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Mathematics Past Questions and Answers
Topic: Definite integral
Classroom
Jamb
Exam year:
Exam year
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
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1992
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2005
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2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
Question type:
Question type
Objective
Theory
Topics:
Topics
[1] NUMBER AND NUMERATION
[1].1 Number bases
[1].1.1 operations in different number bases from 2 to 10
[1].1.2 conversion from one base to another including fractional parts
[1].2 Fractions, Decimals, Approximations and Percentages
[1].2.1 Fractions
[1].2.2 Decimals
[1].2.3 Significant figures
[1].2.4 decimal places
[1].2.5 Percentages errors
[1].2.6 Simple interest
[1].2.7 Profit and loss percent
[1].2.8 Ratio, proportion and rate
[1].2.9 Shares and valued added tax
[1].2.10 Approximations
[1].3 Indices, Logarithms and Surds
[1].3.1 Laws of Indices
[1].3.2 equations involving indices
[1].3.3 Standard form
[1].3.4 Laws of Logarithms
[1].3.5 Logarithm of any positive number to a given base
[1].3.6 change of bases in logarithm and application
[1].3.7 relationship between indices and logarithm
[1].3.8 Surds
[1].4 Sets
[1].4.1 Types of sets
[1].4.2 algebra of sets
[1].4.3 Venn diagrams and their applications
[2] ALGEBRA
[2].1 Polynomials
[2].1.1 Change of subject of formula
[2].1.2 Multiplication and division of polynomials
[2].1.3 Factorization of polynomials of degree not exceeding 3
[2].1.4 Roots of a polynomials not exceeding degree 3
[2].1.5 Factor and remainder theorems
[2].1.6 Simultaneous equations including one linear one quadratic
[2].1.7 Graphs of polynomials of degree not greater than 3
[2].2 Variation
[2].2.1 Direct
[2].2.2 Inverse
[2].2.3 Joint
[2].2.4 Partial
[2].2.5 Percentage increase and decrease
[2].3 Inequalities
[2].3.1 analytical and graphical solutions of linear inequalities
[2].3.2 quadratic inequalities with integral roots only
[2].4 Progression
[2].4.1 Nth term of a progression
[2].4.2 Sum of Arithmetic progression
[2].4.3 Sum of Geometric progression
[2].5 Binary Operations
[2].5.1 properties of closure, commutativity, associativity and distributivity
[2].5.2 Identity element (simple cases only)
[2].5.3 Inverse element (simple cases only)
[2].6 Matrices and Determinants
[2].6.1 algebra of matrices not exceeding 3 x 3
[2].6.2 Determinants of a matrix not exceeding 3 x 3
[2].6.3 Inverse of 2 x 2 matrices; [excluding quadratic and higher degree equations].
[2].6.4 Addition and Subtraction of matrices
[2].6.5 Multiplication of matrices
[2].6.6 Transpose of matrices
[3] GEOMETRY AND TRIGONOMETRY
[3].1 Euclidean Geometry
[3].1.1 Properties of angles and lines
[3].1.2 Polygons: triangles, quadrilaterals and general polygons
[3].1.3 Circle: angle properties, cyclic quadrilaterals and intersecting chords
[3].1.4 Construction
[3].2 Mensuration
[3].2.1 lengths and areas of plane geometrical figures
[3].2.2 Lengths of arcs
[3].2.3 Chords of a circle
[3].2.4 Perimeters and areas of sectors
[3].2.5 Segments of circles
[3].2.6 Surface areas and Volumes of simple solids
[3].2.7 Surface areas and Volumes of composite figures
[3].2.8 The earth as a sphere
[3].2.9 Longitudes and Latitudes
[3].2.10 Plane geometric shapes
[3].3 Loci
[3].3.1 locus in 2 dimensions based on geometric principles relating to lines and curves.
[3].4 Coordinate Geometry
[3].4.1 midpoint of a line segment
[3].4.2 Gradient of a line segment
[3].4.3 Distance between two points
[3].4.4 Parallel and perpendicular lines
[3].4.5 Equations of straight lines
[3].5 Trigonometry
[3].5.1 trigonometrical ratios of angles
[3].5.2 Angles of elevation
[3].5.3 Angles of depression
[3].5.4 Bearings
[3].5.5 areas and solutions of triangle
[3].5.6 graphs of sine and cosine
[3].5.7 sine and cosine formulae
[4] CALCULUS
[4].1 Differentiation
[4].1.1 Limit of a function
[4].1.2 differentiation of explicit algebraic and simple trigonometrical functions – sine, cosine and tangent.
[4].2 Application of differentiation
[4].2.1 Rate of change
[4].2.2 Maxima
[4].2.3 Minima
[4].3 Integration
[4].3.1 integration of explicit algebraic
[4].3.2 integration of simple trigonometrical functions
[4].3.3 area under the curve.
[4].3.4 Definite integral
[4].3.5 Indefinite integral
[5] STATISTICS
[5].1 Representation of data
[5].1.1 frequency distribution
[5].1.2 Histogram
[5].1.3 Bar chart
[5].1.4 Pie chart
[5].2 Measures of Location
[5].2.1 Mean of ungrouped and grouped data
[5].2.2 Mode of ungrouped and grouped data
[5].2.3 Median of ungrouped and grouped data
[5].2.4 cumulative frequency
[5].3 Measures of Dispersion
[5].3.1 Range
[5].3.2 Mean deviation
[5].3.3 Variance
[5].3.4 Standard deviation
[5].4 Permutation and Combination
[5].4.1 Linear and circular arrangements
[5].4.2 Arrangements involving repeated objects
[5].5 Probability
[5].5.1 experimental probability (tossing of coin, throwing of a dice etc)
[5].5.2 Addition and multiplication of probabilities (mutual and independent cases).
Jamb Mathematics Questions - Definite integral
Question 1:
JAMB 2015
Integral ∫\( (5x^3 + 7x^2 − 2x + 5)\)dx
SchoolNGR Classroom
A
\( \frac{5x^4}{4} + \frac{7x^3}{3} + 2x + C \)
B
\( \frac{5x}{4} + \frac{7x^3}{3} - x^2 + 5x + C \)
C
\( \frac{5x^3}{3} + \frac{7x^2}{x} - x + C \)
D
\( \frac{2x^2}{3} + \frac{x}{5} - C \)
View Answer & Explanation
Question 2:
JAMB 1992
Evaluate the integral \(\int^{\frac{\pi}{4}}_{\frac{\pi}{12}} 2 \cos 2x \mathrm {d} x\)
SchoolNGR Classroom
A
-\(\frac{1}{2}\)
B
-1
C
\(\frac{1}{2}\)
D
1
View Answer & Explanation
Question 3:
JAMB 2015
Integral ∫\( (5x^3 + 7x^2 − 2x + 5)\)dx
SchoolNGR Classroom
A
\( \frac{5x^4}{4} + \frac{7x^3}{3} + 2x + C \)
B
\( \frac{5x}{4} + \frac{7x^3}{3} - x^2 + 5x + C \)
C
\( \frac{5x^3}{3} + \frac{7x^2}{x} - x + C \)
D
\( \frac{2x^2}{3} + \frac{x}{5} - C \)
View Answer & Explanation
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