JAMB MATHEMATICS PAST QUESTIONS (UTME)

In how many ways can the letters LEADER be arranged?

How many times, correct to the nearest whole number, will a man run round a circular track of diameter 100m to cover a distance of 1000m?

Find the equation of the locus of a point p (x, y) such that pv = pw, where v= (1, 1) and w = (3, 5)

An arc of the length 16$\pi$cm subtends an angle of 80^o at the centre of the circle. Find the radius of the circle.

In a class of 40 students, 32 offer Mathematics, 24 offer Physics and 4 offer neither Mathematics nor Physics. How many offer both Mathematics and Physics?

The first and last term of a linear sequence (AP) are 6 and 10 respectively. If the sum of the sequence is 40. Find the number of terms

A man bought a car for N800 and sold it for N520. Find his loss per cent

The extension of a stretched string is directly proportional to its tension. If the extension produced by a tension of 8 Newton’s is 2cm, find the extension produced by a tension of 12 newton’s.

Find the x and y intercepts of the graph of 3x - z $\le$ 9

How many sides has a regular polygon whose interior angles are 120°each

A number of pencils were shared out among Bisi, Sola and Tunde in the ratio of 2:3:5 respectively. If Bisi got 5, how many were shared out?

If the simple interest on a sum of money invested at 3% per annum for 2 and half  years is N123, find the principal.

From a point R, 300m north of P, a man walks eastward to a place Q which is 600m from P. Find the bearing of P from Q, correct to the nearest degree

The probabilities that John and James pass an examination are $\frac{\mathrm{3/}}{4}$and $\frac{\mathrm{5/}}{}$ respectively. Find the probability of both boys failing the examination.

If Q is a factor of 18 and T is prime numbers between 2 and 18. What is Q$\cap$T?

Calculate the range of 20, -6, 25, 30, 21, 28, 32, 33, 34, 5, 3, 2, and 1.

The amount A to which a principal P amounts at r% compound interest for n years is given by the formula A = P(1 + (r ÷ 100))n. Find A, if P = 126, r = 4 and n = 2

Find the range of the following set of numbers 0.4, −0.4, 0.3, 0.47, −0.53, 0.2 and −0.2

A car dealer bought a second-hand car for of 250,000 and spent N 70,000 refurbishing it. He then sold the car for N400,000. What is the percentage gain?

Find the principal which amounts to ₦ 5,500 at a simple interest in 5 years at 2% per annum

If x₁₀ = 23₅. Find x

The mean of 2-t, 4+t, 3-2t, 2+t and t-1 is

An arc of a circle of radius 14cm subtends angle 300° at the centre. Find the perimeter of the sector formed by the arc (take π = $\frac{\mathrm{22/}}{7}$)

If duty is levied at 25%, find the duty to be added to a bill of N80.

Given that Z = {1,2,4,5} what is the power of set Z?

A man sells his new brand car for N420,000 at a gain of 15%. What did it cost him?

If √ (2x + 2) − √x =1 ,find x.

Divide the L.C.M of 48, 64 and 80 by their H.C.F

Calculate the perimeter of a sector of a circle of raduis 12cm and angle 60^o.

From the diagram above, find the value of < OTQ

A car uses one litre of petrol for every 14km. If one litre of petrol cost N63.00, how far can the car go with N900.00 worth of petrol?

Given that A = {1, 5, 7}

B = {3, 9, 12, 15}

C = {2, 4, 6, 8}

Find (A ∪ B) ∪ C

The sum of the interior angles of a polygon is a given as 1080^o. Find the number of the sides of the polygon.

Simplify √30 × √40

If line p = 5x + 3 is parallel to line p = wx + 5. Find the value of w.

The pie chart shows the monthly expenditure of a public servant. The monthly expenditure on housing is twice that of school fees. How much does the worker spend on housing if his monthly income is N7200?

The base in which the operation was performed was

Simplify 4 √[(390695T− 8)½)]

Find the simple interest on N325 in 5years at 3% per annum.

If x + y = 90 simplify (sinx + siny)²−2sinx siny

In the figure, find x

From the diagram above, Find the value of < ROP

In a regular polygon, each interior angle doubles its corresponding exterior angle. Find the number of sides of the polygon

Given that A = {3, 4, 1, 10, ⅓ }

B = {4, 3 ⅓, ⅓, 7}.

Find A∩B

Solve x² − 2x − 3 = 0

From the cyclic quadrilateral above, find < TVS

The table shown gives the marks scored by a group of student in a test. Use the table to answer the question given.

What is the median mark?

An arc subtends an angle of 30^o at the centre of a circle radius 12cm. Calculate the length of the arc.

The probability of an outcome A is 1/6 . The probability of the B outcome is 1/4 . If the probability of A or B or both is 1/12 . What is the probability of both outcomes A and B?

Given the quadrilateral RSTO inscribed in the circle with O as centre. Find the size angle x and given RST = 60^o

What is the loci of a distance 4cm from a given point P?

Calculate the total surface area of a cupboard which measures 12cm by 10cm by 8cm

The angle of elevation of the top of a tree from a point on the ground 60m away from the foot of the tree is 78°. Find the height of the tree correct to the nearest whole number.

From the diagram above, find the required roots/region of x

If the mean of 4, y, 8 and 10 is 7. Find Y?

A man with an annual salary of N2000, has allowances of N600. If Income Tax is 5%. How much tax does he pay each year?

If three staff of Myschool Limited agreed to share their salary arrears in the ration of their ages, which are 18 years, 20 years, 22 years respectively. If the sum of the money collected is N120,000.00K, How much does the second staff received?

Find the range of values of t which satisfies the inequality.

2t − 1 $\le$ 3 and 2− t $\ge$ 5

Simplify (3√64a³)${}^{}$

In how many ways can the word MACICITA be arranged?