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Mathematics
WAEC / WASSCE 2016
Indices, Logarithms & Surds
Solution
A straight line passes through the point P(1,2) and Q
(5,8). Calculate the length PQ
A
\(4\sqrt{11}\)
B
\(4\sqrt{10}\)
C
\(2\sqrt{17}\)
D
\(2\sqrt{13}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
|PQ| = \(\sqrt{(x_2 - X- 1) + (y_2 - y_1)^2}\)
= \(\sqrt{(5 - 1)^2 + (8 - 2)^2}\)
= \(\sqrt{4^2 + 6^2}\)
= \(\sqrt{16 + 36}\)
= \(\sqrt{52}\)
= 2\(\sqrt{13}\)
Source: Myschool Past Questions Archive (Record #46119)
Mathematics
WAEC / WASSCE 2016
Trigonometry, Elevation & Bearings
Solution
If cos \(\theta\) = x and sin 60o = x + 0.5 0o o, find, correct to the nearest degree, the value of \(\theta\)
A
32o
B
40o
C
60o
D
69o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
sin 60o = x + 0.5 0o(given)
0.8660 = x + 0.5
0.8660 - 0.5 = x
x = 0.3660
cos\(\theta\) = x(given)
cos\(\theta\) = 0.3660
Hence, \(\theta\) = cos-1(0.3660)
= 68.53o
= 69o (nearest degree)
Source: Myschool Past Questions Archive (Record #46120)
Mathematics
WAEC / WASSCE 2016
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
Age(years)
13
14
15
16
17
Frequency
10
24
8
5
3
The table shows the ages of students in a club. How many students are in the club?
A
50
B
55
C
60
D
65
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Number of students in the club is
10 + 24 + 8 + 5 + 3 = 50
Source: Myschool Past Questions Archive (Record #46123)
Mathematics
WAEC / WASSCE 2016
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
\(\begin{array}{c|c}
Age(years) & 13 & 14 & 15 & 16 & 17 \\
\hline
Frequency & 10 & 24 & 8 & 5 & 3
\end{array}\)
Find the median age
A
13
B
14
C
15
D
16
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Median = \(\frac{N}{2}\)th age
= \(\frac{50}{2}\)th age
= 25th age
= 14 years
Source: Myschool Past Questions Archive (Record #46126)
Mathematics
WAEC / WASSCE 2016
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, \(\bar{YW}\) is a tangent to the circle at X, |UV| = |VX| and < VXW = 50º. Find the value of < UXY.
Attached Figure / Diagram
A
70o
B
80o
C
105o
D
110o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
In the diagram above, \(x_1\) = 50º(angles in alternate segment)
\(x_1\) = \(x_2\)(base angles of isos. \(\Delta\))
< UXY + \(x_2\) + 50º = 180º(sum of angles on a straight line)
< UXY + 50º + 50º = 180º
< UXY + 100º = 180º
< UXY = 180º - 100º
= 80º
Source: Myschool Past Questions Archive (Record #46153)
Mathematics
WAEC / WASSCE 2016
Linear, Simultaneous & Quadratic Equations
Diagram
Solution
In the diagram, \(\bar{PF}\), \(\bar{QT}\), \(\bar{RG}\) intersect at S and PG||RG. If < SPQ = 113º and < RSt = 22º, find < PSQ
Attached Figure / Diagram
A
22o
B
45o
C
67o
D
89o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
In In the diagram given, \(\alpha\) = 22º (vertically opp. angles), \(\alpha\) = \(\beta\) (alternate angles)
< PSQ + 113º + \(\beta\) = 180º (sum of angles of a \(\Delta\))
< PSQ + 113º + 22º = 180º
< PSQ = 180º - (113 + 22)º
45º
Source: Myschool Past Questions Archive (Record #46170)
Mathematics
WAEC / WASSCE 2016
Linear, Simultaneous & Quadratic Equations
Diagram
Solution
In the diagram, O is the centre of the circle, o and o. Calculate the value of m.
Attached Figure / Diagram
A
30
B
36
C
40
D
72
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
In the diagram above, \(\alpha\) = 2mo (angle at centre = 2 x angle at circumference)
\(\alpha\) + 10mo = 360o (angle at circumference)
\(\alpha\) + 10mo = 360o(angles round a point)
2mo + 10mo = 360o
12mo = 360o
mo = \(\frac{360^o}{12}\)
= 30o
Source: Myschool Past Questions Archive (Record #46171)
Mathematics
WAEC / WASSCE 2016
Plane Geometry, Polygons & Circle Theorems
Solution
Kweku walked 8m up to slope and was 3m above the ground. If he walks 12m further up the slope, how far above the ground will he be?
A
4.5m
B
6.0m
C
7.5m
D
9.0m
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
By similar triangles, \(\frac{8}{3}\) = \(\frac{8 + 12}{h}\)
\(\frac{8}{3} = \frac{20}{h}\)
h = \(\frac{3 \times 20}{8}\)
= 7.5m
Source: Myschool Past Questions Archive (Record #46172)
Mathematics
WAEC / WASSCE 2016
Linear, Simultaneous & Quadratic Equations
Diagram
Solution
In the diagram, TS is a tangent to the circle at S. |PR| and < PQR = 177o. Calculate < PST.
