Articles, Practice Questions

Short Answer Practice Questions

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  • The​​ ____________ of a given number is that number which when multiplied by itself gives a product equal to the given number.

  • In Hexadecimal System, C is representing ____________

  • Another name for bicimal is ____________

  • A sequence in which each term is formed​​ by multiplying the preceding term by a constant is the ​​ ____________

  • If log 36.74= 1.5652, the underlined number is called ​​ ____________

  • A ​​ ____________ is an equation of the form ax2+bx+c=0, where a, b and c are constant and a≠0.

  • ____________ is the reverse of Differentiation.

  • b2-4ac is called ____________

  •  ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ Error ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ X  ​​ ​​ ​​​​ 100​​ is called ____________      ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​    ​​ Actual Measurement  ​​ ​​ ​​​​ 1

  • In a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares of the other two sides and vice-versa is called ____________

  • A quadratic of the form (x+p)2​​ is called a ____________

  • Consider the formula for the volume of a cone V= 1/3πr2h. In this case, the volume is a function of two variables, r and h. the volume​​ varies directly as the square of radius and as the height. This is called ____________ Variation.

  • An expression in which highest power of the unknown is 1 is called ____________

  • ____________ is a sequence in which the difference between any term is constant.

  • If a>0, the parabola y=ax2+bx+c faces upward and has a ____________ point.

  • A ____________ is a rectangular array of numbers that are enclosed within brackets.

  • The relationship between two variables in which their product remains constant is called ____________

  • A number written in the form A x 10n​​ where 0<A<10 and n an integer is said to be in ____________

  • The transpose of the matrix of cofactors of the matrix A is called____________

  • A matrix in which the number of rows equal number of columns is called ____________ Matrix.

  • The x-coordinate of any given point on the graph is called ____________

  • The ____________ states that if a polynomial function f(x) is divided by x-a, we obtain a quotient Q(x), and the remainder is F(a).

  • A cubic equation has ____________ roots.

  • Expression which contain two terms such as 3a+2c, 16x-4x2​​ are called ____________

  • The ____________ of a number to a certain base is the power to which the base must be raised to obtain the number.

  • The ____________ of two sets A and B,​​ written as AnB, consists of elements which belong to both A and B.

  • A pyramid is a solid with a polygon base which meets to a common point called the ____________

  • A statement which compares two expressions which are not equal is called ____________

  • A number​​ whose square root cannot be expressed as a fraction or a quotient of two integers is called a ____________

  • An algebraic expression that contains only one term such as 3x, 8y2, 15y are called ____________

  • A ____________ is a general name for any group or collection of distinct elements.

  • Half of a diameter is called ____________

  • If 00<θ<900​​ and θ is in the first quadrant, all the trigonometrical ratios are ____________

  • Circles and rectangles which are representations of sets are called ____________

  • If a pyramid, standing on a horizontal flat surface is cut through parallel to the flat surface, the top part is a smaller pyramid and the remaining part is called a ____________

  • Another name for Empty set is ____________

  • The ____________ states that is x-a is a factor of the polynomial function F(x) then F(a)=0

  • A ____________ of a circle is a portion enclosed by two radii and an arc of the circle.

  • ​​ A ____________ illustrates pictorially the relationship between two variables.

  • The values of x that satisfy the​​ quadratic equation are called the ____________ of the equation.

  • Range is classified into two ____________ and ____________​​ 

  • ____________ are formed at the point of intersection of two lines.

  • Each angle in a square or a rectangle is ____________

  • If the standard deviation is S and the mean is​​ , the relative dispersion which is also called the coefficient of dispersion or ____________

  • A ____________ is the straight line, curve or traced by a moving point P.

  • The perimeter of a segment is calculated by ____________

  • The latitude of the equator is ____________

  • ____________ is a triangle in which there are no equal sides.

  • The values of X that satisfy the quadratic equation are called the ____________ of the equation.

  • The average of the sum of the deviations of the​​ observations from the mean where all the deviations are taken as positive is called the ____________

  • A ____________ is an angle that is greater than 1800​​ but less than 3600.

  • ​​ Payments to sales people are called ____________

  • The ____________ is a positional average.

  • ____________ is the distance round the boundary of a closed plane figure.

  • Data which is not organized and presented in a definite order of magnitude is called ____________

  • The points where the straight line cuts the X and Y axes are called ____________

  • When the cumulative frequencies are plotted against corresponding upper class boundaries the line graph obtained is called the ____________

  • The set S of all possible outcomes or equiprobable outcomes of a given experiment is called a ____________

  • The ____________ of a place on the earth’s surface is the angular displacement in degrees north or south of the equator.

