Available Questions 601 found Page 16 of 31
Standalone Questions
#900
Mathematics
Integrals
SA
APPLY
2023
KNOWLEDGE
3 Marks
28. (a) Find: $\int\frac{e^{x}}{\sqrt{5-4e^{x}-e^{2x}}}dx$
Key:
Sol:
Sol:
#899
Mathematics
Integrals
SA
APPLY
2023
KNOWLEDGE
3 Marks
27. (b) OR: Evaluate: $\int_{-2}^{2}\frac{x^{2}}{1+5^{x}}dx$
Key:
Sol:
Sol:
#898
Mathematics
Integrals
SA
APPLY
2023
KNOWLEDGE
3 Marks
27. (a) Evaluate: $\int_{\pi/4}^{\pi/2}e^{2x}(\frac{1-\sin 2x}{1-\cos 2x})dx$
Key:
Sol:
Sol:
#897
Mathematics
Integrals
SA
APPLY
2023
KNOWLEDGE
3 Marks
26. Find: $\int\frac{x^{2}+x+1}{(x+1)^{2}(x+2)}dx$
Key:
Sol:
Sol:
#896
Mathematics
Integrals
SA
APPLY
2023
KNOWLEDGE
3 Marks
Evaluate : $\int_{0}^{\frac{\pi}{2}}e^{x }\sin x~dx$.
OR
Find: $\int\frac{1}{\cos(x-a)\cos(x-b)}dx$
OR
Find: $\int\frac{1}{\cos(x-a)\cos(x-b)}dx$
Key:
Sol:
Sol:
#895
Mathematics
Integrals
SA
APPLY
2023
KNOWLEDGE
3 Marks
Find:$\int \frac{1}{\sqrt{x}(\sqrt{x}+1)(\sqrt{x}+2)} \, dx$
Key:
Sol:
Sol:
#894
Mathematics
Integrals
SA
APPLY
2023
KNOWLEDGE
3 Marks
Evaluate $\int_{0}^{\frac{\pi}{2}}[\log(\sin~x)-\log(2\cos~x)]dx.$
Key:
Sol:
Sol:
#893
Mathematics
Integrals
LA
APPLY
2023
KNOWLEDGE
5 Marks
Evaluate: $\int_ 0 ^{π/2} [\sin 2x \tan⁻¹(\sin x)] dx$
Key:
Sol:
Sol:
#892
Mathematics
Integrals
SA
APPLY
2023
KNOWLEDGE
3 Marks
(a) Evaluate: $\int_0^{2\pi} \frac{1}{1 + e^{\sin x}} dx $
OR
(b) Find: $\int \frac{x⁴} { ((x-1)(x²+1))}dx.$
OR
(b) Find: $\int \frac{x⁴} { ((x-1)(x²+1))}dx.$
Key:
Sol:
Sol:
#891
Mathematics
Matrices and Determinants
LA
APPLY
2023
Competency
5 Marks
If $A=\begin{bmatrix}3 & 2\\ 5 & -7\end{bmatrix}$, then find $A^{-1}$ and use it to solve the following system of equations : $3x+5y=11, 2x-7y=-3$.
Key:
Sol:
Sol:
#890
Mathematics
Matrices and Determinants
LA
APPLY
2023
KNOWLEDGE
5 Marks
If $A=\begin{bmatrix}1 & 0 & 2\\ 0 & 2 & 1\\ 2 & 0 & 3\end{bmatrix}$, then show that $A^{3}-6A^{2}+7A+2I=O$
Key:
Sol:
Sol:
#889
Mathematics
Matrices and Determinants
LA
APPLY
2023
Competency
5 Marks
32. Find the inverse of the matrix $A=\begin{bmatrix}1 & -1 & 2\\ 0 & 2 & -3\\ 3 & -2 & 4\end{bmatrix}$. Using the inverse, solve the system of linear equations $x-y+2z=1; 2y-3z=1; 3x-2y+4z=3$.
Key:
Sol:
Sol:
#888
Mathematics
Matrices and Determinants
SA
APPLY
2023
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
If $A=\begin{bmatrix}1 & 2 & 3\\ 3 & -2 & 1\\ 4 & 2 & 1\end{bmatrix}$, then show that A³ - 23A - 40I = O.
Key:
Sol:
Sol:
#887
Mathematics
Three Dimensional Geometry
LA
APPLY
2023
Competency
5 Marks
Find the equations of all the sides of the parallelogram ABCD whose vertices are $A(4,7,8), B(2,3,4), C(-1,-2,1)$ and $D(1,2,5)$. Also, find the coordinates of the foot of the perpendicular from A to CD.
Key:
Sol:
Sol:
#886
Mathematics
Three Dimensional Geometry
LA
APPLY
2023
Competency
5 Marks
Find the value of $b$ so that the lines $\frac{x-1}{2}=\frac{y-b}{3}=\frac{z-3}{4}$ and $\frac{x-4}{5}=\frac{y-1}{2}=z$ are intersecting lines. Also, find the point of intersection of these given lines.
Key:
Sol:
Sol:
#885
Mathematics
Three Dimensional Geometry
VSA
APPLY
2023
KNOWLEDGE
2 Marks
If the angle between the lines $\frac{x-5}{\alpha}=\frac{y+2}{-5}=\frac{z+\frac{24}{5}}{\beta}$ and $\frac{x}{1}=\frac{y}{0}=\frac{z}{1}$ is $\frac{\pi}{4}$, find the relation between $\alpha$ and $\beta$.
Key:
Sol:
Sol:
#884
Mathematics
Three Dimensional Geometry
LA
APPLY
2023
Competency
5 Marks
35. (b) OR: Find the angle between the lines $2x=3y=-z$ and $6x=-y=-4z$.
Key:
Sol:
Sol:
#883
Mathematics
Three Dimensional Geometry
LA
APPLY
2023
Competency
5 Marks
35. (a) Show that the following lines do not intersect each other : $\frac{x-1}{3}=\frac{y+1}{2}=\frac{z-1}{5};\frac{x+2}{4}=\frac{y-1}{3}=\frac{z+1}{-2}$
Key:
Sol:
Sol:
#882
Mathematics
Three Dimensional Geometry
VSA
APPLY
2023
Competency
2 Marks
25. (b) OR: The equations of a line are $5x-3=15y+7=3-10z$. Write the direction cosines of the line and find the coordinates of a point through which it passes.
Key:
Sol:
Sol:
#881
Mathematics
Three Dimensional Geometry
VSA
APPLY
2023
KNOWLEDGE
2 Marks
25. (a) Find the vector equation of the line passing through the point $(2, 1, 3)$ and perpendicular to both the lines $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{3} ; \frac{x}{-3}=\frac{y}{2}=\frac{z}{5}$
Key:
Sol:
Sol: