2021 - JAMB Mathematics Past Questions and Answers - page 3
The locus of a point which moves so that it is equidistant from two intersecting straight lines is the?
perpendicular bisector of the two lines
angle bisector of the two lines
bisector of the two lines
line parallel to the two lines
4, 16, 30, 20, 10, 14 and 26 are represented on a pie chart. Find the sum of the angles of the bisectors representing all numbers equals to or greater than 16
48o
84o
92o
276o
Sum of 4, 16, 30, 20, 10, 14 and 26
= 120
numbers \(\geq\) 16 are 16 + 30 + 20 + 26 = 92
sum of angles = \(\frac{92}{120}\) x \(\frac{360^o}{1}\)
= 276\(^o\)
The mean of ten positive numbers is 16. When another number is added, the mean becomes 18. Find the eleventh number
3
16
38
30
Given that the mean of 10 positive numbers = 16
Sum of numbers = 16 x 10 = 160
Mean of 11 numbers = 18
Total sum of numbers = 11 x 18
= 198
The 11th number = 198 - 160
= 38
Two numbers are removed at random from the numbers 1, 2, 3 and 4. What is the probability that the sum of the numbers removed is even?
\(\frac{2}{3}\)
\(\frac{1}{2}\)
\(\frac{1}{3}\)
\(\frac{1}{4}\)
\(\begin{array}{c|c} 1 & 2 & 3 & 4\\hline 1(1, 1) & (1, 2) & (1, 3) & (1, 4)\ \hline 2(2, 1) & (2 , 2) & (2, 3) & (2, 4) \ \hline 3(3, 1) & (3, 2) & (3, 3) & (3, 4)\ \hline 4(4, 1) & (4, 2) & (4, 3) & (4, 4)\end{array}\)
Sample space = 16
Sum of numbers removed: (2), 3, (4), 5
3, (4), 5, (6)
(4), 5, (6), 7
(5), 6, 7, (8)
Even numbers count: 8
Pr(even sum) = \(\frac{8}{16}\)
= \(\frac{1}{2}\)
Find the probability that a number selected at random from 41 to 56 is a multiple of 9
\(\frac{1}{8}\)
\(\frac{2}{15}\)
\(\frac{3}{16}\)
\(\frac{7}{8}\)
Given the range of number 41 to 56, we have:
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56
The numbers that are multiple of 9 are: 45, 54
P(multiple of 9) = \(\frac{2}{16}\)
= \(\frac{1}{8}\)
Musa borrows N10.00 at 2% per month simple interest and repays N8.00 after 4 months. How much does he still owe?
N10.80
N10.67
N2.80
N2.67
I = \(\frac{PRT}{100}\)
= \(\frac{10 \times 2 \times 4}{100}\)
= \(\frac{4}{5}\)
= 0.8
Total amount = N10.80
Musa repays N8.00
Remainder = 10.80 - 8.00
= N2.80
Simplify 2log \(\frac{2}{5}\) - log\(\frac{72}{125}\) + log 9
1 - 4 log3
-1 + 2 log 3
-1 + 5 log2
1 - 2log 2
2log \(\frac{2}{5}\) - log\(\frac{72}{125}\) + log 9
[\(\frac{2}{5}\))2 x 9] = log \(\frac{4}{25}\) x \(\frac{9}{1}\) x \(\frac{125}{72}\)
= log \(\frac{72}{125}\)
= log \(\frac{5}{2}\)
= log \(\frac{10}{4}\)
= log 10 - log 4
= log10 - log2\(^2\)
= 1 - 2 log2
A car travels from calabar to Enugu, a distance of P km with an average speed of U km per hour and continues to benin, a distance of Q km, with an average speed of Wkm per hour. Find its average speed from Calabar to Benin
\(\frac{(p + q)}{pw + qu}\)
\(\frac{uw(p + q)}{pw + qu}\)
\(\frac{uw(p + q)}{pw}\)
\(\frac{uw}{pw + qu}\)
Average speed = \(\frac{total distance}{total time}\)
Calabar to Enugu in time t1,
t1 = \(\frac{P}{U}\)
Enugu to Benin:
t2 \(\frac{q}{w}\)
Average speed = \(\frac{p + q}{t_1 + t_2}\)
= \(\frac{p + q}{p/u + q/w}\)
= p + q x \(\frac{uw}{pw + qu}\)
= \(\frac{uw(p + q)}{pw + qu}\)
If w varies inversely as \(\frac{uv}{u + v}\) and w = 8 when
u = 2 and v = 6, find a relationship between u, v, w.
uvw = 16(u + v)
16uv = 3w(u + v)
uvw = 12(u + v)
12uvw = u + v
W \(\alpha\) \(\frac{\frac{1}{uv}}{u + v}\)
w = \(\frac{\frac{k}{uv}}{u + v}\)
= \(\frac{k(u + v)}{uv}\)
w = \(\frac{k(u + v)}{uv}\)
w = 8, u = 2 and v = 6
8 = \(\frac{k(2 + 6)}{2(6)}\)
= \(\frac{k(8)}{12}\)
k = 12
12 ( u + v) = uwv
If g(x) = x\(^2\) + 3x find g(x + 1) - g(x)
(x + 2)
2(x + 2)
(2x + 1)
(x2 + 4)
g(x) = x2 + 3x
When g(x + 1) = (x + 1)^2 + 3(x + 1)
= x\(^2\) + 1 + 2x + 3x + 3
= x\(^2\) + 5x + 4
g(x + 1) - g(x) = x2 + 5x + 8 - (x\(^2\) + 3x)
= x\(^2\) + 5x + 4 - x2 -3x
= 2x + 4 or 2(x + 4)
= 2(x + 2)