ERC BECE MATHEMATICS 2024

 ERC MATHEMATICS 2024:

Instruction: Answer all the questions in this section.

1.       What is the place value of 5 in the figure 2567894013? A. Five hundred thousand   B. five million  C. fifty million   D. Five hundred million

2.       Write 411 in roman numerals  A. CDXI  B. CDII   C. CXV  D. CDIX

3.       What is the greatest common factor of 42, 70 and 98?   A. 2  B. 4  C. 7  D. 14

4.       Identify the prime factor of 60  A. 3 and 5   B. 2, 3 and 5  C. 2 and 3  D. 1 and 2

5.       Express 360 as a product of its prime factor   A. 2³ x 3² x 5   B. 2² x 3³ x 5²  C.  2³ x 3² x 5²   D. 2⁴ x 3³ x 5

6.       Write 0.00682 in standard form  A. 6.82 x 10^-4  B. 6.82 x 10^-3  C. 6.82 x 10^-2   D. 6.82 x 10^-4    

7.       What is the H.C.F of 4m²n² and 8m²n²  A. 4mn  B. 4m²n²   C. 8 m²n²  D. 80mn

8.       Find the H.C.F of 54, 36 and 72  A. 18  B. 16  C. 12  D. 8

9.       Find the smallest number that can be completely divisible by 12, 15 and 25  A. 120  B. 150  C. 180  D. 300

10.   What is the least number that must multiply 84 to give a perfect square?  A. 2  B. 17  C. 21  D. 33

11.   Find the LCM of 12, 18 and 32   A. 288  B. 298   C. 299  D. 388

12.   Express 32 thousandths as a decimal number  A. 0.032  B. 0.0032  C. 0.00032   D. 32000

13.   \(\text{Find the square root of } 3\frac{6}{25}\ \ \text{A. } 1\frac{4}{5}\ \ \text{B. } 1\frac{3}{5}\ \ \text{C. } 1\frac{2}{5}\ \ \text{D. } 1\frac{1}{5}\)

14.   Simplify \(1\frac{3}{4} - \left(2\frac{1}{3} + 4\right)\ \ \text{A. } 2\frac{3}{4}\ \ \text{B. } 1\frac{3}{4}\ \ \text{C. } -2\frac{3}{4}\ \ \text{D. } -3\frac{3}{4}\)

15.   Which of the following fraction is equivalent to\(\frac{3}{5}?\ \ \text{A. } \frac{9}{27}\ \ \text{B. } \frac{12}{20}\ \ \text{C. } \frac{8}{16}\ \ \text{D. } \frac{4}{18}\)

16.   Express 0.03076 to three (3) significant figures   A. 0.030   B. 0.0307  C. 0.0308   D. 0.03078

17.   Change 91.3% to a decimal fraction    A. 0.913   B. 91.3  C. 913.0   D. 9130

18.   The  following graph represent   A. x ˂ 2  B x ≤ 2   C. x ≥ 2    D. x > 2

19.   Find the range of values of x which satisfies the inequality \(\frac{1}{2}x\)  + 5 ≤ 3  A. x ≤ - 4   B. x ≤ -1  C. x ≥ -1   D. x ≥ -4

20.   \(\text{Simplify } \frac{\sqrt{45}}{125}\ \ \text{A. } \frac{9}{25}\ \ \text{B. } \frac{3}{5}\ \ \text{C. } \frac{3}{4}\ \ \text{D. } \frac{4}{5}\)

21.   Express 0.000095 in standard form.   A. 9.5 x 10^-6   B. 9.5 x 10^-5   C. 9.5 x 10⁶     D. 9.5 x 10⁵

22.      If m = 2, n = 5 and y = 3, evaluate  \(\frac{m(n+y)}{nm}\)   A. 16.0   B. 1.6    C. 0.16   D. 0.016

23.   Which of the following numbers is non-rational A. √10   B. √64  C. 3/5   D. 0.02

24.   Evaluate 1101_two x  101_two A. 100001_two  B. 110001_two  C. 1000001_two   D. 1010011_two

25.   What is the bill of a house that consume 1000 units of electricity, if the first 100 units are charged at ₦10.00 per unit and the remaining unit at ₦5.00 per unit  A. ₦4500.00   B. ₦5000.00  C. ₦5500.00  D. ₦6000.00

26.   The ratio of sheep to goat on a farm is 5:8, if there are 50 sheep on the farm calculate the total number of livestock on the farm.  A. 130  B. 90  C. 80  D. 40

27.   A car travel for 500km on 50 litres of petrol. How many kilometers will it travel on 35 litres  A. 75km  B. 85km  C. 350km  D. 380km

28.   If it takes a driver 5 hours to drive a distance of 600km, calculate the average speed.  A. 100km/h   B. 120km/h   C. 150km/h  D. 180km/h

29.   A 50kg bag of rice is reduced by 15% find the quantity of the rice left  A. 42.5kg   B. 35kg  C. 29.5kg   D. 7.5kg

30.   Simplify 3a – 5(b – 2a) + 2b  A. a – 3b  B. a – 7b  C. 13a – 3b  D. 5a – 7b

31.   Factorize 24pq – 16p²  A. 8p(3q +2p)  B. 8p(3q – 2p)  C. 8(3pq + 2p)  D. 8(3pq – 2p²)

32.   Solve the following pair of simultaneous equation  2x – y = 5 and x – 2y = 4  A. x = - 2; y = -1   B. x = -2; y = 1   C. x = 2; y = 1  D. x = 2; y = - 1 

33.   An investor invested 200,000 in a company that pay 5% interest per annum. How much will he get after 3 years?  A. ₦230,000    B. ₦205,000   C. ₦170,000  D. ₦30,000

