Mathematics (Core), 2018, JAMB Exam, Exam, Paper 1 | Objectives

Paper Info

Year :

2018

Title :

Mathematics (Core)

Exam :

JAMB Exam

Paper 1 | Objectives

31 - 40 of 62 Questions

#	Question	Ans
31.	A man stands on a tree 150cm high and sees a boat at an angle of depression of 74°. Find the distance of the boat from the base of the tree. A. 52cm B. 43cm C. 40cm D. 15cm Show Content Detailed Solution Tan 74 = 150/x x = 150/tan 74 = 43.01cm There is an explanation video available below.	B
32.	Integrate the expression 6x\(^2\) - 2x + 1 A. 3x\(^3\) - 2x\(^2\) + x + c B. 2x\(^3\) - x\(^2\) + x + c C. 2x\(^3\) – 3x\(^2\) + c D. x\(^3\) + x\(^2\) – x + c Show Content Detailed Solution There is an explanation video available below.	B
33.	In how many ways can the letters LEADER be arranged? A. 72 B. 144 C. 360 D. 720 Show Content Detailed Solution The word LEADER has 1L 2E 1A 1D and 1R making total of 6! \(\frac{6}{1!2!1!1!1!}\) = \(\frac{6!}{2!}\) = \(\frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 1}\) = 360 There is an explanation video available below.	C
34.	In the figure below, /MX/ = 8cm, /XN/ = 12cm, /NZ/ = 4cm and ∠ XMN = ∠ XZY. Calculate /YM/ A. 32cm B. 24 cm C. 16 cm D. 12 cm Show Content Detailed Solution From the figure, ∠ XMN = ∠ XZY Angle X is common So, ∠ XNM = ∠ XYZ Then from the angle relationship \(\frac{XM}{XZ}\) = \(\frac{XN}{XY}\) = \(\frac{MN}{ZY}\) XM = 8, XZ = 12 + 4 = 16, XN = 12, XY = 8 + YM \(\frac{8}{16}\) = \(\frac{12}{(8 + YM) }\) Cross multiply 8(8 + YM) = 192 64 + 8YM = 192 8YM = 128 YM = \(\frac{128}{8}\) = 16cm There is an explanation video available below.	C
35.	Express 495g as a percentage of 16.5kg A. 3% B. 3 \(\frac{1}{3}\)% C. 15% D. 30% Show Content Detailed Solution The two numbers must be expressed in the same unit. To convert 495g to kg, it will be divided by 1000 495g = \(\frac{495}{1000}\) = 0.495kg To express in percentage, 0.495 will be divided by 16.5 and then multiplied by 100 % will be added to the answer \(\frac{0.4950}{16.5}\) x 100 = 3% There is an explanation video available below.	A
36.	Evaluate (2√3 - 4) (2√3 + 4) A. -4 B. -2 C. 2 D. 4 Show Content Detailed Solution 2√3 - 4) ( 2√3 + 4) = 12 + 8√3 - 8√3 – 16 = 12 – 16 = -4 The two expressions in the bracket are conjugate of each other There is an explanation video available below.	A
37.	Find the equation of the tangent at the point (2, 0) to the curve y = x\(^2\) - 2x A. y = 2x - 4 B. y = 2x + 4 C. y = 2x - 2 D. y = 2x + 2 Show Content Detailed Solution The gradient to the curve is found by differentiating the curve equation with respect to x So \(\frac{dy}{dx}\) 2x - 2 The gradient of the curve is the same with that of the tangent. At point (2, 0) \(\frac{dy}{dx}\) = 2(2) - 2 = 4 – 2 = 2 The equation of the tangent is given by (y - y1) \(\frac{dy}{dx}\) (x – x1) At point (x1, y1) = (2, 0) y - 0 = 2(x - 2) y = 2x - 4 There is an explanation video available below.	A
38.	This questions What is the minimum value of the graph? A. -5.3 B. 0.5 C. 3 D. 8 Show Content Detailed Solution The minimum value is the lowest value of the curve on y axis which gives a value of -5.3 There is an explanation video available below.	A
39.	Evaluate log\(_2\) 8 – log\(_3\) \(\frac{1}{9}\) A. -1 1\(\frac{1}{2}\) B. -1 C. 1 D. 5 Show Content Detailed Solution log\(_2\) 8 – log\(_3\) \(\frac{1}{9}\) = log \(_2\) 2\(^3\) – log\(_3\) 9\(^{-1}\) = log\(_2\) 2\(^3\) – log\(_3\) 3\(^{-2}\) Based on law of logarithm = 3 log\(_2\) 2 – (-2 log\(_3\) 3) But log\(_2\) 2 = 1, log\(_3\) 3 = 1 So, = 3 + 2 = 5 There is an explanation video available below.	D
40.	Tanθ is positive and Sinθ is negative. In which quadrant does θ lies A. Second only B. Third only C. Fourth only D. First and third only Show Content Detailed Solution First quadrant: Sin, Cos and Tan are all positive Second quadrant: Sin is positive, Cos is negative and Tan is negative Third quadrant: Tan is positive, Sin is negative and Cos is negative Fourth quadrant: Cos is positive, Sin is negative and Tan is negative The correct option is the third quadrant only where Tanθ is positive and Sinθ is negative There is an explanation video available below.	B

