JAMB 2026 · Mathematics
JAMB maths formulas: the complete UTME sheet
The UTME gives you an on-screen calculator and nothing else. No formula booklet, no reminders, no mercy. Forty questions in roughly half an hour leaves no time to derive anything, so these formulas have to live in your head. This page groups them by topic, flags the ones candidates misremember, and shows where each one earns its marks.
How to use this sheet
Do not read it like a novel. Pick one topic, close the page, and write its formulas on paper from memory. Check what you wrote against the table. Anything you missed or mangled goes on a shortlist, and that shortlist is what you test yourself on tomorrow before you practise questions on the topic. Recognising a formula on a screen feels like knowing it. Reproducing it, under time, with nothing in front of you, is knowing it.
There is no formula sheet in the hall
The CBT gives you an on-screen calculator and nothing more. Maths carries 40 questions, roughly 89 of the 400 marks, at about 2.22 marks each. Every formula below is one you may need within 45 seconds of meeting a question.
Indices, logarithms and surds
The laws of indices and logarithms open more JAMB questions than any other cluster. They are short, they look alike, and mixing two of them up produces a wrong option that JAMB has helpfully included among your choices.
| Formula | What it gives you | Where it shows up |
|---|---|---|
| am × an = am+n | Product of powers with the same base | Simplifying indices, exponential equations |
| am ÷ an = am−n | Quotient of powers | Simplification, solving for x in the index |
| (am)n = amn | Power of a power | Equations like 8x = 2x+4 |
| a0 = 1 and a−n = 1/an | Zero and negative indices | Evaluating expressions, standard form |
| a1/n = n√a, so am/n = (n√a)m | Fractional index as a root | Evaluating 272/3 and its cousins |
| log(ab) = log a + log b | Log of a product | Condensing and expanding log expressions |
| log(a/b) = log a − log b | Log of a quotient | Same, plus log equations |
| log an = n log a | Log of a power | Bringing the unknown down from an index |
| loga a = 1 and loga 1 = 0 | The two anchor values | Quick evaluation steps |
| loga b = log b ÷ log a | Change of base | Logs the tables or calculator cannot do directly |
| √(ab) = √a × √b | Splitting a surd | Simplifying √48 into 4√3 |
| Multiply by (√a − √b) over itself | Rationalising a denominator of √a + √b | "Express with a rational denominator" questions |
The trap: there is no law for log(a + b), and √(a + b) is not √a + √b. The laws only work on products, quotients and powers. Every year, options are built to catch candidates who invent an addition law.
Quadratic equations
Always try factorising first, because a quadratic that factorises is a 20-second question. The formula is the fallback, not the first move. Root questions are a separate skill: JAMB loves asking about the sum and product of roots precisely because both can be read straight off the equation without solving it, and candidates who start solving waste a minute they do not have.
| Formula | What it gives you | Where it shows up |
|---|---|---|
| x = [−b ± √(b² − 4ac)] ÷ 2a | Roots of ax² + bx + c = 0 | Any quadratic that refuses to factorise |
| α + β = −b/a | Sum of the roots | Root questions without solving |
| αβ = c/a | Product of the roots | Same family |
| x² − (sum)x + (product) = 0 | Builds an equation from given roots | "Find the equation whose roots are..." |
| b² − 4ac | The discriminant: positive means two real roots, zero means equal roots, negative means no real roots | "For what value of k are the roots equal?" |
The trap: the sum of roots is minus b over a. The product carries no minus. Candidates swap the signs constantly, and JAMB always lists the sign-swapped answer as an option.
Sequences and series
| Formula | What it gives you | Where it shows up |
|---|---|---|
| Tn = a + (n − 1)d | nth term of an AP | "Find the 15th term", finding d from two terms |
| Sn = (n/2)[2a + (n − 1)d] | Sum of the first n terms of an AP | Sums, and finding n from a given sum |
| Sn = (n/2)(a + l) | AP sum when the last term l is known | Faster than the full formula |
| Tn = arn−1 | nth term of a GP | "Find the 6th term", finding r |
| Sn = a(rn − 1)/(r − 1), r ≠ 1 | Sum of the first n terms of a GP | GP sums |
| S∞ = a/(1 − r), only when |r| < 1 | Sum to infinity of a GP | "Find the sum to infinity of..." |
The trap: the GP power is n − 1, not n. And the sum to infinity does not exist unless the common ratio is a fraction strictly between −1 and 1. If a question offers you a sum to infinity with r = 2, the correct response is that no such sum exists.
