2010
1. Find the domain of
Options:
A.
B.
C.
D.
2. Find the value of leaving your answer in surd form
Options:
A.
B.
C.
D.
3. If , where
is a constant. Find
Options:
A.
B.
C.
D.
4. If , find the value of
Options:
A.
B.
C.
D.
5. Simplify
Options:
A.
B.
C.
D.
6. The coefficient of the 7th term in the binomial expansion of in ascending powers of
Options:
A.
B.
C.
D.
7. The roots of a quadratic equation are and
. Find its equation
Options:
A.
B.
C.
D.
8. If is a factor of
, find the value of constant
Options:
A.
B.
C.
D.
9. If ,
, determine the two possible values of
Options:
A.
B.
C.
D.
10. For what values of is
undefined
Options:
A. or
B. or
C. or
D. or
11. Calculate the length of the line joining points and
, correct to one decimal place
Options:
A.
B.
C.
D.
12. If , find
Options:
A.
B.
C.
D.
13. Calculate the acute angle between the lines and
, correct to one decimal place
Options:
A.
B.
C.
D.
14. Evaluate
Options:
A.
B.
C.
D.
15. If , find the value of
Options:
A.
B.
C.
D.
16. Given is the domain of
, find the range of
Options:
A.
B.
C.
D.
17. The third term of a geometric progression (G.P) is and the sixth term is
. Find the common ratio
Options:
A.
B.
C.
D.
18. Find the axis of symmetry of the curve
Options:
A.
B.
C.
D.
19. Find the equation of the tangent to the curve at point
Options:
A.
B.
C.
D.
20. The mean age of 15 pupils in a class is years. One new pupil joined the class and the mean changed to
years. Calculate the age of the new pupil
Options:
A. years
B. years
C. years
D. years
21. The distance metres of a particle from a fixed point at time
seconds is given by
, where
is a constant. If the acceleration at
secs is
, find the value of
Options:
A.
B.
C.
D.
22. The probabilities that a husband and wife will be alive in 15 years time are and
respectively. Find the probability that only one of them will be alive at that time
Options:
A.
B.
C.
D.
23. In a class of 50 pupils, 35 like Science and 30 like History. What is the probability of selecting a pupil who likes both Science and History?
Options:
A.
B.
C.
D.
24. are points in a plane such that
,
,
and
. Find
Options:
A.
B.
C.
D.
25. Find the least value of for which
,
Options:
A.
B.
C.
D.
26. If and
where
is the origin and
is the midpoint of
, find
Options:
A.
B.
C.
D.
27. Find the direction cosines of the vector
Options:
A.
B.
C.
D.
28. Yomi was asked to label four seats . What is the probability he labelled them in alphabetical order?
Options:
A.
B.
C.
D.
29. Two forces and
act on a body of mass
. Find the magnitude of the acceleration of the body in
Options:
A.
B.
C.
D.
30. Two particles are fired together along a smooth horizontal surface with velocities and
. If they move at
to each other, find the distance between them in
seconds
Options:
A.
B.
C.
D.
31. Two forces and
act on a particle. Find the magnitude and direction of
Options:
A.
B.
C.
D.
32. A stone is thrown vertically upwards and its height at any time seconds is
. Find the maximum height reached
Options:
A.
B.
C.
D.
33. Given that and
when
, find the equation for
Options:
A.
B.
C.
D.
34. If , evaluate
Options:
A.
B.
C.
D.
35. A company took delivery of 12 vehicles made up of 7 buses and 5 saloon cars for two departments. If the Personnel department is to have at least 3 saloon cars, in how many ways can these vehicles be distributed equally between the departments?
Options:
A.
B.
C.
D.
36. A bicycle wheel of diameter covered a distance of
in
. How many radians per second did it turn?
Options:
A.
B.
C.
D.
37. The initial velocity of an object is . If the acceleration of the object is
and it moved for
seconds, find the final velocity
Options:
A.
B.
C.
D.
38. Find the maximum value of
Options:
A.
B.
C.
D.
39. Simplify
Options:
A.
B.
C.
D.
40. What is the angle between and
Options:
A.
