Mathematics (Core), 1979, JAMB Exam, Exam, Paper 1 | Objectives

Paper Info

Year :

1979

Title :

Mathematics (Core)

Exam :

JAMB Exam

Paper 1 | Objectives

11 - 20 of 51 Questions

#	Question	Ans
11.	A trader goes to Ghana for y days with y cedis. For the first x days, he spends X cedis per day. The amount he has to spend per day for the rest of his stay is A. \(\frac{y(y - x)}{y - x}\) cedis B. \(\frac{Yy - Xx)}{y - x}\) cedis C. \(\frac{Y - Xy)}{y - x}\) cedis D. \(\frac{Y - X}{y - x}\) cedis E. \(\frac{Y - Xx}{y - x}\) cedis Show Content Detailed Solution The amount he has to spend per day for the rest of his stay is \(\frac{Y - Xx}{y - x}\) cedis	E
12.	Multiply (3x + 5y + 4z) by (2x - 3y + z) A. 6x² + xy - 15y² + 4z² + 11xz - 7yz B. 6x² + 3xy - 15y² + 4z² C. 6x² + 3xy - y² + 4z² D. 6x² + 3xy - 15y + z² Show Content Detailed Solution (3x + 5y + 4z)(2x - 3y + z) 6x² + 9xy + 3x² + 10xy - 15y² + 5yz + 8xz - 12yz + 4z² = 6x² + xy - 15y² + 4z² + 11xz - 7yz	A
13.	A square of cardboard is taped at the perimeter by a piece of ribbon 20cm long. What is the area of the board? A. 20sq.cm B. 100sq.cm C. 25sq.cm D. 16sq.cm E. 36sq.cm Show Content Detailed Solution Area of a square = 4(5) where S is each sides of the square Perimeter = 20(given) 4S = 20 S = \(\frac{20}{4}\) = 5 Area s² = 5² = 25	C
14.	Rationalize the denominator of the expression \(\frac{6 + 2\sqrt{5}}{4 - 3\sqrt{6}}\) A. \(\frac{12+ 4\sqrt{5 + 7} 5 + 6\sqrt{3}}{39}\) B. \(\frac{-(24 + 18\sqrt{6} + 8\sqrt{5} + 6\sqrt{30})}{39}\) C. \(\frac{24 + 3\sqrt{6 + 8} 5 + 6\sqrt{30}}{19}\) D. \(\frac{-15 + 3\sqrt{5 + 18} 5 + 6\sqrt{30}}{36}\) E. \(\frac{-(12 + 4\sqrt{5} +9\sqrt{6} + 3\sqrt{30})}{19}\) Show Content Detailed Solution Rationalize using the reciprocal of the denominator to multiply through (i.e. Multiply both numerator and denominator using \(4 + 3\sqrt{6}\) ) Watch your signs in the course of this.	E
15.	Simplify \(\frac{5^x \times 25^{x - 1}}{125^{x + 1}}\) A. 5^{2x + 1} B. 5^{x + 1} C. 5^-5 D. 5² E. 5³ Show Content Detailed Solution \(\frac{5^x \times 25^{x - 1}}{125^{x + 1}}\) = \(\frac{5^x \times 5^{2x - 2}}{5^{3x + 3}}\) = \(\frac{5^{x + 2x - 2}}{5^{3x + 3}}\) = \(\frac{5^{3x - 2}}{5^{3x + 3}}\) = 5\(^{3x - 2 - 3x - 3}\) = 5\(^{-5}\)	C
16.	A steel ball of radius 1 cm is dropped into a cylinder of radius 2cm and height 4cm. If the cylinder is now filled with water, what is the volume of the water in the cylinder? A. \(\frac{44}{3}\)\(\pi\)cm³ B. 12\(\pi\)cm³ C. \(\frac{38}{3}\)\(\pi\)cm³ D. \(\frac{40}{3}\)\(\pi\)cm³ E. \(\frac{32}{33}\)\(\pi\)cm³ Show Content Detailed Solution Volume of steel ball = \(\frac{4\pi r^2}{3}\) = \(\frac{4}{3}\) \(\pi\) x 1 = \(\frac{4 \pi}{3}\)cm³ Vol. of cylinder = \(\pi\)r²h = \(\pi\) x 2² x 3 Vol. of water = 16\(\pi\) - \(\frac{4 \pi}{3}\) = \(\frac{48 - 4 \pi}{3}\) = \(\frac{44 \pi}{3}\)cm³	A
17.	Simplify \(\frac{x^2 + y^2 + xy}{x + y}\) - \(\frac{x^2 + y^2}{x - y}\) A. \(\frac{x^2 + y^2} {(x - y)^2}\) B. \(\frac{2y^3} {y^2 - x^2}\) C. \(\frac{3x^2 + y^2} {(2x - y)^2}\) D. \(\frac{x^2 + y^2} {(x^2 - y)}\) Show Content Detailed Solution \(\frac{x^2 + y^2 + xy}{x + y}\) - \(\frac{x^2 + y^2}{x -y}\) = \(\frac{-y^3 - y^3}{x^2 - y^2}\) = \(\frac{2y^3}{x^2 - y^2}\) = \(\frac{2y^3}{y^2 - x^2}\)	B
18.	A ladder resting on a vertical wall makes an angles whose tangent is 2.4 with the ground. If the distance between the foot of the ladder and the wall is 50cm, What is the length of the ladder? A. 1m B. 1.1m C. 1.2m D. 0.9m E. 1.3m Show Content Detailed Solution If tan\(\theta\) = 2, 4 \(\theta\) = tan^-1(2.4) = 67^o 25 By sin formula \(\frac{x}{sin 90^o}\) = \(\frac{50}{sin 22^o 37}\) = \(\frac{50}{sin(9o - \theta)}\) sin90^o = 1 x = 50 cosec 22^o 37 = 50 x 2.604x = 130cm but 100cm = 1m 130cm = 1.3m	E
19.	Simplify 2\(\frac{5}{12}\) - 1\(\frac{7}{8}\) x \(\frac{6}{5}\) A. \(\frac{1}{6}\) B. \(\frac{13}{20}\) C. \(\frac{11}{30}\) D. \(\frac{9}{4}\) E. \(\frac{5}{3}\) Show Content Detailed Solution 2\(\frac{5}{12}\) - 1\(\frac{7}{8}\) x \(\frac{6}{5}\) = \(\frac{29}{12}\) - \(\frac{15}{8}\) x \(\frac{6}{5}\) = \(\frac{29}{12}\) - \(\frac{9}{4}\) = \(\frac{29 - 27}{12}\) = \(\frac{2}{12}\) = \(\frac{1}{6}\)	A
20.	One of the following statements is wrong. Which is it? A. If a triangle is equiangular then it is also equilateral B. If a triangle is equilateral then it is also then it is also equiangular C. If two triangles are similar then they are also congurent D. The sum of the interior angles of any triangle is 180 degrees Show Content Detailed Solution Two similar triangles are not also congruent	C