Variation
| Formula | What it gives you | Where it shows up |
|---|---|---|
| y ∝ x, so y = kx | Direct variation | "y varies directly as x..." |
| y ∝ 1/x, so y = k/x | Inverse variation | "y varies inversely as x..." |
| y ∝ xz, so y = kxz | Joint variation | "y varies jointly as x and z..." |
| y = kx + c (two constants) | Partial variation | "y is partly constant and partly varies as x..." |
The routine never changes: write the relationship, use the given pair of values to find k, then answer the question asked. Partial variation has two unknown constants, so it always hands you two pairs of values and expects two simultaneous equations.
Mensuration
| Formula | What it gives you | Where it shows up |
|---|---|---|
| A = ½bh, or A = ½ab sin C | Area of a triangle | Plane shapes, composite figures |
| A = ½(a + b)h | Area of a trapezium | Plane shapes |
| A = πr² and C = 2πr | Area and circumference of a circle | Everywhere |
| Arc length = (θ/360) × 2πr | Length of an arc subtending θ at the centre | Arcs, perimeter of a sector |
| Sector area = (θ/360) × πr² | Area of a sector | Sectors, cones formed from sectors |
| V = πr²h, curved surface = 2πrh | Cylinder | Volume and surface questions |
| V = ⅓πr²h, curved surface = πrl | Cone, where l is the slant height | Cones, frustum setups |
| l² = r² + h² | Slant height of a cone from Pythagoras | Whenever l is not given directly |
| V = (4/3)πr³, surface = 4πr² | Sphere | Spheres and hemispheres |
| V = lbh, and V = l³ for a cube | Cuboid and cube | Boxes, tanks, melting-and-recasting questions |
The traps: the cone's curved surface uses the slant height l, not the vertical height h, and questions deliberately give you h so you must find l first. Also watch for diameter given where the formula wants radius. Halve it before anything else touches the calculator.
Circle theorems
These are rules rather than formulas, and JAMB states its questions almost exactly in their language:
- The angle at the centre is twice the angle at the circumference standing on the same arc.
- Angles in the same segment are equal.
- The angle in a semicircle is 90°.
- Opposite angles of a cyclic quadrilateral add up to 180°.
- A tangent is perpendicular to the radius at the point of contact.
- Two tangents drawn from the same external point are equal in length.
- Alternate segment theorem: the angle between a tangent and a chord equals the angle in the alternate segment.
Most circle questions chain two of these together. Draw the figure, mark every angle you can deduce, and the target angle usually falls out in two steps.
Trigonometry
| Formula | What it gives you | Where it shows up |
|---|---|---|
| sin θ = opp/hyp, cos θ = adj/hyp, tan θ = opp/adj | SOHCAHTOA, for right-angled triangles | Heights, distances, bearings |
| a/sin A = b/sin B = c/sin C | Sine rule, any triangle | Two angles and a side, or two sides and a non-included angle |
| a² = b² + c² − 2bc cos A | Cosine rule, any triangle | Two sides and the included angle, or all three sides |
| sin 30° = ½, cos 30° = √3/2, tan 30° = 1/√3 | The 30° values | Non-calculator reasoning, exact-value questions |
| sin 45° = cos 45° = 1/√2, tan 45° = 1 | The 45° values | Same |
| sin 60° = √3/2, cos 60° = ½, tan 60° = √3 | The 60° values | Same |
The trap: the cosine rule subtracts 2bc cos A. When the included angle is obtuse, cos A is negative, so the subtraction becomes an addition through the signs. Trust the formula and let the signs do the work; do not "fix" it by hand.
Coordinate geometry
| Formula | What it gives you | Where it shows up |
|---|---|---|
| d = √[(x2 − x1)² + (y2 − y1)²] | Distance between two points | Lengths, radii, perimeters on the plane |
| M = ((x1 + x2)/2, (y1 + y2)/2) | Midpoint of a segment | Midpoints, centres of circles from a diameter |
| m = (y2 − y1)/(x2 − x1) | Gradient through two points | Almost every line question |
| y = mx + c, or y − y1 = m(x − x1) | Equation of a straight line | "Find the equation of the line through..." |
| Parallel: m1 = m2. Perpendicular: m1m2 = −1 | Gradient conditions | Perpendicular and parallel line questions |
The trap: for a perpendicular line, take the negative reciprocal. A gradient of ¾ becomes −4/3, not −¾ and not 4/3. Both half-done versions will be waiting among the options.
Calculus
| Formula | What it gives you | Where it shows up |
|---|---|---|
| d/dx (xn) = nxn−1 | Differentiating a power: multiply by the power, reduce it by one | Gradients, rates of change |
| d/dx (axn) = anxn−1, constants differentiate to 0 | Coefficients and constants | Polynomials term by term |
| ∫xn dx = xn+1/(n + 1) + c, n ≠ −1 | Integrating a power: raise the power by one, divide by the new power | Indefinite and definite integrals |
| dy/dx = 0 | Locates turning points | Maximum and minimum questions |
| d²y/dx² < 0 at a maximum, > 0 at a minimum | Classifies a turning point | "Find the maximum value of y" |
The traps: when integrating, divide by the new power, not the old one. And in an indefinite integral, the missing + c is often exactly what separates two options.