  • A ____________ is a figure bounded by three straight lines.

  • The ____________ is determined by observation and not by​​ calculation, considering only the frequency of occurrence of the modal observation.

  • The measure of dispersion which is obtained by computing the root mean square of the deviations from the mean is called ____________

  • The sum of the exterior angles of any polygon is ____________

  • The bisector of an angle of a triangle that divides the opposite side is the ratio of the sides containing the angles. The above is called ____________ theorem.

  • A tabular arrangement of numerical data by classes, together with corresponding classes frequencies is called ____________

  • When the angle of a minor sector is θ0, the angle of corresponding major sector is ____________

  • The sum of the principal and the interest is called ____________

  • If the product of any two numbers​​ equals 1, then the two numbers are called ____________ of each other.

  • When two or more triangles are equal in all respects, they are said to be ____________

  • A four-sided closed figure is called a ____________

  • If​​ a,​​ b​​ and​​ c​​ are three consecutive terms of an​​ A.P, then​​ b​​ is the ____________ of​​ a​​ and​​ c.

  • If the maximum value of sinθ is 1, i.e when θ = 900, the maximum value is ____________

  • If we know the values of α+β ​​ and αβ for a given equation, we can calculate the values of other functions of α and β, provided they are ____________

  • Near 900​​ and 2700​​ tanθ increases very rapidly and the curve approaches the vertical lines through 900​​ and 2700​​ on each side but never actually touches these lines. Such lines are called ____________ to the curve.

  • The sum of first 45 natural numbers are ____________

  • If a, b, c are consecutive terms of a G.P, then b is the ____________ of a and c.

  • N tends to infinity can be denoted as ____________

  • If a>b, then ax < bx and ​​ a/x < ​​ b/x ​​ if x is ____________

  • The centre of gravity of a triangle is called ____________

  • The point where the three medians of a triangle meet is called ____________

  • The notation ꞁxꞁ means the modulus or ____________ of x.

  • Write 10,500,300,000,000,000 in words ____________________________________________________

  • Write MCMIX in ordinary numeral. ________________________________________________

  • The angle subtended at the circumference is twice the angle of the centre subtended by the same arc. YES/NO____________

  • Angles in the same segment of a circle are not always equal. YES/NO ____________

  • A tangent to a circle is perpendicular to the radius drawn from the point of contact. YES/NO ____________

  • The angle between a tangent and a chord drawn from the point of contact is equal to any angle in the alternate segment. YES/NO ____________

  • The two tangents drawn from an external point to a circle are not the same length. YES/NO ____________

  • A quadrilateral is cyclic, if and only if the sum of each pair of opposite angles is right angle. YES/NO ____________

  • If AB and CD are two​​ chords of a circle which cut at a point P (which may be inside or outside a circle) then, PA.PB=PC.PD. YES/NO ____________

  • If P is a point outside a circle and T, A, B ​​ are points on the circle such that PT is a tangent and PAB is a secant then PT2=PA.PB.​​ YES/NO ____________

  • A segment of a circle is the part of the plane bounded by an arc and its chord. YES/NO ____________

  • The angle subtended by a diameter at the circumference is equal to two right angles. YES/NO __________

  • Polynomials = Quotient X Divisor​​ + ​​ ____________

  • The ____________ of conjugate surds is not a surd.

  • If D is negative (D<0 or b2<4ac), then there is no real value for​​ D. The equation has ____________ roots.      

  •  ​​​​ A  ​​ ​​ ​​ ​​ ​​​​ B  ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ C  ​​ ​​ ​​ ​​ ​​​​ From this figure, the points A, B and C​​ are said to be _________

  • The three altitudes intersect in a simple point is called _________

  • The algebraic procedure of calculating the derivatives is called _________

  • The derivation of a function is the slope or _________ of the curve at any given point.

  • A point on a curve at which dy/dx = 0 is called a _________

  • In integration, the function to be integrated is called the _________

  • A solid which has a central axis of symmetry is a solid of _________

  • Acute triangles only have two angles acute. YES/NO ____________

  • Quadrilaterals are also sometimes called tetragons. YES/NO ____________

  • All squares belong to the rhombus family. YES/NO ____________

  • Some parallelograms have lines of symmetry depending on whether they are also squares, rectangles of rhombuses but​​ most do not. YES/NO ____________

  • Convex shapes have at least one reflex angle. YES/NO ____________

  • Irregular shapes are always concave. YES/NO ____________

  • Ellipse is like circle which have 2 lines of symmetry. YES/NO ____________

  • The perimeter of crescents is made from three circular arcs. YES/NO ____________

  • Cuboid is an example of 3D shapes. YES/NO ____________

  • ____________ is a shape with 20 faces, 30 edges and 12 vertices.