11.	A trader goes to Ghana for y days with y cedis. For the first x days, he spends X cedis per day. The amount he has to spend per day for the rest of his stay is A. \(\frac{y(y - x)}{y - x}\) cedis B. \(\frac{Yy - Xx)}{y - x}\) cedis C. \(\frac{Y - Xy)}{y - x}\) cedis D. \(\frac{Y - X}{y - x}\) cedis E. \(\frac{Y - Xx}{y - x}\) cedis Show Content Detailed Solution The amount he has to spend per day for the rest of his stay is \(\frac{Y - Xx}{y - x}\) cedis	E
12.	Multiply (3x + 5y + 4z) by (2x - 3y + z) A. 6x² + xy - 15y² + 4z² + 11xz - 7yz B. 6x² + 3xy - 15y² + 4z² C. 6x² + 3xy - y² + 4z² D. 6x² + 3xy - 15y + z² Show Content Detailed Solution (3x + 5y + 4z)(2x - 3y + z) 6x² + 9xy + 3x² + 10xy - 15y² + 5yz + 8xz - 12yz + 4z² = 6x² + xy - 15y² + 4z² + 11xz - 7yz	A
13.	A square of cardboard is taped at the perimeter by a piece of ribbon 20cm long. What is the area of the board? A. 20sq.cm B. 100sq.cm C. 25sq.cm D. 16sq.cm E. 36sq.cm Show Content Detailed Solution Area of a square = 4(5) where S is each sides of the square Perimeter = 20(given) 4S = 20 S = \(\frac{20}{4}\) = 5 Area s² = 5² = 25	C
14.	Rationalize the denominator of the expression \(\frac{6 + 2\sqrt{5}}{4 - 3\sqrt{6}}\) A. \(\frac{12+ 4\sqrt{5 + 7} 5 + 6\sqrt{3}}{39}\) B. \(\frac{-(24 + 18\sqrt{6} + 8\sqrt{5} + 6\sqrt{30})}{39}\) C. \(\frac{24 + 3\sqrt{6 + 8} 5 + 6\sqrt{30}}{19}\) D. \(\frac{-15 + 3\sqrt{5 + 18} 5 + 6\sqrt{30}}{36}\) E. \(\frac{-(12 + 4\sqrt{5} +9\sqrt{6} + 3\sqrt{30})}{19}\) Show Content Detailed Solution Rationalize using the reciprocal of the denominator to multiply through (i.e. Multiply both numerator and denominator using \(4 + 3\sqrt{6}\) ) Watch your signs in the course of this.	E
15.	Simplify \(\frac{5^x \times 25^{x - 1}}{125^{x + 1}}\) A. 5^{2x + 1} B. 5^{x + 1} C. 5^-5 D. 5² E. 5³ Show Content Detailed Solution \(\frac{5^x \times 25^{x - 1}}{125^{x + 1}}\) = \(\frac{5^x \times 5^{2x - 2}}{5^{3x + 3}}\) = \(\frac{5^{x + 2x - 2}}{5^{3x + 3}}\) = \(\frac{5^{3x - 2}}{5^{3x + 3}}\) = 5\(^{3x - 2 - 3x - 3}\) = 5\(^{-5}\)	C