31.	A man stands on a tree 150cm high and sees a boat at an angle of depression of 74°. Find the distance of the boat from the base of the tree. A. 52cm B. 43cm C. 40cm D. 15cm Show Content Detailed Solution Tan 74 = 150/x x = 150/tan 74 = 43.01cm There is an explanation video available below.	B
32.	Integrate the expression 6x\(^2\) - 2x + 1 A. 3x\(^3\) - 2x\(^2\) + x + c B. 2x\(^3\) - x\(^2\) + x + c C. 2x\(^3\) – 3x\(^2\) + c D. x\(^3\) + x\(^2\) – x + c Show Content Detailed Solution There is an explanation video available below.	B
33.	In how many ways can the letters LEADER be arranged? A. 72 B. 144 C. 360 D. 720 Show Content Detailed Solution The word LEADER has 1L 2E 1A 1D and 1R making total of 6! \(\frac{6}{1!2!1!1!1!}\) = \(\frac{6!}{2!}\) = \(\frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 1}\) = 360 There is an explanation video available below.	C
34.	In the figure below, /MX/ = 8cm, /XN/ = 12cm, /NZ/ = 4cm and ∠ XMN = ∠ XZY. Calculate /YM/ A. 32cm B. 24 cm C. 16 cm D. 12 cm Show Content Detailed Solution From the figure, ∠ XMN = ∠ XZY Angle X is common So, ∠ XNM = ∠ XYZ Then from the angle relationship \(\frac{XM}{XZ}\) = \(\frac{XN}{XY}\) = \(\frac{MN}{ZY}\) XM = 8, XZ = 12 + 4 = 16, XN = 12, XY = 8 + YM \(\frac{8}{16}\) = \(\frac{12}{(8 + YM) }\) Cross multiply 8(8 + YM) = 192 64 + 8YM = 192 8YM = 128 YM = \(\frac{128}{8}\) = 16cm There is an explanation video available below.	C
35.	Express 495g as a percentage of 16.5kg A. 3% B. 3 \(\frac{1}{3}\)% C. 15% D. 30% Show Content Detailed Solution The two numbers must be expressed in the same unit. To convert 495g to kg, it will be divided by 1000 495g = \(\frac{495}{1000}\) = 0.495kg To express in percentage, 0.495 will be divided by 16.5 and then multiplied by 100 % will be added to the answer \(\frac{0.4950}{16.5}\) x 100 = 3% There is an explanation video available below.	A

36.	Evaluate (2√3 - 4) (2√3 + 4) A. -4 B. -2 C. 2 D. 4 Show Content Detailed Solution 2√3 - 4) ( 2√3 + 4) = 12 + 8√3 - 8√3 – 16 = 12 – 16 = -4 The two expressions in the bracket are conjugate of each other There is an explanation video available below.	A
37.	Find the equation of the tangent at the point (2, 0) to the curve y = x\(^2\) - 2x A. y = 2x - 4 B. y = 2x + 4 C. y = 2x - 2 D. y = 2x + 2 Show Content Detailed Solution The gradient to the curve is found by differentiating the curve equation with respect to x So \(\frac{dy}{dx}\) 2x - 2 The gradient of the curve is the same with that of the tangent. At point (2, 0) \(\frac{dy}{dx}\) = 2(2) - 2 = 4 – 2 = 2 The equation of the tangent is given by (y - y1) \(\frac{dy}{dx}\) (x – x1) At point (x1, y1) = (2, 0) y - 0 = 2(x - 2) y = 2x - 4 There is an explanation video available below.	A
38.	This questions What is the minimum value of the graph? A. -5.3 B. 0.5 C. 3 D. 8 Show Content Detailed Solution The minimum value is the lowest value of the curve on y axis which gives a value of -5.3 There is an explanation video available below.	A
39.	Evaluate log\(_2\) 8 – log\(_3\) \(\frac{1}{9}\) A. -1 1\(\frac{1}{2}\) B. -1 C. 1 D. 5 Show Content Detailed Solution log\(_2\) 8 – log\(_3\) \(\frac{1}{9}\) = log \(_2\) 2\(^3\) – log\(_3\) 9\(^{-1}\) = log\(_2\) 2\(^3\) – log\(_3\) 3\(^{-2}\) Based on law of logarithm = 3 log\(_2\) 2 – (-2 log\(_3\) 3) But log\(_2\) 2 = 1, log\(_3\) 3 = 1 So, = 3 + 2 = 5 There is an explanation video available below.	D
40.	Tanθ is positive and Sinθ is negative. In which quadrant does θ lies A. Second only B. Third only C. Fourth only D. First and third only Show Content Detailed Solution First quadrant: Sin, Cos and Tan are all positive Second quadrant: Sin is positive, Cos is negative and Tan is negative Third quadrant: Tan is positive, Sin is negative and Cos is negative Fourth quadrant: Cos is positive, Sin is negative and Tan is negative The correct option is the third quadrant only where Tanθ is positive and Sinθ is negative There is an explanation video available below.	B

Prev
1
2
3
4
5
6
7
Next