B.
C.
D.
2011
1. A binary operation * is defined on the set of real numbers , by
. Find the identity element under the operation *.
A.
B.
C.
D.
2. Express in radians, leaving your answer in terms of
.
A.
B.
C.
D.
3. If , find
.
A.
B.
C.
D.
4. Evaluate
A.
B.
C.
D.
5. Find the remainder when is divided by
.
A.
B.
C.
D.
6. A function is defined by . Find
.
A.
B.
C.
D.
7. Simplify
A.
B.
C.
D.
8. Solve
A.
B.
C.
D.
9. The equation of a circle is . Find its radius
A.
B.
C.
D.
10. , where
and
are constants. If
and
, find
.
A.
B.
C.
D.
11. The sum and product of the roots of a quadratic equation are and
respectively. Find its equation.
A.
B.
C.
D.
12. is defined on the set of real numbers,
. Find the gradient of
at
.
A.
B.
C.
D.
13. Find
A.
B.
C.
D.
14. If , find
.
A.
B.
C.
D.
15. A line is perpendicular to and passes through the point
. Find its equation.
A.
B.
C.
D.
16. Solve
A.
B.
C.
D.
17. The inverse of a function is given by .
A.
B.
C.
D.
18. If , find
.
A.
B.
C.
D.
19. The fourth term of a geometric sequence is and the sixth term is
. Find the common ratio.
A.
B.
C.
D.
20. What percentage increase in the radius of a sphere will cause its volume to increase by ?
A.
B.
C.
D.
21. Evaluate , leaving your answer in surd form.
A.
B.
C.
D.
22. Find the equation of a circle with centre and radius
.
A.
B.
C.
D.
23. Determine the coefficient of in the expansion of
.
A.
B.
C.
D.
24. The mean of and
is
. Find the median.
A.
B.
C.
D.
25. The probability that Kofi and Ama hit a target in a shooting competition are and
respectively. What is the probability that only one of them hit the target?
A.
B.
C.
D.
26. In how many ways can prefects be chosen out of
prefects?
A.
B.
C.
D.
27. Find the standard deviation of the numbers and
.
A.
B.
C.
D.
28. The table shows the distribution of marks of students in a class. Find the upper class boundary of the modal class.
Marks | No of students
5-7 | 4
8-10 | 7
11-13 | 26
14-16 | 41
17-19 | 14
20-22 | 8
A.
B.
C.
D.
29. If , find the value of
?
A.
B.
C.
D.
30. Four doctors and two nurses are to sit round a circular table. In how many ways can this be done if the nurses are to sit together?
A.
B.
C.
D.
31. A basket contains red and
white identical balls. A ball is drawn from the basket at random. Calculate the probability that it is either white or red.
A.
B.
C.
D.
32. A force of acting on a body of mass
initially at rest causes it to move a distance of
along a straight line for
secs. Find the value of
.
A.
B.
C.
D.
33. Two forces and
act on an object at an angle of
to each other. Find the magnitude of the resultant.
A.
B.
C.
D.
34. A body of mass changes its speed from
to
in
seconds by the action of an applied force
. Find the value of
.
A.
B.
C.
D.
35. A particle starts from rest and moves in a straight line such that its velocity, , at time
seconds is given by
. Calculate the distance covered in the first
seconds.
A.
B.
C.
D.
36. A particle starts from rest and moves in a straight line such that its velocity, , at time
seconds is given by
. Determine the acceleration when
secs.
A.
B.
C.
D.
37. Given that and
, which of the following statements is true?
A. and
are collinear
B. and
are perpendicular
C. The magnitude of is
units
D. The projection of on
is
units.
38. The functions and
are defined on the set,
, of real numbers by
and
. Find
.
A.
B.
C.
D.
39. Find the unit vector in the direction of .
A.
B.
C.
D.
40. Find, correct to two decimal places, the acute angle between and
.
A.
B.
C.
D.
2012
WAEC 2012 Mathematical Questions
1. Which of the following sets is equivalent to ?
A.
B.
C.
D.
2. Simplify:
A.
B.
C.
