Mathematics (Core), 2008, JAMB Exam, Exam, Paper 1 | Objectives

Paper Info

Year :

2008

Title :

Mathematics (Core)

Exam :

JAMB Exam

Paper 1 | Objectives

11 - 20 of 49 Questions

#	Question	Ans
11.	A book seller sells Mathematics and English books. If 30 customers buy Mathematics books, 20 customers buy English books and 10 customers buy the two books. How many customers has he altogether? A. 30 B. 40 C. 50 D. 60 Show Content Detailed Solution n(M) only = 30-10 = 20 n(E) only = 20-10 = 10 n(M∩E) = 10 ∴M∪E = 20+10+10 = 40 There is an explanation video available below.	B
12.	Make Q the subject of formula when \(L=\frac{4}{3}M\sqrt{PQ}\) A. \(\frac{9L^2}{16M^2P}\) B. \(\frac{3L}{4M\sqrt{P}}\) C. \(\frac{\sqrt{3L}}{4MP}\) D. \(\frac{3L^2}{16M^2}P\) Show Content Detailed Solution \(L=\frac{4}{3}M\sqrt{PQ}\\ =\frac{3}{4M} \times L = \sqrt{PQ}\\ =\left(\frac{3L}{4M}\right)^2=(\sqrt{PQ})^2\\ =\frac{9L^2}{16M^2}=PQ\\ =Q=\frac{9L^2}{16M^2 P}\) There is an explanation video available below.	A
13.	If 2x\(^2\) - kx - 12 is divisible by x-4, Find the value of k. A. 4 B. 5 C. 6 D. 7 Show Content Detailed Solution 2x2 - kx - 12 is divisible by x-4 implies x is a factor ∴ x = 4 f(4) implies 2(4)2 - k(4) - 12 = 0 32 - 4k - 12 = 0 -4k + 20 = 0 -4k = -20 k = 5 There is an explanation video available below.	B
14.	Factorize completely; (4x+3y)\(^2\) - (3x-2y)\(^2\) A. (x+5y)(7x+y) B. (x+5y)(7x-y) C. (x-5y)(7x+y) D. (x-5y)(7x-y) Show Content Detailed Solution (4x+3y)2 - (3x-2y)2 (4x+3y+3x-2y)(4x+3y-(3x-2y)) (4x+3y+3x-2y)(4x+3y-3x+2y) (x+5y)(7x+y) There is an explanation video available below.	A
15.	If x - 3 is directly proportional to the square of y and x = 5 when y =2, find x when y = 6. A. 30 B. 21 C. 16 D. 12 Show Content Detailed Solution (x – 3) ∝ y2 X-3 = Ky2 K = X-3 / y2 = 5-2/22 = 2/4 = 1/2 ∴X-3 = 1/2y2 X-3 = 1/2 (6)2 X-3 = 1/2 x 36/1 X-3 = 18 X = 21 There is an explanation video available below.	B
16.	If p varies inversely as the square of q and p=8 when q=4, find q when p =32 A. \(\pm\)16 B. \(\pm\)8 C. \(\pm\)4 D. \(\pm\)2 Show Content Detailed Solution p ∝ 1/q p = k/q K = q\(^2\)p = 4\(^2\)(8) ∴p = 128/q 32 = 128/q q\(^2\) = 128/32 q\(^2\) = 4 q = √4 = \(\pm\) 2 There is an explanation video available below.	D
17.	Find the range of values of x which satisfy the inequalities 4x - 7 \(\leq\) 3x and 3x - 4 \(\leq\) 4x A. -4 \(\leq\) x \(\leq\) 7 B. -7 \(\leq\) x \(\leq\) 4 C. x \(\geq\) -7 D. -7 \(\leq\) x \(\leq\) 6 Show Content Detailed Solution 4X - 7 \(\leq\) 3X and 3X - 4 \(\leq\) 4X 4X - 3X \(\leq\) 7 and 3X - 4X \(\leq\) 4 X \(\leq\) 7 and -X \(\leq\) 4 = X \(\geq\) -4 Range -4 \(\leq\) x \(\leq\) 7 There is an explanation video available below.	A
18.	Solve the quadratic inequalities x\(^2\) - 5x + 6 ≥ 0 A. x ≤ 2, x ≥ 3 B. x ≤ 3, x ≥ 2 C. x ≤ -2, x ≥ -3 D. x ≤-3, x ≥ 2 Show Content Detailed Solution x\(^2\) - 5x + 6 = 0 (X-2)(X-3) = 0 X-2 = 0 implies X = 2 X-3 = 0 implies X = 3 ∴ x ≤ 3, x ≥ 2 There is an explanation video available below.	B
19.	The fifth term of an A.P is 24 and the eleventh term is 96. Find the first term. A. 12 B. 4 C. -12 D. -24 Show Content Detailed Solution U5 = 24, n = 5 and U11 = 96, n = 11 Un = a + (n-1)d 24 = a + (5-1)d imply 24 = a+4d .....eqn1 96 = a + (11-1)d imply 96 = a+10d ...eqn2 eqn1 - eqn2 -72 = -6d d = 72/6 = 12 but 24 = a+4d 24 = a + 4(12) 24 = a + 48 a = 24-48 a = -24 There is an explanation video available below.	D
20.	A binary operation * is defined on the set of positive integers is such xy = 2x-3y+2 for all positive integers x and y. The binary operation is? A. commutative and close on the set of positive integers B. neither commutative nor closed on the set of positive integers C. commutative but not closed on the set of positive integers D. not cummutative but closed on the set of positive integers Show Content Detailed Solution X Y = 2X - 3Y + 2 2*3 = 2(2) - 3(3) + 2 =4-9+2 = -3 But -3 does not belong to positive integer There is an explanation video available below.	B