  • If two integers a and b have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1, they are said to be ____________

  • The set of numbers denoted by Q is called ____________

  • The name of one term of a sequence which we can use the relation again and again to find the other terms is called ____________

  • If D=b2​​ – 4ac is a perfect square, the roots will be ____________ numbers.

  • The method of differentiating composite functions is called the ____________.

  • Another name for the maximum and minimum points of a curve is called ____________

  • The result of an​​ integration is called ____________

  • ∫F(x)dx is called ____________

  • A and B are ____________ events if either A or B must happen.

  • Another name for central tendency is called ____________

  • This shape  ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ is called ____________

  • ____________ is a mathematical information organized in columns and rows.

  • ____________ is the branch of Mathematics that deals with the collection, organization and interpretation of data.

  • ____________ is a measure of the spread or dispersion of a set of data.

  • ____________ is the degree of asymmetry of a distribution.

  • ____________ is the likelihood that a particular event will occur expressed as a percentage between 0 and 100%.

  • ____________ is the entire set of items from which data can be selected.

  • ____________ is another name for circle graph.

  • ____________ is the probability of an event as determined by comparing the areas (or perimeters, angle measures etc) of the regions of success of an event to the total area of the figure (sample space).

  • A ____________ is defined as coin where the probability of landing heads up or tails up are the same (0.5).

  • The processes in which there are an observable set of outcomes are called ____________

  • ____________ is a subset of the sample space.

  • Let A and B be two​​ events. The probability that A will occur given that B has already occurred is the ____________ of A given B and is denoted by P(A\B).

  • ____________ is the number of ways of picking K unordered outcomes from n possibilities.

  • ____________ Theorem states that, if two angles of a triangle are congruent, the sides opposite these angles are congruent.

  • The ____________ of a number x to the given base b is the power to which b will be raised such that it equals x.

  • If Sn=a+(a+d)+(a+2d)+…………+[a+(n-1)d], this expression is called ____________

  • A mother told her daughter, “I was as old as you are at present at the time of your birth”. If the mother’s present age is 38years. What is the present age of the daughter? ____________

  • If b2-4ac=0, the two roots α and β are real​​ and ____________

  • The function f:x→1/x where x≠0 is called ____________ function

  • In a farewell party, each student paid as much amount in naira as the number of students. If the teacher’s contribution is​​ N200 and the total collection is 1,100. The number of​​ the students in the farewell party is ____________

  • A square matrix A is said to be ____________ if AAT=I

  • A ____________ of the plane is a one-to-one mapping from the set of points in the plane onto itself.

  • The HCF of the two numbers is 68 and their LCM is​​ 2142. If one of the numbers is 204, find the other number. ____________

  • The derivative of cosec x is ____________

  • A ____________ equation is an equation which involves at least one derivative of an unknown function.

  • Gbonjubola secured 40% marks in Geography, 30% in English and 80% in Mathematics. If the maximum marks in these subjects were 60, 50 and 90 respectively. What is her percentage in the aggregate? _______

  • A fraction is undefined if it’s denominator is ____________

  • ____________ is the​​ process whereby the numerator of one side multiplies the denominator of the other side and vice versa and each product is equal to one another.

  • Bolu bought a stereo at 30% discount on its original price. He sold it with a 50% increase on the price he bought. What percentage of profit did he make on the original price? ____________

  • ____________ is the least possible mistake to be obtained in a given result.

  • ____________ is the area of modern Mathematics that considers algebraic structures to be sets with operations defined on them, and extends algebraic concepts usually associated with the real number system to other more general systems, such as groups, rings, fields, modulus and vector spaces.

  • The length of a rectangular field in 20m and its breadth is 10m,​​ if the length is increased by 60% and its breadth is increased by 50%, it’s area will be increased by ____________

  • A three digit angle measured from north in a clockwise direction is called ____________

  • ____________ is an equation used to describe a relationship between two or more variables.

  • The population of a town in the year 2004 was 75,000. If the rate of increase of the population is 20% per annum, what will be its population in 2008? ____________

  • ____________ represents the depth of an object when working with 3D coordinates.