D.
3. Solve the inequality
A.
B. and
C. or
D.
4. Given as the first four terms of an exponential sequence (G.P), find the 8th term in its simplest form.
A.
B.
C.
D.
5. Given and
, find
.
A.
B.
C.
D.
6. Evaluate
A.
B.
C.
D.
7. For triangle QRS, and
, find
A.
B.
C.
D.
8. If is a factor of the polynomial
, find the value of
A.
B.
C.
D.
9. A polynomial is defined by , find
A.
B.
C.
D.
10. The equation of a circle is . Find its radius
A.
B.
C.
D.
11. If the midpoint of the line joining and
is
, find the value of
A.
B.
C.
D.
12. Evaluate
A.
B.
C.
D.
13. If , find the values of
at the turning point
A.
B.
C.
D.
14. Given and
, find
A.
B.
C.
D.
15. A binary operation, , is defined on the set of real numbers by
. Find the identity element
A.
B.
C.
D.
16. The marks obtained by 10 students in a test are: 3, 7, 6, 2, 8, 5, 9, 1, 4 and 10. Find the mean mark
A.
B.
C.
D.
17. For the same test scores, find the variance
A.
B.
C.
D.
18. If denotes the correlation coefficient between two variables, which of the following is always true?
A.
B.
C.
D.
19. A stone is dropped from a height of 45m. Find the time it takes to hit the ground [g = ]
A. seconds
B. seconds
C. seconds
D. seconds
20. Differentiate with respect to
A.
B.
C.
D.
21. Two forces 10N and 6N act in the directions and
respectively. Find the x-component of their resultant
A.
B.
C.
D.
22. Find the unit vector in the direction of the vector
A.
B.
C.
D.
23. In computing the mean of 8 numbers, a boy mistakenly used 17 instead of 25 as one of the numbers and obtained 20 as the mean. Find the correct mean
A.
B.
C.
D.
24. Given and
, find the value of
A.
B.
C.
D.
25. Which of the following is NOT a measure of central tendency?
A. Mean
B. Variance
C. Median
D. Mode
26. A fair die is tossed twice. Find the probability of obtaining a 3 and a 5
A.
B.
C.
D.
27. If , find the value of
A.
B.
C.
D.
28. Find the values of at the point of intersection of the curve
and the line
A.
B.
C.
D.
29. Find the constant term in the binomial expansion of
A.
B.
C.
D.
30. A straight line makes intercepts of and
on the x- and y-axes respectively. Find the equation of the line
A.
B.
C.
D.
31. Find the number of different arrangements of the word IKOTITINA
A.
B.
C.
D.
32. Find the acute angle between the lines and
A.
B.
C.
D.
33. A box contains 4 red and 3 blue identical balls. If two are picked at random, one after the other without replacement, find the probability that one is red and the other is blue
A.
B.
C.
D.
34. The distance in metres covered by a particle in
seconds is
. Find its acceleration
A.
B.
C.
D.
35. The angle of a sector of a circle is radians. If the radius of the circle is
cm, find the length of the arc of the sector
A. cm
B. cm
C. cm
D. cm
36. From the diagram, which of the following represents the vector in component form?
A.
B.
C.
D.
37. From the diagram, is
A.
B.
C.
D.
38. is
A. one-to-one
B. onto
C. a relation
D. a series
39. The diagram is a velocity-time graph of a moving object. Calculate the distance travelled when the acceleration is zero
A. m
B. m
C. m
D. m
40. Simplify
A.
B.
C.
D.
2013
1. A binary operation * is defined on the set of real numbers, , by
. If the identity element under the operation * is 0, find the inverse of
.
A.
B.
C.
D.
2. Solve:
A.
B.
C.
D.
3. Given that , solve for
.
A.
B.
C.
D.
4. Express in terms of
.
A.
B.
C.
D.
5. If and
, find
.
A.
B.
C.
D.
6. Find the third term in the expansion of in ascending powers of
.
A.
B.
C.
D.
7. If , find the possible values of
.
A. and
B. and
C. and
D. and
8. If and
are the roots of the equation
, evaluate
.
