JAMB Mathematics Syllabus for UTME 2027

Our summary: Writing numbers in bases other than ten, and working with remainders after division.

Contents

Objectives

• Perform four basic operations ($\times, +, -, \div$)
• Convert one base to another
• Perform operations in modulo arithmetic

Our summary: Fractions, decimals and rounding, plus everyday money and ratio problems like interest, profit, loss and VAT.

Contents

Objectives

• Perform basic operations ($\times, +, -, \div$) on fractions and decimals
• Express to specified number of significant figures and decimal places
• Calculate simple interest, profit and loss per cent; ratio, proportion, rate and percentage error
• Solve problems involving share and VAT

Our summary: The rules for powers, logarithms and square-root expressions, and how they connect.

Contents

Objectives

• Apply the laws of indices in calculation
• Establish the relationship between indices and logarithms in solving problems
• Solve equations involving indices
• Solve problems in different bases in logarithms
• Simplify and rationalize surds
• Perform basic operations on surds

Our summary: Grouping things into sets, counting them, and showing overlaps with Venn diagrams.

Contents

Objectives

• Identify types of sets, i.e. empty, universal, complements, subsets, finite, infinite and disjoint sets
• Solve problems involving cardinality of sets
• Solve set problems using symbols
• Use Venn diagrams to solve problems involving not more than 3 sets

Our summary: Rearranging formulae, factorising and dividing polynomials, and solving simultaneous equations.

Contents

Objectives

• Find the subject of the formula of a given equation
• Apply factor and remainder theorem to factorize a given expression
• Multiply, divide polynomials of degree not more than 3 and determine values of defined and undefined expression
• Factorize by regrouping difference of two squares, perfect squares and cubic expressions, etc.
• Solve simultaneous equations: one linear, one quadratic
• Interpret graphs of polynomials including applications to maximum and minimum values

Our summary: How one quantity changes with another: direct, inverse, joint and partial variation.

Contents

Objectives

• Solve problems involving direct, inverse, joint and partial variations
• Solve problems on percentage increase and decrease in variation

Our summary: Solving and graphing inequalities, both linear and quadratic.

Contents

Objectives

• Solve problems on linear and quadratic inequalities
• Interpret graphs of inequalities

Our summary: Number patterns where each term follows a rule, and adding up their terms (A.P. and G.P.).

Contents

Objectives

• Determine the nth term of a progression
• Compute the sum of A.P. and G.P.
• Sum to infinity of a given G.P.

Our summary: Rules for combining two elements, and checking properties like closure and identity.

Contents

Objectives

• Solve problems involving closure, commutativity, associativity and distributivity
• Solve problems involving identity and inverse elements

Our summary: Adding and multiplying matrices, finding determinants and inverting 2 x 2 matrices.

Contents

Notes

• Excluding quadratic and higher degree equations.

Objectives

• Perform basic operations ($\times, +, -, \div$) on matrices
• Calculate determinants
• Compute inverses of $2 \times 2$ matrices

Our summary: Angles, lines, polygons and circles, and how to construct special angles.

Contents

Objectives

• Identify various types of lines and angles
• Solve problems involving polygons
• Calculate angles using circle theorems
• Identify construction procedures of special angles, e.g. $30^\circ$, $45^\circ$, $60^\circ$, $75^\circ$, $90^\circ$, etc.

Our summary: Finding lengths, areas and volumes of flat and solid shapes, and distances on the earth.

Contents

Objectives

• Calculate the perimeters and areas of triangles, quadrilaterals, circles and composite figures
• Find the length of an arc, a chord, perimeters and areas of sectors and segments of circles
• Calculate total surface areas and volumes of cuboids, cylinders, cones, pyramids, prisms, spheres and composite figures
• Determine the distance between two points on the earth's surface

Our summary: The path traced by a point that follows a geometric rule.

Contents

Objectives

• Identify and interpret loci relating to parallel lines, perpendicular bisectors, angle bisectors and circles

Our summary: Using coordinates to find midpoints, gradients, distances and equations of straight lines.

Contents

Objectives

• Determine the midpoint and gradient of a line segment
• Find the distance between two points
• Identify conditions for parallelism and perpendicularity
• Find the equation of a line in the two-point form, point-slope form, slope-intercept form and the general form

Our summary: Sine, cosine and tangent, and using them for heights, bearings and triangle areas.

Contents

Objectives

• Calculate the sine, cosine and tangent of angles between $-360^\circ \le \theta \le 360^\circ$
• Apply these special angles, e.g. $30^\circ$, $45^\circ$, $60^\circ$, $75^\circ$, $90^\circ$, $105^\circ$, $135^\circ$ to solve simple problems in trigonometry
• Solve problems involving angles of elevation and depression
• Solve problems involving bearings
• Apply trigonometric formulae to find areas of triangles
• Solve problems involving sine and cosine graphs

Our summary: Finding how fast a function changes, starting from limits.

Contents

Objectives

• Find the limit of a function
• Differentiate explicit algebraic and simple trigonometrical functions

Our summary: Using derivatives for rates of change and for finding the biggest or smallest value.

Contents

Objectives

• Solve problems involving applications of rate of change, maxima and minima

Our summary: Reversing differentiation and finding the area under a curve.

Contents

Objectives

• Solve problems of integration involving algebraic and simple trigonometric functions
• Calculate area under the curve (simple cases only)

Our summary: Showing data in frequency tables, histograms, bar charts and pie charts.

Contents

Objectives

• Identify and interpret frequency distribution tables
• Interpret information on histogram, bar chart and pie chart

Our summary: Finding the typical value of data using mean, mode, median and cumulative frequency.

Contents

Objectives

• Calculate the mean, mode and median of ungrouped and grouped data (simple cases only)
• Use ogive to find the median, quartiles and percentiles

Our summary: Measuring how spread out data is, with range, variance and standard deviation.

Contents

Objectives

• Calculate the range, mean deviation, variance and standard deviation of ungrouped and grouped data

Our summary: Counting the ways to arrange or choose items.

Contents

Objectives

• Solve simple problems involving permutation and combination

Our summary: How likely events are, including combined events.

Contents

Objectives

• Solve simple problems in probability (including addition and multiplication)