2022 - JAMB Mathematics Past Questions and Answers - page 2
The 10th term of an AP is 32. If the first term is 3/2, what is the 4th term?
35/3
64
16
35/2
Tn = a + (n-1)d
10th term = 32
32 = 3/2 + 9d
9d = 32 - 3/2
9d = 61/2
d = 61/18
T4 = 3/2 + 3(61/18)
T4 = 3/2 + 61/6 → 35/3
Tanθ is positive and Sinθ is negative. In which quadrant does θ lies
Third only
Fourth only
First and third only
Second only
In the third quadrant where the tangent of any angle is positive.
The sine and cosine of any angle between 180 and 270 degrees are negative.
In how many ways can the letter of ZOOLOGY be arranged?
720
360
840
120
ZOOLOGY has 7 letters in total, with O repeated thrice hence,
\(\frac{7!}{3!}\) → \(\frac{7*6*5*4*3*2*1}{3*2*1}\)
= 840ways
Find the integral of (2x+1)\(^3\)
\(\frac{{2x+1}^3}{8}\) + C
\(\frac{{2x+1}^4}{8}\) + C
\(\frac{{2x+1}^4}{4}\) + C
\(\frac{{2x+1}^2}{6}\) + C
Using Chain Rule,
u = 2x +1; du = 2dx → dx = \(\frac{du}{2}\)
u\(^3\) = ∫ u\(^3\) \(\frac{du}{2}\) → \(\frac{1}{2}\) ∫ u\(^3\)
= \(\frac{1*u^4}{2*4}\)
= \(\frac{u^4}{8}\) → \(\frac{{2x+1}^4}{8}\) + C
If A = \(\begin{pmatrix} 2 & 1 \ 2 & 3 \ 1 & 2 \end{pmatrix}\) and B = \(\begin{pmatrix} 3 & 2 \ 4 & 2 \end{pmatrix}\). Find AB
\(\begin{pmatrix} 18 & 6 \ 12 & 10 \ 10 & 6 \end{pmatrix}\)
\(\begin{pmatrix} 10 & 6 \ 13 & 10 \ 12 & 6 \end{pmatrix}\)
\(\begin{pmatrix} 10 & 6 \ 12 & 10 \ 11 & 6 \end{pmatrix}\)
\(\begin{pmatrix} 10 & 6 \ 18 & 10 \ 11 & 6 \end{pmatrix}\)
Given that A = \(\begin{pmatrix} 2 & 1 \ 2 & 3 \ 1 & 2 \end{pmatrix}\) and B = \(\begin{pmatrix} 3 & 2 \ 4 & 2 \end{pmatrix}\).
We apply matrice multiplication, considering that the number of columns in A = number of rows in B
AB = \(\begin{pmatrix} (2*3)+(1*4) & (2*2)+(1*2) \ (2*3)+(3*4) & (2*2)+(3*2) \ (1*3)+(2*4) & (1*2)+(2*2) \end{pmatrix}\)
AB = \(\begin{pmatrix} (6+4) & (4+2) \ (6+12) & (4+6) \ (3+8) & (2+4) \end{pmatrix}\)
= \(\begin{pmatrix} 10 & 6 \ 18 & 10 \ 11 & 6 \end{pmatrix}\)
Make v the subject of the formula from r = \( \sqrt \frac{3v}{\pi h} \)
v = 3 \(πr^2\) h
v = \(\frac{πrh}{3}\)
v = \(\frac{πr^2h}{3}\)
v = 3πrh
Given r = \( \sqrt \frac{3v}{\pi h} \)
Square both sides:
r\(^2\) = \(\frac{3v}{πh}\)
cross multiply
3v = r\(^2\) * πh
v = \(\frac{πr^2h}{3}\)
Find the determinant of the matrix A = \(\begin{pmatrix} 2 & 3 \ 1 & 3 \end{pmatrix}\)
4
2
5
3
Evaluate Log\(_2\) 8√2
3.0
4.5
3.5
2.5
Log\(_2\) 8√2 => Log\(_2\) √128
=> Log\(_2\) 128\(^\frac{1}{2}\)
= \(\frac{1}{2}\) * (Log\(_2\) 128)
=> \(\frac{1}{2}\) * (Log\(_2\) 2\(^7\))
= 7 * \(\frac{1}{2}\) * (Log\(_2\) 2)
where (Log\(_2\) 2) = 1
=> 7 * \(\frac{1}{2}\) * 1
= \(\frac{7}{2}\) or 3.5
The locus of points equidistant from a fixed point is a___
circle
perpendicular lines
straight line
bisector
Find the result when the numerator of \(\frac{96}{50}\) is decreased by 37.5% and its denominator decreased by 20%.
1.5
\(\frac{5}{2}\)
\(\frac{96}{48}\)
0.5
Numerator: 96 => 37.5% of 96 = 36
decrease by 36 => 96 - 36
new numerator = 60
Denominator: 50 => 20% of 50 = 10
decrease by 10 => 50 - 10 = 40
new denominator = 40
the new fraction = \(\frac{60}{40}\) or 1.5