Attached Figure / Diagram
A
54o
B
44o
C
34o
D
27o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
In the diagram above, x1 = 180o - 117o = 63o(opposite angles of a cyclic quad.)
x1 = x2 (base angles of isos. \(\Delta\))
x\(_1\) + x\(_2\) + \(\alpha\) = 180º (sum of angles of a \(\Delta\)
63º + 63º + \(\alpha\) = 180º
\(\alpha\) = 180º - (63 + 63)º
= 54º
< PST = 54º (aalternate angles)
Source: Myschool Past Questions Archive (Record #46173)
Mathematics
WAEC / WASSCE 2016
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, PR||SV||WY|, TX||QY|, < PQT = 48o and < TXW = 60o.Find < TQU.
Attached Figure / Diagram
A
120o
B
108o
C
72o
D
60o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
In the diagram, < TUQ + 60o(corresp. angles)
< QTU = 48o (alternate angles)
< QU + 60o + 48o = 180o(sum of angles of a \(\Delta\))
< TQU = 180o - 108o
= 72o
Source: Myschool Past Questions Archive (Record #46174)
Mathematics
WAEC / WASSCE 2016
Indices, Logarithms & Surds
Diagram
Solution
In the diagram, TX is perpendicular to UW, |UX| = 1cm and |TX| = |WX| = \(\sqrt{3}\)cm. Find UTW
Attached Figure / Diagram
A
135o
B
105o
C
75o
D
60o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
In \(\Delta\) UXT, tan\(\alpha\) = \(\frac{1}{\sqrt{3}}\)
\(\alpha\) = tan-1(\(\frac{1}{\sqrt{3}}\))
= 30o
In \(\Delta\)WXT, tan\(\beta\) \(\frac{\sqrt{3}}{\sqrt{3}}\) = 1
\(\beta\) = tan-1(1) = 45o
Hence, o + 45o = 75o
Source: Myschool Past Questions Archive (Record #46175)
Mathematics
WAEC / WASSCE 2016
Statistics (Data Representation, Central Tendency & Dispersion)
Diagram
Solution
The figure is a pie chart which represents the expenditure of a family in a year. If the total income of the family was Le 10,800,000.00, how much was spent on food?
Attached Figure / Diagram
A
Le 2,250,000.00
B
Le 22,700,000.00
C
Le 3,600,000.00
D
Le 4,500,000.00
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
sectoral angle representing food
= 360o - (80 + 70 + 90)o
= 120o
Amount spent on food
= \(\frac{\tect{sectoral angle}}{360^o}\) x Le 10,800,000
= Le 3,600,000
Source: Myschool Past Questions Archive (Record #46180)
Mathematics
WAEC / WASSCE 2016
Permutations, Combinations & Probability
Solution
A fair die is thrown two times. What is the probability that the sum of the scores is at least 10?
A
\(\frac{5}{36}\)
B
\(\frac{1}{6}\)
C
\(\frac{5}{18}\)
D
\(\frac{2}{3}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\begin{array}{c|c}
& 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
1 & 1,1 & 1,2 & 1,3 & 1,4 & 1,5 & 1,6 \\ \hline 2 & 2,1 & 2,2 & 2,3 & 2,4 & 2,5 & 2,6 \\ \hline 3 & 3,1 & 3,2 & 3,3 & 3,4 & 3,5 & 3,6 \\ \hline 4 & 4,1 & 4,2 & 4,3 & 4,4 & 4,5 & 4,6 \\ 5 & 5,1 & 5,2 & 5,3 & 5,4 & 5,5 & 5,6 \\ \hline 6 & 6,1 & 6,2 & 6,3 & 6,4 & 6,5 & 6,6\end{array}\)
From the table above, event space, n(E) = 6
sample space, n(S) = 36
Hence, probability sum of scores is at least 10, is;
\(\frac{n(E)}{n(S)}\)
= \(\frac{6}{36}\)
= \(\frac{1}{6}\)
Source: Myschool Past Questions Archive (Record #46191)
Mathematics
WAEC / WASSCE 2016
Plane Geometry, Polygons & Circle Theorems
Solution
The marks of eight students in a test are: 3, 10, 4, 5, 14, 13, 16 and 7. Find the range
A
16
B
14
C
13
D
11
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
First, arrange the marks in order of magnitude; 3, 4, 5, 7, 10, 13, 14, 16
Hence range = 16 - 3 = 13
Source: Myschool Past Questions Archive (Record #46193)
Mathematics
WAEC / WASSCE 2016
Plane Geometry, Polygons & Circle Theorems
Solution
If log2(3x - 1) = 5, find x.
A
2.00
B
3.67
C
8.67
D
11
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Log2(3x - 1) = 5
Log2(3x - 1) = Log225
Log2(3x - 1) = Log232
3x - 1 = 32
3x = 32 + 1 = 33
x = \(\frac{33}{3}\)
= 11
Source: Myschool Past Questions Archive (Record #46196)