16.	A steel ball of radius 1 cm is dropped into a cylinder of radius 2cm and height 4cm. If the cylinder is now filled with water, what is the volume of the water in the cylinder? A. \(\frac{44}{3}\)\(\pi\)cm³ B. 12\(\pi\)cm³ C. \(\frac{38}{3}\)\(\pi\)cm³ D. \(\frac{40}{3}\)\(\pi\)cm³ E. \(\frac{32}{33}\)\(\pi\)cm³ Show Content Detailed Solution Volume of steel ball = \(\frac{4\pi r^2}{3}\) = \(\frac{4}{3}\) \(\pi\) x 1 = \(\frac{4 \pi}{3}\)cm³ Vol. of cylinder = \(\pi\)r²h = \(\pi\) x 2² x 3 Vol. of water = 16\(\pi\) - \(\frac{4 \pi}{3}\) = \(\frac{48 - 4 \pi}{3}\) = \(\frac{44 \pi}{3}\)cm³	A
17.	Simplify \(\frac{x^2 + y^2 + xy}{x + y}\) - \(\frac{x^2 + y^2}{x - y}\) A. \(\frac{x^2 + y^2} {(x - y)^2}\) B. \(\frac{2y^3} {y^2 - x^2}\) C. \(\frac{3x^2 + y^2} {(2x - y)^2}\) D. \(\frac{x^2 + y^2} {(x^2 - y)}\) Show Content Detailed Solution \(\frac{x^2 + y^2 + xy}{x + y}\) - \(\frac{x^2 + y^2}{x -y}\) = \(\frac{-y^3 - y^3}{x^2 - y^2}\) = \(\frac{2y^3}{x^2 - y^2}\) = \(\frac{2y^3}{y^2 - x^2}\)	B
18.	A ladder resting on a vertical wall makes an angles whose tangent is 2.4 with the ground. If the distance between the foot of the ladder and the wall is 50cm, What is the length of the ladder? A. 1m B. 1.1m C. 1.2m D. 0.9m E. 1.3m Show Content Detailed Solution If tan\(\theta\) = 2, 4 \(\theta\) = tan^-1(2.4) = 67^o 25 By sin formula \(\frac{x}{sin 90^o}\) = \(\frac{50}{sin 22^o 37}\) = \(\frac{50}{sin(9o - \theta)}\) sin90^o = 1 x = 50 cosec 22^o 37 = 50 x 2.604x = 130cm but 100cm = 1m 130cm = 1.3m	E
19.	Simplify 2\(\frac{5}{12}\) - 1\(\frac{7}{8}\) x \(\frac{6}{5}\) A. \(\frac{1}{6}\) B. \(\frac{13}{20}\) C. \(\frac{11}{30}\) D. \(\frac{9}{4}\) E. \(\frac{5}{3}\) Show Content Detailed Solution 2\(\frac{5}{12}\) - 1\(\frac{7}{8}\) x \(\frac{6}{5}\) = \(\frac{29}{12}\) - \(\frac{15}{8}\) x \(\frac{6}{5}\) = \(\frac{29}{12}\) - \(\frac{9}{4}\) = \(\frac{29 - 27}{12}\) = \(\frac{2}{12}\) = \(\frac{1}{6}\)	A
20.	One of the following statements is wrong. Which is it? A. If a triangle is equiangular then it is also equilateral B. If a triangle is equilateral then it is also then it is also equiangular C. If two triangles are similar then they are also congurent D. The sum of the interior angles of any triangle is 180 degrees Show Content Detailed Solution Two similar triangles are not also congruent	C