  • A shape is a called a polygonal pyramid when the base is ____________

  • The subset of the co-domain which is a collection of all the images of the elements of the domain is called the ____________

  • After spending 75% of her income​​ and giving 5% of the remainder in charity. Bimbo is left with​​ N460.75. What is her monthly income? ____________​​ 

  • The point where the tangent touches the line is called ____________

  • The process of differentiating implicit function is called ____________

  • 0.45 of 0.4 of a number is 36. What is the number? ____________

  • The adjoint matrix ​​ of a matrix A denoted by Adj A is the transpose of the matrix formed by substituting each element of the matrix A by its ____________

  • What is the decimal 0.005 written out in​​ words? ____________________________________

  • The set of elements or members relevant to a particular application is called the ____________

  • A law enforcement agency receives a report of a drunk driver on the roadways on August 16 at 11:42p.m and another at​​ 2:19a.m on August 17. How much time has elapsed between reports? ____________

  • The ____________ of a set is the number of elements the set contains.

  • Irrational numbers obtained from the square roots of rational numbers are called ____________

  • A geometric progression is a sequence of numbers in which each term other than the first is obtained from the preceding one by the multiplication of a non-zero constant number called the ____________

  • A rectangular tank is 5 meters long and 0.6 metre wide. The water in it is 0.74m deep. If 1cu metre contains 1000 litres of water, find the amount of water in the tank. ____________

  • One of the most important practical application of arithmetic series is in the calculation of compound interest. YES/NO ____________

  • Is x3​​ +​​ 1/x a polynomial? YES/NO ____________

  • Three cubes of sides 3, 4 and 5cm respectively are melted to form a new cube. Find the side of the new cube. ____________

  • A ____________ is a rectangular array of numbers enclosed within brackets.

  • ____________ is the process of transferring one quantity from one side of an equation to the other side whereby the quantity involved changes its sign to the opposite sign.

  • During the week of cloth sales, all cloth was reduced in the same ratio. If a cloth​​ costing​​ N840 was offered at​​ N640, what would be the sale price of a cloth costing​​ N1050 originally? ____________

  • When a quadratic has the form ax2=c it is called ____________

  • When two triangles have two of their sides and an included angle corresponding equal, the congruence is called ____________

  • If the population of yeast cells grows from 30 to 1920 in a period of 6 hours, what is the rate of growth? ____________

  • ____________ is the number which corresponds to a given logarithm.

  • ____________ of an angle​​ is trigonometric function of the ratio of the adjacent and hypotenuse sides of any angle in right angled triangle.

  • Write 5 million two hundred and six thousand eight in numerals. ____________________________________

  • ____________ of a triangle is a line perpendicular to the base.

  • The formula for the last term T of a Geometric Progression is ____________

  • A salesman buys 600 mangoes daily and sells them at 80 kobo per dozen. How much money does he earn in half a year? ____________

  • ____________ is a number expressed as an ordered pair comprising of real number and an imaginary number, written in the form a+bi, where a and b are real numbers, and i is the imaginary unit.

  • ____________ property is whereby summing two numbers and then multiplying by another number yields the same value as multiplying both values by the other value and then adding them together.

  • A typist uses a sheet of paper of 20cm x 28cm for typing. He leaves a margin of 4cm on either side and 5cm on top and bottom. What fractional part of the paper is used for typing? ____________

  • The mathematical operation where a number (the base) is multiplied by itself a specified number of times (the exponent) is called ____________

  • ____________ is a type of conic section curve, any point of which is equally distant from a fixed point and a fixed straight line.

  • 5 men can complete a job in 4 days. What fraction of the job can a man do in one day? ____________

  • The ____________ of set A and B is the set which consists of elements that are either in A or B or both.

  • If the determinant of a square matrix is equal to zero, the matrix is called ____________

  • 6¾ dozen biros cost​​ N82, what will be the cost of 3⅜ dozens of these biros? ____________

  • Write the predecessor of 800000 ____________

  • Write the successor of 999999 ____________

  • If Y​​ ​​ X and if in addition there is at least one element of X which is not in Y, then Y is a ____________ of X.

  • The difference between the amount and the original principal is called the ____________

  • When a rectangle is inserted in a circle and the four vertices touching the circle, it is called ____________

  • The ____________ of a figure is the side that is perpendicular to the height.

  • What number can replace the asterisk mark in the number 59*3 such that the number is divisible by 9? ________

  • ____________ is the portion of a circle bounded by 2 radii.