A.
B.
C.
D.
9. Given that and
, factorize
.
A.
B.
C.
D.
10. Find the equation of the line that is perpendicular to and bisects the line joining the points
and
.
A.
B.
C.
D.
11. Differentiate
A.
B.
C.
D.
12. The fourth term of an exponential sequence is 192 and its ninth term is 6. Find the common ratio of the sequence.
A.
B.
C.
D.
13. Find the range of values of for which
is less than 1
A.
B.
C.
D.
14. Given that , find
A.
B.
C.
D.
15. Given that and
, find the value of
A. -4
B. -3
C. -1
D. 2
16. An object is thrown vertically upwards from the top of a cliff with a velocity of . Find the time, in seconds, when it is 20 metres above the cliff.
A. 0 and 1
B. 0 and 4
C. 0 and 5
D. 1 and 4
17. Evaluate
A.
B.
C.
D.
18. Find the coordinates of the point which divides the line joining and
internally in the ratio
A.
B.
C.
D.
19. The angle subtended by an arc of a circle at the centre is radians. If the radius of the circle is
cm, calculate the perimeter of the major arc
A.
B.
C.
D.
20. The function . Find
A. 28
B. 26
C. -26
D. -28
21. A committee consists of 5 boys (Kofi, John, Ojo, Ozo and James) and 3 girls (Rose, Ugo and Ama). In how many ways can a sub-committee consisting of 3 boys and 2 girls be chosen, if Ozo must be on the sub-committee?
A. 35
B. 30
C. 18
D. 12
22. Forces and
act on a body as shown in the diagram. Find, correct to the nearest whole number, the horizontal component of the resultant force
A.
B.
C.
D.
23. The sales of five salesgirls on a certain day are as follows: and
. Calculate the standard deviation if the mean sale is
A.
B.
C.
D.
24. A circular ink blot on a piece of paper increases its area at the rate . Find the rate of the radius of the blot when the radius is
.
A.
B.
C.
D.
25. Express in partial fractions
A.
B.
C.
D.
26. Two bodies of masses and
moving with velocities
and
respectively in opposite directions collide. If they move together after collision with velocity
in the direction of the
mass, find the value of
A.
B.
C.
D.
27. The equation of a circle is . Find its radius
A. 5
B.
C.
D.
28. A particle is acted upon by two forces and
inclined at an angle of
to each other. Find the magnitude of the resultant force
A.
B.
C.
D.
29. If and
, find
A. -77
B. -71
C. -53
D. -41
30. If ,
, find
A.
B.
C.
D.
31. Find the upper quartile of the following scores: and
A. 45
B. 41
C. 33
D. 21
32. Given that ,
,
and
, find the value of
A. -5
B. -2
C. 2
D. 5
33. Two out of ten tickets on sale for a raffle draw are winning tickets. If a guest bought two tickets, what is the probability that both tickets are winning tickets?
A.
B.
C.
D.
34. and
are the points
and
respectively. Find the unit vector along
A.
B.
C.
D.
35. If , find
A. 3
B. 2
C.
D. -3
36. Calculate the mean deviation of
A. 2
B. 3
C. 4
D. 5
37. If and
, find
A.
B.
C. 15
D.
38. Find the equation of the straight line that passes through and perpendicular to the line
A.
B.
C.
D.
39. If , find the value of
A. 8
B. 7
C. 6
D. 5
40. A body is kept at rest by three forces ,
and
. Find
A.
B.
C.
D.
2014
WAEC 2014 Mathematics Questions
1. If , find the value of y.
A. 4
B. 2
C. -4
D. -5
2. Simplify:
A.
B.
C.
D.
3. Given that and
are perpendicular, find the value of b.
A. 4
B. 3
C.
D.
4. Given that ,
and
, find b, where b > 0.
A. 8
B. 6
C. 5
D. 4
5. If and
, find the value of k.
A. -67
B. -61
C. 61
D. 67
6. If and
, find the value of (x – y).
A.
B.
C. 1
D.
7. Simplify
A.
B.
C.
D.
8. Using the binomial expansion , find, correct to 3 dp, the value of
.
