Mathematics (Core), 1998, WASSCE/WAEC MAY/JUNE, Exam, Paper 1 | Objectives

Paper Info

Year :

1998

Title :

Mathematics (Core)

Exam :

WASSCE/WAEC MAY/JUNE

Paper 1 | Objectives

1 - 10 of 63 Questions

#	Question	Ans
1.	Find the root of the equation 2x\(^2\) - 3x - 2 = 0 A. x = -2 or 1/2 B. x = -2 or1 C. x = -2 or 2 D. x = -1 or 2 E. x = -1/2 or 2 Show Content Detailed Solution 2x\(^2\) - 3x - 2 = 0 2x\(^2\) - 4x + x - 2 = 0 2x(x - 2) + 1(x - 2) = 0 (2x + 1)(x - 2) = 0 x = \(\frac{-1}{2}\) or x = 2	E
2.	What value of k makes the given expression a perfect square ? m\(^2\) - 8m + k = 0 A. 2 B. 4 C. 8 D. 16 E. 64 Show Content Detailed Solution Take half the coefficient of m and square it => (-8/2)2 = k = 16	D
3.	If log\(_{10}\) q = 2.7078, what is q? A. 5102 B. 849.9 C. 510.2 D. 84.99 E. 51.02 Show Content Detailed Solution q = 10\(^{2.7078}\) Antilog of 2.7078 = 510.2	C
4.	Cos x is negative and sin x is negative.Which of the following is true of x? A. 0^o < x < 90^o B. 90^o < x <180^o C. 180^o < x < 270^o D. 270^o < x <360^o E. -90^o < x <90^o Show Content Detailed Solution In the 3rd quadrant, only the tan of angles are positive. The 3rd quadrant = 180° < x < 270°	C
5.	Simplify 0.63954 ÷ 0.003 giving your answer correct to two significant figures A. 213.18 B. 213.00 C. 213 D. 210 E. 21 Show Content Detailed Solution = \(\frac{0.63954}{0.003}\) moving the decimal places, we have = \(\frac{639.54}{3}\) = 213.18 \(\approxeq\) 210 (to 2 s.f.)	D
6.	If log\(_{10}\) a = 4; what is a? A. 0.4 B. 40 C. 400 D. 1000 E. 10000 Show Content Detailed Solution log\(_{10}\) a = 4 a = 10\(^4\) = 10000	E
7.	A student measured the length of a room and obtained the measurement of 3.99m. If the percentage error of is measurement was 5% and his own measurement was smaller than the length , what is the length of the room? A. 3.78m B. 3.80m C. 4.18m D. 4.20m E. 4.788m Show Content Detailed Solution Let the actual length of the room = y m \(\therefore \frac{y - 3.99}{y} \times 100% = 5%\) \(100(y - 3.99) = 5y \implies 100y - 399 = 5y\) \(100y - 5y = 399 \implies y = \frac{399}{95}\) y = 4.2 m	D
8.	When an aeroplane is 800m above the ground, its angle of elevation from a point P on the ground is 30o. How far is the plane from P by line of sight? A. 400m B. 800m C. 1500m D. 1600m E. 1700m Show Content Detailed Solution From the diagram, \(\sin 30 = \frac{800}{x}\) \(x = \frac{800}{\sin 30} \) = \(\frac{800}{0.5} \) = 1600 m	D
9.	Convert 35 to a number in base two A. 1011_two B. 10011_two C. 100011_two D. 110010_two E. 110001_two Show Content Detailed Solution	C
10.	The nth term of a sequence is represented by 3 x 2^(2-n). Write down the first three terms of the sequence A. ³/₂, 3, 6 B. 6, 3, ³/₂ C. ³/₂, 3, ¹/₃ D. ²/₃, 3, ⁸/₃ E. ³/₂, 0, 6 Show Content Detailed Solution When n = 1, n = 2, n = 3 3 x 2^{2 - 1} = 6 3 x 2^{2 - 2} = 3 3 x 2^{2 - 3} = ³/₂	B

1.	Find the root of the equation 2x\(^2\) - 3x - 2 = 0 A. x = -2 or 1/2 B. x = -2 or1 C. x = -2 or 2 D. x = -1 or 2 E. x = -1/2 or 2 Show Content Detailed Solution 2x\(^2\) - 3x - 2 = 0 2x\(^2\) - 4x + x - 2 = 0 2x(x - 2) + 1(x - 2) = 0 (2x + 1)(x - 2) = 0 x = \(\frac{-1}{2}\) or x = 2	E
2.	What value of k makes the given expression a perfect square ? m\(^2\) - 8m + k = 0 A. 2 B. 4 C. 8 D. 16 E. 64 Show Content Detailed Solution Take half the coefficient of m and square it => (-8/2)2 = k = 16	D
3.	If log\(_{10}\) q = 2.7078, what is q? A. 5102 B. 849.9 C. 510.2 D. 84.99 E. 51.02 Show Content Detailed Solution q = 10\(^{2.7078}\) Antilog of 2.7078 = 510.2	C
4.	Cos x is negative and sin x is negative.Which of the following is true of x? A. 0^o < x < 90^o B. 90^o < x <180^o C. 180^o < x < 270^o D. 270^o < x <360^o E. -90^o < x <90^o Show Content Detailed Solution In the 3rd quadrant, only the tan of angles are positive. The 3rd quadrant = 180° < x < 270°	C
5.	Simplify 0.63954 ÷ 0.003 giving your answer correct to two significant figures A. 213.18 B. 213.00 C. 213 D. 210 E. 21 Show Content Detailed Solution = \(\frac{0.63954}{0.003}\) moving the decimal places, we have = \(\frac{639.54}{3}\) = 213.18 \(\approxeq\) 210 (to 2 s.f.)	D

6.	If log\(_{10}\) a = 4; what is a? A. 0.4 B. 40 C. 400 D. 1000 E. 10000 Show Content Detailed Solution log\(_{10}\) a = 4 a = 10\(^4\) = 10000	E
7.	A student measured the length of a room and obtained the measurement of 3.99m. If the percentage error of is measurement was 5% and his own measurement was smaller than the length , what is the length of the room? A. 3.78m B. 3.80m C. 4.18m D. 4.20m E. 4.788m Show Content Detailed Solution Let the actual length of the room = y m \(\therefore \frac{y - 3.99}{y} \times 100% = 5%\) \(100(y - 3.99) = 5y \implies 100y - 399 = 5y\) \(100y - 5y = 399 \implies y = \frac{399}{95}\) y = 4.2 m	D
8.	When an aeroplane is 800m above the ground, its angle of elevation from a point P on the ground is 30o. How far is the plane from P by line of sight? A. 400m B. 800m C. 1500m D. 1600m E. 1700m Show Content Detailed Solution From the diagram, \(\sin 30 = \frac{800}{x}\) \(x = \frac{800}{\sin 30} \) = \(\frac{800}{0.5} \) = 1600 m	D
9.	Convert 35 to a number in base two A. 1011_two B. 10011_two C. 100011_two D. 110010_two E. 110001_two Show Content Detailed Solution	C
10.	The nth term of a sequence is represented by 3 x 2^(2-n). Write down the first three terms of the sequence A. ³/₂, 3, 6 B. 6, 3, ³/₂ C. ³/₂, 3, ¹/₃ D. ²/₃, 3, ⁸/₃ E. ³/₂, 0, 6 Show Content Detailed Solution When n = 1, n = 2, n = 3 3 x 2^{2 - 1} = 6 3 x 2^{2 - 2} = 3 3 x 2^{2 - 3} = ³/₂	B

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