JAMB MATHEMATICS PAST QUESTIONS (UTME)

Find the mean of 10, 8, 5, 11, 12, 9, 6, 3, 15, and 23.

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

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

In the diagram MN, PQ and RS are parallel lines. What is the value of the angle marked X?

Simplify √30 × √40

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.

A man's initial salary is N540.00 a month and increases after each period of six months by N36.00 a month. Find his salary in the eight month of the third year.

The pie chart shows the allocation of money to each sector in a farm. The total amount allocated to the farm is ₦ 80 000. Find the amount allocated to fertilizer

Find the equation of the line through (5,7) parallel to the line 7x + 5y = 12

Given T = { even numbers from 1 to 12 }
N = {common factors of 6, 8 and 12}
Find T ∩ N

The sum of two numbers is 5; their product is 14. Find the numbers.

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

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

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

If A = (−3,5) and B = (4,−1) find the co-ordinate of the mid point

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

Factorize completely x² + 12xy + y + 3x + 3y - 18

From the cyclic quadrilateral above, find < TVS

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

Two sisters, Taiwo and Kehinde, own a store. The ratio of Taiwo's share to Kehinde's is 11:9. Later Kehinde sells 2/3 of her share to Taiwo for N720.00. Find the value of the store

y is inversely proportional to x and y and 6 when x = 7. Find the constant of the variation

A room is 12m long, 9m wide and 8m high. Find the cosine of the angle which a diagonal of the room makes with the floor of the room

Given that A = {1, 5, 7}

B = {3, 9, 12, 15}

C = {2, 4, 6, 8}

Find (A ∪ B) ∪ C

In how many ways can the letters LEADER be arranged?

If √ (2x + 2) − √x =1 ,find x.

The base in which the operation was performed was

A machine valued at N20,000 depreciates by 10% every year. What will be the value of the machine at the end of two years?

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

A cylindrical tank has a capacity of 3080m³. What is the depth of the tank if the diameter of its base is 14m? Take pi = 22/7.

The area of a circle of radius 4cm is equal to (Take π = 3.142 )

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 = $\frac{\mathrm{22/}}{7}$)

The volume of a cone (s) of height 6cm and base radius 5cm is

A man stands on a tree 150cm high and sees a boat at an angle of depression of 74°. Find the distance of the boat from the base of the tree.

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

In the figure, find x

If x₁₀ = 23₅. Find x

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

What is the place value of 9 in the number 3.0492?

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

Convert 0.04945 to two significant figures

The venn diagram shows a class of 50 students with the games they play. How many students play only two games

If log₅20 = x, find x

Simplify 2.04 × 3.7 (Leave your answer in 2 decimal place)

Calculate the value of x and y if (27^x ÷ 81^x+2y = 9 ,x + 4y = 0

X and Y are two sets such that nX = 15, nY = 12 and n{∩ Y} = 7. Find ∩{X ∪ Y}

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

Simplify (3√64a³)${}^{}$

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

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

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 curved surface area of a cylinder 5cm high is 110cm². Find the radius of its base
π = 22/7

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

In how many ways can the word MATHEMATICS be arranged?

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

Find the sum of the range and the mode of the set of numbers 10, 9, 10, 9, 8, 7, 7, 10, 8, 10, 8, 4, 6, 9, 10, 9, 7, 10, 6, 5

Simplify (0.09)² and give your answer correct to 4 significant figures

Find the gradient of the line joining the points (3, 2) and (1, 4)

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?

Rationalize 5 ÷ (2 − √3)

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