Mathematics (Core), 2004, WASSCE/WAEC MAY/JUNE, Exam, Paper 1 | Objectives

Paper Info

Year :

2004

Title :

Mathematics (Core)

Exam :

WASSCE/WAEC MAY/JUNE

Paper 1 | Objectives

31 - 40 of 50 Questions

#	Question	Ans
31.	Find the average of the first four prime numbers greater than10 A. 20 B. 19 C. 17 D. 15 Show Content Detailed Solution First four prime numbers greater than 10 are 11, 13, 17, 19 The average \(= \frac{11+13+17+19}{4}=15\)	D
32.	Given that \(\sqrt{128}+\sqrt{18}-\sqrt{K} = 7\sqrt{2}\), find K, A. 8 B. 16 C. 32 D. 48 Show Content Detailed Solution \(\sqrt{128} +\sqrt{18}-\sqrt{k}=7\sqrt{2}\\ \sqrt{2\times 64}+\sqrt{9\times 2} - \sqrt{k} = 7\sqrt{2}\\ 8\sqrt{2} + 3\sqrt{2} - \sqrt{k} = 7\sqrt{2}; 11\sqrt{2} - \sqrt{k} = 7\sqrt{2}\\ -\sqrt{k}=7\sqrt{2}-11\sqrt{2}; -\sqrt{k} = -4\sqrt{2}; \sqrt{k}=4\sqrt{2}\\ =\sqrt{4^2\times 2} = \sqrt{16\times 2}; \sqrt{k}=\sqrt{32}; k = 32\)	C
33.	In the diagram, PQRW is a circle. Line P, V and QR are produced to meet at M, where ∠WMR = 30^o and \|WM\| = \|MR\| Find the value of x A. 10^o B. 25^o C. 35^o D. 60^o Show Content Detailed Solution MPQ = PQM = 3x; ∆MPQ MPQ + PQM + PMQ = 180^o; 3x + 3x + 30^o = 180^o 6x \times 30^o = 180^o; 6x + 180^o - 30^o; 6x + 150^o \(x = \frac{150}{6} = 25^{\circ}\)	B
34.	The table above gives the marks scored by a group of students in a test Use the table to answer the Question below What is the median mark? A. 1 B. 2 C. 3 D. 4 Show Content Detailed Solution Median = 0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5 Median mark = \(\frac{3+3}{2} = \frac{6}{2} = 3\)	C
35.	The table above gives the marks scored by a group of students in a test Use the table to answer the Question below What is the probability of selecting a student from the group that scored 2 or 3? A. \(\frac{1}{11}\) B. \(\frac{5}{22}\) C. \(\frac{7}{22}\) D. \(\frac{6}{11}\) Show Content Detailed Solution Prob (2 or 3) = prob(2) + prob(3) Prob (mark 2) \(=\frac{7}{22}\) + Prob(mark 3) = \(\frac{5}{22}\) Prob(2 or 3) \(=\frac{7}{22}+\frac{5}{22}=\frac{12}{22}=\frac{6}{11}\)	D
36.	Find the range of values of x for which\(\frac{x+2}{4}-\frac{x+1}{3}>\frac{1}{2}\) A. x > 4 B. x > -4 C. x < 4 D. x < -4 Show Content Detailed Solution \(\frac{x+2}{4}-\frac{x+1}{3}>\frac{1}{2}\\ \frac{3(x+2)-4(x+1)>6}{12}; 3x + 6 – 4x – 4 > 6\ -x +2>6; -x > 4; x < -4\)	D
37.	A boy walks 800m in 20 minutes. Calculate his average speed in km per hour A. 2.4 B. 4 C. 16 D. 24 Show Content Detailed Solution \(Average \hspace{1mm}speed = \frac{Distance}{Time\hspace{1mm} taken}\\ Distance = 800m = \frac{800}{1000}km = 0.8km\\ Time\hspace{1mm}taken = 20\hspace{1mm}minutes = \frac{20}{60}hr=\frac{1}{3}hr\\Average \hspace{1mm} speed = \left(0.8\div \frac{1}{3}\right)km/hr = (0.8\times3)km/hr\\=2.4km/hr\)	A
38.	Simplify \(\frac{2}{a+b}-\frac{1}{a-b}\) A. \(\frac{3}{a+b}\) B. \(\frac{a-3b}{a^2-b^2}\) C. \(\frac{3a-b}{a^2 – b^2}\) D. \(\frac{a-3b}{a^2+b^2}\) Show Content Detailed Solution Simplify \(\frac{2}{a+b}-\frac{1}{a-b}; \frac{2(a-b)-1(a+b)}{(a+b)(a-b)}\) = \(\frac{2a-2b-a-b}{(a+b)(a-b)}\) = \(\frac{a-3b}{a^2 - ab + ab - b^2}\) = \(\frac{a-3b}{a^2-b^2}\)	B
39.	The diagram is a circle centre O. Find the value of x A. 30^o B. 50^o C. 61^o D. 78^o E. 65.5\(^{\circ}\) Show Content Detailed Solution ∠PQR (Reflex) = 360° – 68° = 292° ∠PQR = 2∠PQR 292° = 4x + 30° 4x = 292 – 30 = 262 \(x = \frac{262}{4}=65.5°\)	E
40.	Use the graph to answer the Question below What are the roots of the equation x² + 3x - 4 = 0? A. 1, 4 B. -1, -4 C. -1, 4 D. -4, 1 Show Content Detailed Solution x² + 3x – 4 = 0 has roots value at the curve makes touches with the x – axis. The curve contact is at x = -4 and +1.	D