  • ____________ is the product of all consecutive integers up to a given number (used to give the number of permutations of a set of objects).

  • A married couple has eight sons and six​​ daughters. The sons gave birth to four children each while the daughters gave birth to 5 children each. How many members are there in the family? ____________

  • ____________ is a subsidiary collection of objects that all belong to, or is contained in, an original given set.

  • A shape which has no lines of symmetry is called ____________

  • In a University hall, there are 1,681 chairs arranged in such a way that row contains as many chairs as the number of chairs in a row. What is the number of chairs in each row?​​ ____________

  • ____________ is a method of solving probability questions by listing all the outcomes of an event and the probabilities are calculated by multiplying down the branches.

  • The distance between the apex and the meeting points of the diagonals of a​​ base is called ____________

  • What is the product of the largest and smallest four digit numbers formed by using the digits 5, 6, 1 and 2? ____________

  • The set of all ​​ the subsets of a set is called ____________

  • ____________ is about arrangement of​​ things about a circular object.

  • There is a piece of cloth 680cm long and 160cm wide. Square handkerchiefs of maximum size are to be made from this cloth so that there is no wastage of the cloth. Find the length of each handkerchief? ____________

  • The arrangement of objects in which order is not taken into account is called ____________

  • The straight line, perpendicular to the tangent at the point of contact of the tangent to the curve is called the ____________ to the curve.

  • An even number when added to another prime number will result in prime and odd numbers only? YES/NO _____

  • The angle subtended at the centre of the great or small circle by the minor arc joining two places in the great or small circle is called ____________

  • The distance of the arc of a great circle subtending an angle of 1 minute at the centre of the Earth is called ________________________

  • Four bells begin tolling at the same time and continue to do so at intervals of 22, 26, 28 and 30 seconds respectively. The bells will toll together after every ____________ seconds.

  • Longitude 00​​ is called ____________

  • If the three angles of one triangle are respectively equal to the three angles of another, the two triangles are ____________

  • Every set is a subset of itself and also a subset of the ____________

  • Akin ranked 11th​​ from the top and 40th​​ from the bottom in a class. How many students are there in the class?

  • If two finite sets A and B are disjoint, then n(AᴜB)= ____________

  • Discuss the following with at least 100 words: Inscribed and E-scribed Circles, Longitude and Latitude, Cosine Rule and Sine Rule.

  • Joke is getting married 2 days later, at an outdoor ceremony in the desert. In recent years, it has rained only 10days each year. Unfortunately, the meteorologist has predicted rain for 2days time. When it actually rains, the meteorologist correctly forecasts rain 80 of the time. When it doesn’t rain, he incorrectly forecasts rain 20 of the time. What is the probability that it will rain on the day of Joke’s wedding? ____________

  • If the mean of the numbers u, w, x, y, z is a, find the mean of u+b, w+2b, x-b, y-2b, z.

  • The mode of the positive integers 4, 6, 9, 11, 12, 19, a, b is 9 and their mean is b. Find the values of a and b.

  • Calculate the centre and radius of the circle 4x2​​ + 4(y- 6/4)2=4

  • Make n the subject of the relation Sn​​ =​​ n/2[2a+(n-1)d]

  • A lady invested a total of​​ N100,000 in two companies which paid dividends of 14% and 10% respectively. If she received a total of​​ N13,200, calculate how much did she invest at both rates?

  • Find the values of y​​ in (30x3-1) +​​  ​​ ​​ ​​ ​​​​ 1  ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​  ​​ ​​ ​​ ​​ ​​​​ =  ​​​​ 10

1 +  ​​ ​​​​  ​​​​ 1​​  ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ y

 ​​ ​​ ​​ ​​​​ 3-1​​ +​​ 1/y

  • X and Y are points on the parallel of latitude 700N, their longitudes being 1370W and 430E respectively. Calculate the following:

    • The distance measured apart along the​​ parallel of latitude

    • The distance measured apart along the great circle.

  • w ​​ x

    y  ​​​​ z

    Let U be a square matrix of order n. Define a Matrix Ui​​ by means of the formula: Ui​​ =​​ iU+(1-i)UT

​​ 

​​ 

Compute Ui​​ explicitly for​​ i​​ = ​​ ½, 1 and 2 if U =​​  

  • The expression ax2​​ + bx + c is a ____________ equation.

  • Peter Venn was the originator of Venn Diagrams. YES/NO ____________

 

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