Year : 
1988
Title : 
Mathematics (Core)
Exam : 
WASSCE/WAEC MAY/JUNE

Paper 1 | Objectives

31 - 40 of 41 Questions

# Question Ans
31.

Which of the regions P, Q, R, S and T satisfies the following 0 < y < 1, y < x + 2, x < 0

A. P

B. Q

C. R

D. S

E. T

E
32.

A cone is made from a sector of circle of radius 14cm and angle of 90o. What is the area of the curved surface of the cone? (Take x = 22/7)

A. 22cm2

B. 38.5cm2

C. 77cm2

D. 154cm2

E. 308cm2

Detailed Solution

Length of arc =
θ/360
* 2πr


=> r =
90/360
*
14/4
= 3
33.

In the diagram above, O is the centre of the circle through points L, M and N, if ∠MLN = 74o and ∠MNL = 39o, calculate ∠LON.

A. 67o

B. 100o

C. 113o

D. 126o

E. 134o

Detailed Solution

From the diagram, < LMN = 180° - (74° + 39°) (sum of angle in a triangle)
= 67°
< LON = 2 x 67° (angle subtended at the centre is twice the angle at the circumference)
= 134°
34.

A rope of length 18m is used to form a sector of a circle of radius 3.5m on a school playing field. What is the size of the angle of the sector, correct to the nearest degree?

A. 33o

B. 40o

C. 90o

D. 180o

E. 270o

Detailed Solution

Circumference = 2πr
2 x 22/7 x 3.5 ≅ 22m
22m = 360o
11m = 360/22 x 11 = 180o
35.

In the diagram above, PR is perpendicular from P to QS, PQ = 2cm, QR = 1cm and PR = RS. what is the size of the angle QPS?

A. 135o

B. 105o

C. 90o

D. 75o

E. 60o

Detailed Solution

\(\Delta RPS\) = Isosceles triangle
\(\therefore < RPS = \​​​​​​​frac{180° - 90°}{2}\)
= 45°
In \(\Delta QPR\),\(\sin < QPR = \frac{1}{2}\)
= 30°
\(\therefore < QPS = 30° + 45° = 75°\)
36.

Cotonou and Niamey are on the same line of longitude and Niamey is 7o north of Cotonou. If the radius of the earth is 6400km, how far is Niamey north of Cotonou along the line of longitude, correct to the nearest kilometer? [Take π = 22/7]

A. 391km

B. 503km

C. 782km

D. 1006km

E. 2012km

Detailed Solution

θ/360
* 2πR


=
7/360
* 2 *
22/7
* 6400 = 782km
37.

If Q = (all perfect squares less than 30) and P = (all odd numbers from 1 to 10). Find Q ∩ P.

A. (1, 4, 9, 16, 25)

B. (1, 3, 4, 5, 7, 9, 16, 25)

C. (1, 3, 5, 7, 9)

D. (1, 9)

E. Φ

Detailed Solution

Q = {1, 4, 9, 16, 25} P = { 1, 3, 5, 7, 9}
Q ∩ P = { 1, 9}
38.

The histogram below shows the number of candidates, in thousands, obtaining given ranges of marks in a State examination. Find the total number of candidates that sat for the examination

A. 80,000

B. 120,000

C. 250,000

D. 260,000

E. 270,000

Detailed Solution

No of candidates = { 5 + 10 + 60 + 80 + 50 + 30 + 5 + 5 + 5}thousand = 270 x 1000 = 270000
39.

The histogram below shows the number of candidates, in thousands, obtaining given ranges of marks in a State examination. How many candidates scored at most 30%?

A. 15,000

B. 20,000

C. 25,000

D. 35,000

E. 60,000

Detailed Solution

Those who scored at most 30% = ( 5 + 10 + 20)thousand = 35000
40.

The surnames of 40 children in a class arranged in alphabetical order. 16 of the surnames begins with O and 9 of the surname begins with A, 14, of the letters of the alphabet do not appear as the first letter of a surname

A. 5/8

B. 7/8

C. 9/16

D. 14/25

E. 39/40

Detailed Solution

No. of possible outcome = 40
No. of expected outcome = 16 + 9 = 25
Probability = 25/40 = 5/8
31.