31.	Find the average of the first four prime numbers greater than10 A. 20 B. 19 C. 17 D. 15 Show Content Detailed Solution First four prime numbers greater than 10 are 11, 13, 17, 19 The average \(= \frac{11+13+17+19}{4}=15\)	D
32.	Given that \(\sqrt{128}+\sqrt{18}-\sqrt{K} = 7\sqrt{2}\), find K, A. 8 B. 16 C. 32 D. 48 Show Content Detailed Solution \(\sqrt{128} +\sqrt{18}-\sqrt{k}=7\sqrt{2}\\ \sqrt{2\times 64}+\sqrt{9\times 2} - \sqrt{k} = 7\sqrt{2}\\ 8\sqrt{2} + 3\sqrt{2} - \sqrt{k} = 7\sqrt{2}; 11\sqrt{2} - \sqrt{k} = 7\sqrt{2}\\ -\sqrt{k}=7\sqrt{2}-11\sqrt{2}; -\sqrt{k} = -4\sqrt{2}; \sqrt{k}=4\sqrt{2}\\ =\sqrt{4^2\times 2} = \sqrt{16\times 2}; \sqrt{k}=\sqrt{32}; k = 32\)	C
33.	In the diagram, PQRW is a circle. Line P, V and QR are produced to meet at M, where ∠WMR = 30^o and \|WM\| = \|MR\| Find the value of x A. 10^o B. 25^o C. 35^o D. 60^o Show Content Detailed Solution MPQ = PQM = 3x; ∆MPQ MPQ + PQM + PMQ = 180^o; 3x + 3x + 30^o = 180^o 6x \times 30^o = 180^o; 6x + 180^o - 30^o; 6x + 150^o \(x = \frac{150}{6} = 25^{\circ}\)	B
34.	The table above gives the marks scored by a group of students in a test Use the table to answer the Question below What is the median mark? A. 1 B. 2 C. 3 D. 4 Show Content Detailed Solution Median = 0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5 Median mark = \(\frac{3+3}{2} = \frac{6}{2} = 3\)	C
35.	The table above gives the marks scored by a group of students in a test Use the table to answer the Question below What is the probability of selecting a student from the group that scored 2 or 3? A. \(\frac{1}{11}\) B. \(\frac{5}{22}\) C. \(\frac{7}{22}\) D. \(\frac{6}{11}\) Show Content Detailed Solution Prob (2 or 3) = prob(2) + prob(3) Prob (mark 2) \(=\frac{7}{22}\) + Prob(mark 3) = \(\frac{5}{22}\) Prob(2 or 3) \(=\frac{7}{22}+\frac{5}{22}=\frac{12}{22}=\frac{6}{11}\)	D

36.	Find the range of values of x for which\(\frac{x+2}{4}-\frac{x+1}{3}>\frac{1}{2}\) A. x > 4 B. x > -4 C. x < 4 D. x < -4 Show Content Detailed Solution \(\frac{x+2}{4}-\frac{x+1}{3}>\frac{1}{2}\\ \frac{3(x+2)-4(x+1)>6}{12}; 3x + 6 – 4x – 4 > 6\ -x +2>6; -x > 4; x < -4\)	D
37.	A boy walks 800m in 20 minutes. Calculate his average speed in km per hour A. 2.4 B. 4 C. 16 D. 24 Show Content Detailed Solution \(Average \hspace{1mm}speed = \frac{Distance}{Time\hspace{1mm} taken}\\ Distance = 800m = \frac{800}{1000}km = 0.8km\\ Time\hspace{1mm}taken = 20\hspace{1mm}minutes = \frac{20}{60}hr=\frac{1}{3}hr\\Average \hspace{1mm} speed = \left(0.8\div \frac{1}{3}\right)km/hr = (0.8\times3)km/hr\\=2.4km/hr\)	A
38.	Simplify \(\frac{2}{a+b}-\frac{1}{a-b}\) A. \(\frac{3}{a+b}\) B. \(\frac{a-3b}{a^2-b^2}\) C. \(\frac{3a-b}{a^2 – b^2}\) D. \(\frac{a-3b}{a^2+b^2}\) Show Content Detailed Solution Simplify \(\frac{2}{a+b}-\frac{1}{a-b}; \frac{2(a-b)-1(a+b)}{(a+b)(a-b)}\) = \(\frac{2a-2b-a-b}{(a+b)(a-b)}\) = \(\frac{a-3b}{a^2 - ab + ab - b^2}\) = \(\frac{a-3b}{a^2-b^2}\)	B
39.	The diagram is a circle centre O. Find the value of x A. 30^o B. 50^o C. 61^o D. 78^o E. 65.5\(^{\circ}\) Show Content Detailed Solution ∠PQR (Reflex) = 360° – 68° = 292° ∠PQR = 2∠PQR 292° = 4x + 30° 4x = 292 – 30 = 262 \(x = \frac{262}{4}=65.5°\)	E
40.	Use the graph to answer the Question below What are the roots of the equation x² + 3x - 4 = 0? A. 1, 4 B. -1, -4 C. -1, 4 D. -4, 1 Show Content Detailed Solution x² + 3x – 4 = 0 has roots value at the curve makes touches with the x – axis. The curve contact is at x = -4 and +1.	D