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Mathematics
WAEC / WASSCE 2005
Permutations, Combinations & Probability
Solution
A fair die is tossed once, what is the probability of obtaining neither 5 or 2
A
\(\frac{5}{6}\)
B
\(\frac{2}{3}\)
C
\(\frac{1}{2}\)
D
\(\frac{1}{6}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Probability of obtaining a 5 is P(5)=\(\frac{1}{6}\)
Probability of obtaining a 2 is P(2)=\(\frac{1}{6}\)
Probability of obatining either 2 or 5 = P(2∪5) = \(\frac{2}{6}\)
Probability of obtaining neither 5 or 2 = \(1 - \frac{2}{6}=\frac{4}{6}=\frac{2}{3}\)
Source: Myschool Past Questions Archive (Record #26677)
Mathematics
WAEC / WASSCE 2005
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, KL//MN, ∠LKP = 30o and ∠NMP = 45o. Find the size of the reflex ∠KPM.
Attached Figure / Diagram
A
285o
B
255o
C
225o
D
210o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
∠KPM = 360o - (30 + 45)o
= 360o - 75o = 285o
Source: Myschool Past Questions Archive (Record #26678)
Mathematics
WAEC / WASSCE 2005
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, PR is a diameter, ∠PRQ = (3x-8)o and ∠RPQ = (2y-7)o. s x in terms of y
Attached Figure / Diagram
A
\(x=\frac{75-2y}{3}\)
B
\(x=\frac{105-3y}{2}\)
C
\(x=\frac{105-2y}{3}\)
D
\(x=\frac{75-3y}{2}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
180 = ∠RPQ + ∠PRQ + ∠PQR Since PQR = 90 (theorem: angle in a semi circle)
180 = ∠RPQ + ∠PRQ + 90 => 180o = (3x-8)o+(2y-7)o+90o; 90+8+7 = 3x+2y =>\(\frac{105-2y}{3}=x\)
Source: Myschool Past Questions Archive (Record #26679)
Mathematics
WAEC / WASSCE 2005
Number Bases & Modular Arithmetic
Solution
Convert 101101two to a number in base ten
A
61
B
46
C
45
D
44
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
1011012 = 1 x 25 + 0 x 24 + 1 x 23 + 1 x 22 + 0 x 21 + 1 x 20 = 32 + 0 + 8 + 4 + 0 + 1 = 4510
Source: Myschool Past Questions Archive (Record #26680)
Mathematics
WAEC / WASSCE 2005
Indices, Logarithms & Surds
Solution
Solve the equation 2\(^7\) = 8\(^{5-x}\)
A
\(\frac{5}{8}\)
B
\(\frac{8}{3}\)
C
\(\frac{3}{2}\)
D
\(\frac{15}{4}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
2\(^7\) = 8\(^{5-x}\)
2\(^7\) = 2\(^{3(5 - x)}\)
7 = 15 - 3x
7 - 15 = - 3x
-8 = -3x
x = \(\frac{8}{3}\)
Source: Myschool Past Questions Archive (Record #26681)
Mathematics
WAEC / WASSCE 2005
Linear, Simultaneous & Quadratic Equations
Solution
expand (2x-3y)(x-5y)
A
\(2x^2 + 13xy - 15y^2\)
B
\(2x^2 - 13xy - 15y^2\)
C
\(2x^2 + 13xy + 15y^2\)
D
\(2x^2 - 13xy + 15y^2\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\((2x-3y)(x-5y)=2x^2 - 10xy - 3xy + 15y^2\\
=2x^2 - 13xy + 15y^2\)
Source: Myschool Past Questions Archive (Record #26682)
Mathematics
WAEC / WASSCE 2005
Algebraic Expressions, Polynomials & Factorisation
Solution
Make f the subject of the relation \(v = u + ft\)
A
\(\frac{v-u}{t}\)
B
\(\frac{u-v}{t}\)
C
\(t(v+u\)
D
\(\frac{v}{u}-t\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(v=u+ft \Rightarrow v-u=ft\Rightarrow f=\frac{v-u}{t}\)
Source: Myschool Past Questions Archive (Record #26683)
Mathematics
WAEC / WASSCE 2005
Indices, Logarithms & Surds
Solution
The lengths of the adjacent sides of a right - angled triangle are xcm, (x-1)cm. If the length of the hypotenuse is \(\sqrt{13}cm\), find the value of x
A
2
B
3
C
4
D
5
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Using Pythagoras' theorem
\(x^2+(x-1)^2 = (\sqrt{13})^2\)
x\(^2\) + x\(^2\) - 2x + 1 = 13
2x\(^2 - 2x\) - 12 = 0
dividing through by 2
x\(^2\) - x- 6 = 0; (x-3)(x-2) = 0
x = 3 or -2