Which of the regions P, Q, R, S and T satisfies the following 0 < y < 1, y < x + 2, x < 0

A. P

B. Q

C. R

D. S

E. T

E
32.

A cone is made from a sector of circle of radius 14cm and angle of 90o. What is the area of the curved surface of the cone? (Take x = 22/7)

A. 22cm2

B. 38.5cm2

C. 77cm2

D. 154cm2

E. 308cm2

Detailed Solution

Length of arc =
θ/360
* 2πr


=> r =
90/360
*
14/4
= 3
33.

In the diagram above, O is the centre of the circle through points L, M and N, if ∠MLN = 74o and ∠MNL = 39o, calculate ∠LON.

A. 67o

B. 100o

C. 113o

D. 126o

E. 134o

Detailed Solution

From the diagram, < LMN = 180° - (74° + 39°) (sum of angle in a triangle)
= 67°
< LON = 2 x 67° (angle subtended at the centre is twice the angle at the circumference)
= 134°
34.

A rope of length 18m is used to form a sector of a circle of radius 3.5m on a school playing field. What is the size of the angle of the sector, correct to the nearest degree?

A. 33o

B. 40o

C. 90o

D. 180o

E. 270o

Detailed Solution

Circumference = 2πr
2 x 22/7 x 3.5 ≅ 22m
22m = 360o
11m = 360/22 x 11 = 180o
35.

In the diagram above, PR is perpendicular from P to QS, PQ = 2cm, QR = 1cm and PR = RS. what is the size of the angle QPS?

A. 135o

B. 105o

C. 90o

D. 75o

E. 60o

Detailed Solution

\(\Delta RPS\) = Isosceles triangle
\(\therefore < RPS = \​​​​​​​frac{180° - 90°}{2}\)
= 45°
In \(\Delta QPR\),\(\sin < QPR = \frac{1}{2}\)
= 30°
\(\therefore < QPS = 30° + 45° = 75°\)
36.

Cotonou and Niamey are on the same line of longitude and Niamey is 7o north of Cotonou. If the radius of the earth is 6400km, how far is Niamey north of Cotonou along the line of longitude, correct to the nearest kilometer? [Take π = 22/7]

A. 391km

B. 503km

C. 782km

D. 1006km

E. 2012km

Detailed Solution

θ/360
* 2πR


=
7/360
* 2 *
22/7
* 6400 = 782km
37.

If Q = (all perfect squares less than 30) and P = (all odd numbers from 1 to 10). Find Q ∩ P.

A. (1, 4, 9, 16, 25)

B. (1, 3, 4, 5, 7, 9, 16, 25)

C. (1, 3, 5, 7, 9)

D. (1, 9)

E. Φ

Detailed Solution

Q = {1, 4, 9, 16, 25} P = { 1, 3, 5, 7, 9}
Q ∩ P = { 1, 9}
38.

The histogram below shows the number of candidates, in thousands, obtaining given ranges of marks in a State examination. Find the total number of candidates that sat for the examination

A. 80,000

B. 120,000

C. 250,000

D. 260,000

E. 270,000

Detailed Solution

No of candidates = { 5 + 10 + 60 + 80 + 50 + 30 + 5 + 5 + 5}thousand = 270 x 1000 = 270000
39.

The histogram below shows the number of candidates, in thousands, obtaining given ranges of marks in a State examination. How many candidates scored at most 30%?

A. 15,000

B. 20,000

C. 25,000

D. 35,000

E. 60,000

Detailed Solution

Those who scored at most 30% = ( 5 + 10 + 20)thousand = 35000
40.

The surnames of 40 children in a class arranged in alphabetical order. 16 of the surnames begins with O and 9 of the surname begins with A, 14, of the letters of the alphabet do not appear as the first letter of a surname

A. 5/8

B. 7/8

C. 9/16

D. 14/25

E. 39/40

Detailed Solution

No. of possible outcome = 40
No. of expected outcome = 16 + 9 = 25
Probability = 25/40 = 5/8