Statistics
| Formula | What it gives you | Where it shows up |
|---|---|---|
| Mean = Σx ÷ n, or Σfx ÷ Σf for a frequency table | The average | Raw lists and frequency tables |
| Median = middle value of the ordered data | The centre by position; with an even count, average the two middle values | "Find the median of..." |
| Mode = the most frequent value | The commonest observation | Frequency tables, bar charts |
| Range = highest − lowest | The simplest spread measure | Quick one-mark questions |
| Mean deviation = Σ|x − x̄| ÷ n | Average distance from the mean | Small data sets |
| SD = √[Σ(x − x̄)² ÷ n] | Standard deviation | Spread questions; variance is the SD squared |
For grouped data, work with class midpoints: the midpoint of the class 10 to 14 is 12, and that 12 is your x in Σfx. Forgetting the ordering step before reading a median, and using class boundaries where midpoints belong, are the two habitual errors here.
Permutations, combinations and probability
| Formula | What it gives you | Where it shows up |
|---|---|---|
| nPr = n! ÷ (n − r)! | Arrangements of r items from n, where order matters | Arranging people, digits, letters |
| nCr = n! ÷ [r!(n − r)!] | Selections of r items from n, where order does not matter | Choosing committees, teams |
| P(E) = favourable outcomes ÷ total outcomes | Basic probability | Dice, cards, balls in a bag |
| P(not A) = 1 − P(A) | Complement | "Probability that at least one..." shortcuts |
| P(A or B) = P(A) + P(B), if A and B cannot happen together | Mutually exclusive events | "Red or white ball" questions |
| P(A and B) = P(A) × P(B), if A and B are independent | Combined independent events | Two picks with replacement, coin plus die |
The trap: "without replacement" changes the second probability, because both the favourable count and the total have shrunk by one. Read the question twice before you multiply.
The calculator and the formula-first habit
The CBT's on-screen calculator is a mouse-driven tool, slower than the Casio in your school bag, and exam day should not be your first meeting with one. Use it for awkward arithmetic only: dividing by 7, square roots, trig values. Steps your times tables cover are faster in your head, and against multiple-choice options, estimating the size of the answer often eliminates two options before you compute anything.
Write the formula down before you substitute. On your rough sheet, one line for the formula, one line for the substitution, then compute. It feels slower. It is faster, because sign errors and swapped values announce themselves on paper, while a formula held in your head silently mutates under exam pressure. The candidates who "knew it but wrote minus instead of plus" skipped this line.
Practising with JAMB Pro
A formula sheet tells you what to know. Past questions tell you whether you know it. JAMB Pro carries 1,207 real JAMB Mathematics past questions, and every one has a worked explanation underneath, so when a formula lets you down you see exactly which line went wrong. The Timed CBT mock includes the on-screen calculator, the real two-hour timer and the question navigator, so the tool you meet in the hall is one you have already used for weeks. The Progress tab tracks your accuracy, which turns "I think I am weak in mensuration" into a number you can act on. Free, no sign-up, no ads, and Maths works offline once downloaded.
Put the formulas under exam pressure
1,207 real JAMB Maths questions with worked explanations, timed CBT mocks with the on-screen calculator, and a Progress tab that finds your weak topics. Free and offline.
Frequently asked
Does JAMB give you a formula sheet in the exam?
No. The UTME provides an on-screen calculator inside the CBT, but no formula sheet or booklet. Every formula you need, from the quadratic formula to the cosine rule, must come out of your own head, which is why you drill them until writing them is automatic.
Which JAMB maths formulas are easiest to get wrong?
The classics: the sum of roots is minus b over a (candidates drop the minus), the nth term of a GP uses the power n minus 1 (not n), the cosine rule subtracts 2bc cos A (candidates add it), and a sum to infinity only exists when the common ratio sits strictly between minus 1 and 1.
How many marks is Mathematics worth in JAMB?
Maths is 40 of the 180 UTME questions. At roughly 2.22 marks per question, that is about 89 of the 400 total marks. There is no negative marking, so answer every question, even the ones you have to guess after eliminating impossible options.
What is the best way to memorise JAMB maths formulas?
Write them, do not read them. Before each practice session, reproduce one topic's formulas on paper from memory, then check against a sheet like this one. Follow up with past questions on that same topic, because recalling a formula under time pressure is a separate skill from recognising it on a page.