Source: Myschool Past Questions Archive (Record #26684)
Mathematics
WAEC / WASSCE 2005
Permutations, Combinations & Probability
Solution
The probability that John and James pass an examination are 3/4 and 3/5 respectively, find the probability of both boys failing the examination
A
\(\frac{1}{10}\)
B
\(\frac{3}{10}\)
C
\(\frac{9}{20}\)
D
\(\frac{11}{20}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Prob.(John pass)\(=frac{3}{4}\) prob.(John fail) \(=1-frac{3}{4}=\frac{1}{4}\)
Prob.(James pass) \(=frac{3}{5}\) Prob.(James fail) \(=1-frac{3}{5}=\frac{2}{5}\)
Prob(both boys fail)\(=frac{1}{4}\times \frac{2}{5}=\frac{1}{10}\)
Source: Myschool Past Questions Archive (Record #26685)
Mathematics
WAEC / WASSCE 2005
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram PQ and MN are straight lines. Find the value of x
Attached Figure / Diagram
A
13o
B
17o
C
28o
D
30o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
The straight line MN = 180 = 2(x+30o) + 86o =>
180 = 2x + 60o + 86o => 180o = 2x + 146o => 2x = 180 - 46 = 34o => x = 34/2 = 17o
Source: Myschool Past Questions Archive (Record #26686)
Mathematics
WAEC / WASSCE 2005
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, PQRS is a parallelogram and ∠QRT = 30o. Find x
Attached Figure / Diagram
A
95o
B
100o
C
120o
D
150o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Since ∠QRS = 180o - 30o = 150o and ∠SPQ = ∠QRS (theorem opp. angles in a parallelogram are equal) ∴ x = 150o
Source: Myschool Past Questions Archive (Record #26687)
Mathematics
WAEC / WASSCE 2005
Trigonometry, Elevation & Bearings
Solution
From a point R, 300m north of P, man walks eastward to a place Q which is 600m from P. Find the bearing of P from Q, correct to the nearest degreeee
A
026o
B
045o
C
210o
D
240o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(cos\theta = \frac{adj}{hyp}=\frac{300}{600}=\frac{1}{2}\\
\theta = cos^{-1}(0.5000)=60^{\circ}\)
The bearing of P from \(Q = \theta + 180 = 60 + 180 = 240^{\circ}\)
Source: Myschool Past Questions Archive (Record #26688)
Mathematics
WAEC / WASSCE 2005
Indices, Logarithms & Surds
Solution
What is the diameter of a circle of area 77cm2 [Take \(\pi = \frac{22}{7}\)]
A
\(\frac{\sqrt{2}}{7}cm\)
B
\(3\frac{1}{2}cm\)
C
7cm
D
\(7\sqrt{2}cm\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(A=\pi r^2 \Rightarrow 77 = \frac{22}{7} \times \frac{r^2}{1}\Rightarrow r^2 = \frac{77\times 7}{22} \Rightarrow r^2 = \frac{49}{2}\\
\Rightarrow r = \sqrt{\frac{49}{2}}=\frac{7}{\sqrt{2}}. Since D = 2r ∴ D = 2 \times \frac{7}{\sqrt{2}} = \frac{14}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = 7\sqrt{2}cm\)
Source: Myschool Past Questions Archive (Record #26689)
Mathematics
WAEC / WASSCE 2005
Linear, Simultaneous & Quadratic Equations
Solution
Solve the equation 2x - 3y = 22; 3x + 2y = 7
A
-5
B
-4
C
4
D
5
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
2x - 3y = 22 ---- eqn I
3x + 2y = 7 ---- eqn II
multiply eqn I by 2
4x - 6y = 44 ---- eqn III
multiply eqn II by 3
9x + 6y = 21 ---- eqn IV
Adding eqn III and IV
=> 13x = 65 => x = 5
Substituting 5 for x in eqn II
3x5 + 2y = 7 => 2y = -8
y = -4
Source: Myschool Past Questions Archive (Record #26690)
Mathematics
WAEC / WASSCE 2005
Linear, Simultaneous & Quadratic Equations
Solution
Solve the equation \(\frac{2y-1}{3} - \frac{3y-1}{4} = 1\)
A
-8
B
-13
C
13
D
19
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{4(2y-1)-3(3y-1)}{12}=12 \Rightarrow 8y - 4 - 9y + 3 = 12 \\
\Rightarrow -y-1=12\Rightarrow -y=13\Rightarrow y=-13\)
Source: Myschool Past Questions Archive (Record #26691)