34.   R varies directly as S and inversely as T. if R = 8 when S = 4 and T = 3, then R is equal to _____ \(\text{A. } \frac{3T}{2S}\ \ \text{B. } \frac{3S}{3T}\ \ \text{C. } \frac{6S}{T}\ \ \text{D. } \frac{6T}{S}\)

35.   If the area of a square tile is 4cm². How many tiles is needed to cover a floor measuring 12m by 8m?  A. 600 tiles B. 2400 tiles  C. 28000  D. 3840 tiles

36.   Find the circumference of a circle whose diameter is 21cm.\(\pi = \frac{22}{7}\)  A. 22cm  B. 32cm  C. 33cm   D. 66cm 

37.   Find the perimeter of the triangle below.  A. 3cm  B. 4cm  C. 6cm  D. 12cm

38.   Calculate the area of the trapezium below   A.  720cm²   B. 360 cm²   C. 256 cm²  D. 180 cm² 

39.   (i) A rhombus has two (2) lines of symmetry  (ii) A kite has two (2) lines of symmetry (iii) A decagon has nine (9) sides  (iv) A sphere has four (4) angles.  Which of the above statement is correct  A. i    B. i, ii and iii    C. ii and iv   D. ii

40.   Which of the following shapes has equal sides?  A. Triangle  B. Kite   C. Rhombus  D. Hexagon

41.   The scale factor of two similar portraits is 2:5, if the area of the smaller portrait is 120cm². Calculate the area of the larger portrait.   A. 750cm²  B. 300 cm²   C. 60 cm²   D. 48 cm²

42.   A polygon with 8 sides is called _____  A. hexagon  B. octagon   C. pentagon  D. nonagon 

43.   ________ is the formula for calculating sum of interior angles of a polygon  A. (2n + 2)180°   B. (2n – 2) 180°   C. (n + 2) 180°   D. (n – 2) 180°

44.   How many vertices have cuboids?  A. 8  B. 12  C. 13  D. 14

45.   Find the value of x in the diagram below   A. 1.   B. 2   C. 3  D. 4

46.   The value of the angle marked θ in the diagram below is _____   A. 80°  B. 180°   C. 240°  D. 270°

47.   Find the value of θ in the diagram below.   A. 40°   B. 60°  C. 70°   D. 180°

48.   Complete the following set of Pythagorean tripe 5, 12, _____   A. 19  B. 16   C. 14  D. 13

49.   Which of the following angles can be constructed using a pair of compass and ruler only?  A. 85°  B. 95°  C. 105°  D.  117°

50.   What is the reciprocal \(\text{of } \frac{1}{2}r\ \ \text{A. } \frac{2}{r}\)  B. 2r   C. 1   D. -2

51.   If the bearing of A from B is 150°, what is the bearing of B from A?   A. 360°   B. 330°   C. 240°  D. 180°

52.   If P varies as Q and K is constant then the formula connecting P and Q is ______  A. P = KQ   B. P = K + Q   C. P = Q/K    D. P = K/Q  

53.   If the mean of 12, 15, x, 13 and 17 is 16, find the value of x.  A. 23  B. 19   C. 18  D. 14

The table below is recorded of the favorite games of some students in school

Types of Games	wrestling	Lawn Tennis	Football	Table Tennis	Athlete
Number of Students	2	4	24	16	4

Use the information to answer questions 54 – 56

54.   What game was the most favorite for most students?  A. wrestling  B. Lawn tennis  C. Table tennis   D. Football  

55.   What is the least liked by the students?  A. Wrestling   B. Lawn tennis  C. Football  D. Table tennis 

56.   What is the probability that a student picked at random from the school liked Lawn tennis most? A. 0.08  B. 0.2  C. 0.48  D. 0.16

57.   There are 10 red pens and 25 blue pens in a pack of 50 pens. If the rest of the pens are black. Find the probability of picking a black pen from the pack  A. 3/10  B. 3/6   C. 2/5  D. 7/10

58.   The probability that it will rain in a particular month is 0.68. what is the probability that it will not rain.  A. 0.48  B. 0.42  C. 0.32  D. 0.30

59.   The mode of the numbers 3, 5, 10, 5, 4, 3, 5, 6 and 8 is _____    A. 3  B. 4  C. 5  D. 6

60.   Find the median of the following set of numbers 5, 6, 4, 2, 3, 2, 8, 4, and 5  A. 8   B. 6  C. 5  D. 4

 

SECTION B: ESSAY

Instruction: Answer all Questions Each. Each question carries 10 mark.

Note: calculators are not allowed

1a. use the triangle below to answer the following questions

(i). What is the sum of all its sides and simplify the resulting algebraic expression?  

(ii). Calculate the value of x if the perimeter of the triangle is 46cm.

(iii) Calculate the length of each side of the triangle

b. Solve X² + 7x + 10 = 0 

2a. the pie chart bellows the distribution of a man’s monthly income.

(i). What is the size of the angle represented by OTHERS?

(ii). If the man’s monthly income is ₦180,000. How much does he spend on transportation?

(ii). What percentage of his monthly income does he save. Correct your answers to two (2) significant figures

b. \(\frac{6\frac{3}{4}}{\left(21\frac{1}{3} \times 2\frac{1}{4} - 21\right)}\)

3a. solve the equation  \(\frac{2(2x + 1)}{3} = \frac{x - 3}{2}\)

(ii). Find the reciprocal of 0.004

b. solve the simultaneous equation  3x + 2y = 5 and  2x – 3y = -1

4a. using a pair of compass and a ruler only construct a triangle <ABC such that ABC = 60°, <BAC = 45° and /AB/ = 5.6cm. measure /BC/ and /AC/.

b. make J the subject of the formula in the equation  T = ½AJ² + trs.