Year : 
2021
Title : 
Mathematics (Core)
Exam : 
WASSCE/WAEC MAY/JUNE

Paper 1 | Objectives

41 - 49 of 49 Questions

# Question Ans
41.

\(\overline{XY}\) is a line segments with the coordinates X (- 8,- 12) and Y(p,q). if the midpoint of \(\overline{XY}\) is (-4,-2) find the coordinates of Y.

A. (-6,-2)

B. (0,8)

C. (4,10)

D. (0,4)

Detailed Solution

The formula for midpoint = \(\frac{x_1 + x_2}{2}\), \(\frac{y_1 + y_2}{2}\)
(-4,-2) = (x,y)
x = \(\frac{x_1 + x_2}{2}\)
-4 = \(\frac{-8 + p}{2}\)
-4 * 2 = -8 + p
-8 + 8 = p
: p = 0
y = \(\frac{y_1 + y_2}{2}\)
-2 = \(\frac{-12 + q}{2}\)
-2 * 2 = -12 + q
-4 + 12 = q
: q = 8
42.

500 tickets were sold for a concert tickets for adults and children were sold at $4.50 and $3.00 respectively if the total receipts for the concerts was $1987.50 how many tickets for adults were sold?

A. 325

B. 235

C. 175

D. 400

Detailed Solution

A for Adults
C for children
a + c = 500
c = 500 - a
4.5a + 3c = 1987.50
where c = 500 - a
4.5a + 3(500 - a) = 1987.50
4.5a - 3a = 1987.50 - 1500
1.5a = 487.5
a = 487.5 / 1.5
a = 325 tickets
c = 500 - a
c = 500 - 325
c = 175 tickets

Check:
from 4.5a + 3c
4.5 (325) = 1,462.5
+
3(175) = 525

43.

The distance d between two villages east more than 18 KM but not more than 23KM.which of these inequalities represents the statements?

A. 18 ≤ d ≤ 23

B. 18 < d < 23

C. 18 ≤ d < 23

D. 18 < d ≤ 23

Detailed Solution

distance d more than 18 KM = d > 18 0r 18 < d
distance d but not more than 23 KM = d ≤ 23
Mathematically; 18 < d ≤ 23
44.

The pie chart represents the distribution of fruits on display in the shop if there are 60 apples on display how many oranges are there?

A. 80

B. 270

C. 120

D. 90

Detailed Solution

Total angles = 360°
100 + 60 + 80 + M = 360
M = 360 - 240 = 120
Orange (M) = 120° and F ( fruits in total)
For Apples:
\(\frac{80}{360} \times F\) = 60
F = \(\frac{60 \times 360}{80}\)
F = 270 fruits in total
For Orange
= \(\frac{120}{360} \times 270\)
= 90 oranges
45.

A box contains 40 identical balls of which 10 are red and 12 are blue. if a ball is selected at random from the box what is the probability that it is neither red nor blue?

A. \(\frac{9}{20}\)

B. \(\frac{3}{10}\)

C. \(\frac{1}{4}\)

D. \(\frac{11}{20}\)

Detailed Solution

Total number = 40
number of red = 10
Pr (R) = \(\frac{10}{40}\)

Pr(blue) = \(\frac{12}{40}\)

probability (neither red nor blue)
= 1 - \(\frac{10}{40}\) - \(\frac{12}{40}\)
= \(\frac{40 -12 -10}{40}\)
= \(\frac{18}{40}\) or \(\frac{9}{20}\)
46.

A fair die is tossed twice what is the probability of get a sum of at least 10.

A. \(\frac{5}{36}\)

B. \(\frac{2}{3}\)

C. \(\frac{5}{18}\)

D. \(\frac{1}{6\)

Detailed 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
47.

A man will be (x+10)years old in 8years time. If 2years ago he was 63 years., find the value of x

A. 55

B. 63

C. 57

D. 67

Detailed Solution

A man will be (x+10) years old in 8years time.
As at today, he is x + 2 years of age.

The man was 63 years old 2 years ago, so he is 63+2=65 now.

8 years from now, he will be 65+8=73.

He will be (x+10) years old when he is 73. So

x+10=73
x=73-10=63

48.

The equation of a line is given as 3 x - 5y = 7. Find its gradient (slope)

A. \(\frac{5}{3}\).

B. \(\frac{3}{5}\).

C. \(\frac{-3}{5}\).

D. \(\frac{-5}{3}\).

Detailed Solution

the form y=mx+c
where m is the gradient and c is the y-intercept.
the equation to gives 5y=-3x+7.
comparing this with the general equation y=mx+c,
you can see that m= the gradient= \(\frac{-3}{5}\).
49.

For what value of x is \(\frac{4 - 2x}{x + 1}\) undefined.

A. 2

B. -1

C. 1

D. -2

Detailed Solution

A rational expression is undefined when the denominator is equal to zero.
when x = -1
The denominator in this equation : x + 1
--> -1 + 1 = 0
This expression is undefined when x = -1


41.