A. 64.245
B. 61.255
C. 60.255
D. 60.245
9. If and
are factors of
, find the third factor.
A.
B.
C.
D.
10. If 2, (k+1), 8, … form an exponential sequence (GP), find the values of k.
A. -3 and 5
B. 5 and -5
C. 3 and -3
D. -5 and 3
11. A box contains 5 red and k blue balls. A ball is selected at random from the box. If the probability of selecting a blue ball is , find the value of k.
A. 5
B. 6
C. 8
D. 10
12. If , find the value of (P + Q).
A. -2
B. -1
C. 0
D. 1
13. Find the derivative of with respect to x.
A.
B.
C.
D.
14. If , find
, the inverse of T.
A.
B.
C.
D.
15. A function is defined by . Find
, the inverse of h.
A.
B.
C.
D.
16. A function is defined by . Find
.
A. 6
B.
C.
D.
17. The radius of a sphere is increasing at a rate . Find the rate of increase in the surface area, when the radius is 2cm.
A.
B.
C.
D.
18. Age in years
10 – 14: 6
15 – 19: 8
20 – 24: 14
25 – 29: 10
30 – 34: 12
What is the class mark of the median class?
A. 17
B. 22
C. 27
D. 32
19. For the same age distribution as previous question, in which group is the upper quartile?
A. 15 – 19
B. 20 – 24
C. 25 – 29
D. 30 – 34
20. Find the mean of the distribution for the same age data.
A. 23.4
B. 23.6
C. 24.3
D. 24.6
21. If has equal roots, find the values of P.
A. -1 and
B. 1 and
C. -1 and
D. 1 and
22. Integrate with respect to x.
A.
B.
C.
D.
23. Given that and
, find
.
A.
B.
C.
D.
24. Find the angle between and
.
A. 180°
B. 90°
C. 45°
D. 0°
25. Find the coefficient of in the binomial expansion of
in ascending powers of x.
A. 432
B. 194
C. 144
D. 108
26. If a fair coin is tossed four times, what is the probability of obtaining at least one head?
A.
B.
C.
D.
27. Forces 90N and 120N act in the directions 120° and 240° respectively. Find the resultant of these forces.
A.
B.
C.
D.
28. The deviations from the mean of a set of numbers are and
, where k is a constant. Find the value of k.
A. 3
B. 2
C. -2
D. -3
29. Find the equation of a circle with centre (2, -3) and radius 2 units.
A.
B.
C.
D.
30. The first term of a linear sequence is 9 and the common difference is 7. If the nth term is 380, find the value of n.
A. 45
B. 54
C. 56
D. 65
31. For what values of m is a perfect square?
A.
B.
C.
D.
32. A particle accelerates at and travels a distance of 250m in 6 seconds. Find the initial velocity of the particle.
A. 5.7
B. 6.0
C. 60.0
D. 77.5
33. In how many ways can 9 people be seated on a bench if only 3 places are available?
A. 1200
B. 504
C. 320
D. 204
34. Find the variance of 1, 2, 0, -3, 5, -2, 4.
A.
B.
C.
D.
35. If the points (-1, t-1), (t, t-3) and (t-6, 3) lie on the same straight line, find the values of t.
A. t = -2 and 3
B. t = 2 and -3
C. t = 2 and 3
D. t = -2 and -3
36. A ball is thrown vertically upwards with a velocity of . Calculate the maximum height reached. [g =
]
A. 15.25m
B. 13.25m
C. 11.25m
D. 10.25m
37. Find the distance between the points (2, 5) and (5, 9).
A. 4 units
B. 5 units
C. 12 units
D. 14 units
38. Find .
A.
B. 0
C.
D. -7
39. Evaluate .
A.
B.
C.
D.
40. Express (14N, 240°) as a column vector.
A.
B.
C.
D.
2015
1. Simplify
A.
B.
C.
D.
2. Solve:
A.
B.
C.
D.
3. Solve:
A.
B.
C.
D.
4. If , find the value of
A.
B.
C.
D.
5. Find the 3rd term of in descending order of
A.
B.
C.