
3. (a) Simplify , leaving the answer in standard form.
(3b) (i) Make r the subject of the relation:
(ii) From (b)(i), find the value of r when y = 3 and x = 10
(3c) Juliet bought 1,756 kg of frozen chicken, 675 g of vegetables, and 95 g of corn oil from a shopping mall. What is the total weight of the items she bought in kilograms?
Weight of chicken = 1,756 kg (Already in Kilograms so no conversion is needed
Weight of vegetables in kilograms =
Weight of Corn Oil in kilograms =
Total weight of items = 1756 + 0.675 + 0.095 = 1756.77 kg
4. (a) The sum of the interior angles of a regular polygon is 900°. Find the number of sides of the polygon.
(4b) Using a ruler and a pair of compasses only, construct:
(i)Triangle XYZ such that the length XY = 10cm, angle XYZ = 30 degrees and length YZ = 9cm:
(ii) Perpendicular line from Z to meet line XY at P
(iii) measure the (1) length PZ (2) Angle XZY
(iv) Calculate,correct to the nearest whole number,the area of triangle XYZ
(iii) measure the:
(α) length = 4.5 cm – 4.6 cm
(β) angle = 86° to 87°
(iv) calculate, correct to the nearest whole number, the area of triangle .
Area of a triangle = (1/2) × Base × Height
Area of triangle XYZ = (1/2) × XY × PZ
= × 10cm × 4.5
= × 45
= 22.5
≈ 23 cm2 (to nearest whole number)
5. (a) A property worth GHc 10,480.00 is shared between a widow and her 10 children in the ratio 1 : 4 respectively. The children shared their portions equally. Find each child’s share.
(5b) The data shows the distribution of marks in a class test.
27 55 19 65 69 46
38 42 14 57 11 13
14 67 22 10 25 17
45 39 61 52 43 24
28 63 56 49 64 32
Use the data to answer the following questions:
(i) make a Stem and Leaf plot of the data;
(ii) how many students scored more than 10 marks and less than 20 marks?
(iii) what is the probability of a student scoring less than 20 marks?
Stem  Leaf 
1  0, 1, 3, 4, 4, 7, 9 
2  2, 4, 5, 7, 8, 
3  2, 8, 9 
4  2, 3, 5, 6, 9 
5  2, 5, 6, 7, 
6  1, 3, 4, 5, 7, 9 
(ii) how many students scored more than 10 marks and less than 20 marks?
= 6 students
(iii) what is the probability of a student scoring less than 20 marks?
6. (a) An aeroplane left the Kotoka International Airport on Wednesday at 7:26 pm and reached its destination after nine hours thirty minutes. Find the day and the time the aeroplane reached its destination.
(6b)
(i) Using a scale of 2 cm to 2 units on both axes, draw two perpendicular axes Ox and Oy on a graph sheet for
.
(ii) Draw on this graph, indicating the coordinates of all vertices, the quadrilateral ABCD with vertices A(0,10), B(6,2) , C(3,11) and D(4,3).
(iii) Draw the line X = 2 to meet AB at P and CD at Q
(iv) Measure angles BPQ and PQD
(i) State the relationship between:
(α) angles BPQ and PQD;
(β) lines AB and CD.
(iv) Measure angles BPQ and PQD
Angle BPQ = 26°
Angle PQD = 26°
(i) State the relationship between:
(α) angles BPQ and PQD : They are alternate angles
(β) lines AB and CD : They are parallel