11.	A book seller sells Mathematics and English books. If 30 customers buy Mathematics books, 20 customers buy English books and 10 customers buy the two books. How many customers has he altogether? A. 30 B. 40 C. 50 D. 60 Show Content Detailed Solution n(M) only = 30-10 = 20 n(E) only = 20-10 = 10 n(M∩E) = 10 ∴M∪E = 20+10+10 = 40 There is an explanation video available below.	B
12.	Make Q the subject of formula when \(L=\frac{4}{3}M\sqrt{PQ}\) A. \(\frac{9L^2}{16M^2P}\) B. \(\frac{3L}{4M\sqrt{P}}\) C. \(\frac{\sqrt{3L}}{4MP}\) D. \(\frac{3L^2}{16M^2}P\) Show Content Detailed Solution \(L=\frac{4}{3}M\sqrt{PQ}\\ =\frac{3}{4M} \times L = \sqrt{PQ}\\ =\left(\frac{3L}{4M}\right)^2=(\sqrt{PQ})^2\\ =\frac{9L^2}{16M^2}=PQ\\ =Q=\frac{9L^2}{16M^2 P}\) There is an explanation video available below.	A
13.	If 2x\(^2\) - kx - 12 is divisible by x-4, Find the value of k. A. 4 B. 5 C. 6 D. 7 Show Content Detailed Solution 2x2 - kx - 12 is divisible by x-4 implies x is a factor ∴ x = 4 f(4) implies 2(4)2 - k(4) - 12 = 0 32 - 4k - 12 = 0 -4k + 20 = 0 -4k = -20 k = 5 There is an explanation video available below.	B
14.	Factorize completely; (4x+3y)\(^2\) - (3x-2y)\(^2\) A. (x+5y)(7x+y) B. (x+5y)(7x-y) C. (x-5y)(7x+y) D. (x-5y)(7x-y) Show Content Detailed Solution (4x+3y)2 - (3x-2y)2 (4x+3y+3x-2y)(4x+3y-(3x-2y)) (4x+3y+3x-2y)(4x+3y-3x+2y) (x+5y)(7x+y) There is an explanation video available below.	A
15.	If x - 3 is directly proportional to the square of y and x = 5 when y =2, find x when y = 6. A. 30 B. 21 C. 16 D. 12 Show Content Detailed Solution (x – 3) ∝ y2 X-3 = Ky2 K = X-3 / y2 = 5-2/22 = 2/4 = 1/2 ∴X-3 = 1/2y2 X-3 = 1/2 (6)2 X-3 = 1/2 x 36/1 X-3 = 18 X = 21 There is an explanation video available below.	B

16.	If p varies inversely as the square of q and p=8 when q=4, find q when p =32 A. \(\pm\)16 B. \(\pm\)8 C. \(\pm\)4 D. \(\pm\)2 Show Content Detailed Solution p ∝ 1/q p = k/q K = q\(^2\)p = 4\(^2\)(8) ∴p = 128/q 32 = 128/q q\(^2\) = 128/32 q\(^2\) = 4 q = √4 = \(\pm\) 2 There is an explanation video available below.	D
17.	Find the range of values of x which satisfy the inequalities 4x - 7 \(\leq\) 3x and 3x - 4 \(\leq\) 4x A. -4 \(\leq\) x \(\leq\) 7 B. -7 \(\leq\) x \(\leq\) 4 C. x \(\geq\) -7 D. -7 \(\leq\) x \(\leq\) 6 Show Content Detailed Solution 4X - 7 \(\leq\) 3X and 3X - 4 \(\leq\) 4X 4X - 3X \(\leq\) 7 and 3X - 4X \(\leq\) 4 X \(\leq\) 7 and -X \(\leq\) 4 = X \(\geq\) -4 Range -4 \(\leq\) x \(\leq\) 7 There is an explanation video available below.	A
18.	Solve the quadratic inequalities x\(^2\) - 5x + 6 ≥ 0 A. x ≤ 2, x ≥ 3 B. x ≤ 3, x ≥ 2 C. x ≤ -2, x ≥ -3 D. x ≤-3, x ≥ 2 Show Content Detailed Solution x\(^2\) - 5x + 6 = 0 (X-2)(X-3) = 0 X-2 = 0 implies X = 2 X-3 = 0 implies X = 3 ∴ x ≤ 3, x ≥ 2 There is an explanation video available below.	B
19.	The fifth term of an A.P is 24 and the eleventh term is 96. Find the first term. A. 12 B. 4 C. -12 D. -24 Show Content Detailed Solution U5 = 24, n = 5 and U11 = 96, n = 11 Un = a + (n-1)d 24 = a + (5-1)d imply 24 = a+4d .....eqn1 96 = a + (11-1)d imply 96 = a+10d ...eqn2 eqn1 - eqn2 -72 = -6d d = 72/6 = 12 but 24 = a+4d 24 = a + 4(12) 24 = a + 48 a = 24-48 a = -24 There is an explanation video available below.	D
20.	A binary operation * is defined on the set of positive integers is such xy = 2x-3y+2 for all positive integers x and y. The binary operation is? A. commutative and close on the set of positive integers B. neither commutative nor closed on the set of positive integers C. commutative but not closed on the set of positive integers D. not cummutative but closed on the set of positive integers Show Content Detailed Solution X Y = 2X - 3Y + 2 2*3 = 2(2) - 3(3) + 2 =4-9+2 = -3 But -3 does not belong to positive integer There is an explanation video available below.	B