\(\overline{XY}\) is a line segments with the coordinates X (- 8,- 12) and Y(p,q). if the midpoint of \(\overline{XY}\) is (-4,-2) find the coordinates of Y.

A. (-6,-2)

B. (0,8)

C. (4,10)

D. (0,4)

Detailed Solution

The formula for midpoint = \(\frac{x_1 + x_2}{2}\), \(\frac{y_1 + y_2}{2}\)
(-4,-2) = (x,y)
x = \(\frac{x_1 + x_2}{2}\)
-4 = \(\frac{-8 + p}{2}\)
-4 * 2 = -8 + p
-8 + 8 = p
: p = 0
y = \(\frac{y_1 + y_2}{2}\)
-2 = \(\frac{-12 + q}{2}\)
-2 * 2 = -12 + q
-4 + 12 = q
: q = 8
42.

500 tickets were sold for a concert tickets for adults and children were sold at $4.50 and $3.00 respectively if the total receipts for the concerts was $1987.50 how many tickets for adults were sold?

A. 325

B. 235

C. 175

D. 400

Detailed Solution

A for Adults
C for children
a + c = 500
c = 500 - a
4.5a + 3c = 1987.50
where c = 500 - a
4.5a + 3(500 - a) = 1987.50
4.5a - 3a = 1987.50 - 1500
1.5a = 487.5
a = 487.5 / 1.5
a = 325 tickets
c = 500 - a
c = 500 - 325
c = 175 tickets

Check:
from 4.5a + 3c
4.5 (325) = 1,462.5
+
3(175) = 525

43.

The distance d between two villages east more than 18 KM but not more than 23KM.which of these inequalities represents the statements?

A. 18 ≤ d ≤ 23

B. 18 < d < 23

C. 18 ≤ d < 23

D. 18 < d ≤ 23

Detailed Solution

distance d more than 18 KM = d > 18 0r 18 < d
distance d but not more than 23 KM = d ≤ 23
Mathematically; 18 < d ≤ 23
44.

The pie chart represents the distribution of fruits on display in the shop if there are 60 apples on display how many oranges are there?

A. 80

B. 270

C. 120

D. 90

Detailed Solution

Total angles = 360°
100 + 60 + 80 + M = 360
M = 360 - 240 = 120
Orange (M) = 120° and F ( fruits in total)
For Apples:
\(\frac{80}{360} \times F\) = 60
F = \(\frac{60 \times 360}{80}\)
F = 270 fruits in total
For Orange
= \(\frac{120}{360} \times 270\)
= 90 oranges
45.

A box contains 40 identical balls of which 10 are red and 12 are blue. if a ball is selected at random from the box what is the probability that it is neither red nor blue?

A. \(\frac{9}{20}\)

B. \(\frac{3}{10}\)

C. \(\frac{1}{4}\)

D. \(\frac{11}{20}\)

Detailed Solution

Total number = 40
number of red = 10
Pr (R) = \(\frac{10}{40}\)

Pr(blue) = \(\frac{12}{40}\)

probability (neither red nor blue)
= 1 - \(\frac{10}{40}\) - \(\frac{12}{40}\)
= \(\frac{40 -12 -10}{40}\)
= \(\frac{18}{40}\) or \(\frac{9}{20}\)
46.

A fair die is tossed twice what is the probability of get a sum of at least 10.

A. \(\frac{5}{36}\)

B. \(\frac{2}{3}\)

C. \(\frac{5}{18}\)

D. \(\frac{1}{6\)

Detailed 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
47.

A man will be (x+10)years old in 8years time. If 2years ago he was 63 years., find the value of x

A. 55

B. 63

C. 57

D. 67

Detailed Solution

A man will be (x+10) years old in 8years time.
As at today, he is x + 2 years of age.

The man was 63 years old 2 years ago, so he is 63+2=65 now.

8 years from now, he will be 65+8=73.

He will be (x+10) years old when he is 73. So

x+10=73
x=73-10=63

48.

The equation of a line is given as 3 x - 5y = 7. Find its gradient (slope)

A. \(\frac{5}{3}\).

B. \(\frac{3}{5}\).

C. \(\frac{-3}{5}\).

D. \(\frac{-5}{3}\).

Detailed Solution

the form y=mx+c
where m is the gradient and c is the y-intercept.
the equation to gives 5y=-3x+7.
comparing this with the general equation y=mx+c,
you can see that m= the gradient= \(\frac{-3}{5}\).
49.

For what value of x is \(\frac{4 - 2x}{x + 1}\) undefined.

A. 2

B. -1

C. 1

D. -2

Detailed Solution

A rational expression is undefined when the denominator is equal to zero.
when x = -1
The denominator in this equation : x + 1
--> -1 + 1 = 0
This expression is undefined when x = -1