# NDA MATHEMATICS 2014 PAST QUESTIONS AND ANSWERS

1.

**ANSWER: --**

2. Find the value of x for
which the function y= x^{3}- x has a minimum value.

A. ^{-}^{√}^{3}/_{3}

B. ^{-}^{√}^{3}/_{3}

C. ^{-}^{√}^{3}/_{3}

D. √3

**ANSWER: C**

3.

**ANSWER: --**

4. If the maximum value of y= 1 + hx - 3x^{2}
is 13. Find h.

A. 13

B. 12

C. 11

D. 10

**ANSWER: B**

5. How many two-digit numbers can be formed from the
digits 0, 1, 2, 3. If a digit can be repeated and no number may begin with 0?

A. 4

B. 12

C. 16

D. 20

**ANSWER: B**

6. The sum of four numbers is 1,214^{5}. What
is the average expressed in base five?

A. 114

B. 141

C. 401

D. 411

**ANSWER: B**

7. Given:

U= {Even numbers between 0 and 30}

P={Multiples of 6 between 0 and 30}

Q={Multiples of 4 between 0 and 30}

Find (PꓴQ)’

A. {2,10,14,22,26}

B. {0,10,14,22,26}

C. {2,4,14,18,26}

D. {0,2,6,22,26}

**ANSWER: --**

8. x varies directly as the product of u and y and
inversely as their sum. If x =3 when u =3 and v= 1, what is the value of x if u
= 3 and v = 3?

A. 3

B. 4

C. 6

D. 9

**ANSWER: C**

9. Find the range of the values of x satisfying the
inequalities 5+x ≤ 8 and 13 + x ≥ 7

A. -3 ≤ x ≤ 3

B. 3 ≤ x ≤ 6

C. -6 ≤ x ≤ 3

D. -6 ≤ x ≤ -3

**ANSWER: C**

Find the value of x

A. 5

B. 2

C. -2

D. -5

**ANSWER: --**

11. What is the maximum error in the number 0.09800
ft^{3}, assuming that it is recorded accurately?

A. 0.0005 ft^{3}

B. 0.0005 x 108 ft^{3}

C. 0.000005 ft^{3}

D. 0.00005 ft^{3}

**ANSWER: C**

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12. Udoh deposited ₦1500.00 in the bank. At the end of
5 years, the simple interest on the principal was ₦5500. At what rate per annum
was the interest paid?

A. 11%

B. 7^{1}/_{3}%

C. 5%

D. 3^{1}/_{2}%

**ANSWER: B**

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

A. 15

B. 25

C. 30

D. 50

**ANSWER: B**

14. In 1984, Ike was 24 years old and his father was
45 years old, in what year was Ike exactly half his father’s age?

A. 1982

B. 1981

C. 1979

D. 1978

**ANSWER: B**

15. If U and V are two distinct fixed points and W is
a variable point such that UWV is a straight angle. What is the locus of W?

A. The perpendicular bisector of UV

B. A circle with UV are radius

C. A line parallel to the line UV

D. A circle with the line UV as the diameter

**ANSWER: A**

16. Find the mean of the data :7, -3, 4, 2, 5, -9, 4,
8, -6, 12

A. 4

B. 3

C. 3

D. 1

**ANSWER: C**

17.

The distribution above shows the number of days a
group of 260 students were absent from school in a particular term. How many students
were absent for at least four days in the terms?

A. 210

B. 160

C. 120

D. 40

**ANSWER: B**

18. A number was chosen at random from the numbers 1 to
30 inclusive. What is the probability that the number will be divisible by 5?

A. ^{1}/_{30}

B. ^{1}/_{5}

C. ^{5}/_{30}

D.^{ 1}/_{3}

**ANSWER: B**

19. A rectangular picture 6cm by 8cm is enclosed by a France
½ cm wide, calculate the area of the frame.

A. 15 sq.cm

B. 20 sq.cm

C. 13 sq.cm

D. 16 sq.cm

**ANSWER: A**

20. For what values of x is x + 3(2-x) ≥ 4 – x?

A. x = 0

B. x ≤ 1

C. x ≥ 2

D. x ≤ 2

**ANSWER: C**

22. Evaluate log ^{2}/_{3} (^{27}/_{8})
= x

A. x = 2

B. x = -3

C. x = -2

D. x = 3

**ANSWER: B**

23. Perform the indicated operations:

A. ½ + ^{i}/_{2}

B. ^{1}/_{2}- ^{i}/_{2}

C. ^{1}/_{3} – ^{i}/_{3}

D. ^{1}/_{3} + ^{i}/_{3}

_{}**ANSWER: B**

_{}

A. 1

B. -1

C. 2

D. 3

**ANSWER: B**

25. A car of mass 1000kg has a uniform acceleration of
3m/s^{2}. Find the external force applied to the car.

A. 4 x 10^{3} N

B. 3 x 10 N

C. 3 x 10^{-3} N

D. 4 x 10^{-3} N

**ANSWER: B**

26. Halima scored the following marks in various subjects:
X,72, 60, 73 and 90 and have an average of 70%. Find the value of X.

A. 35

B. 45

C. 55

D. 65

**ANSWER: C**

27. A student obtained the following grade points out
of 5 points: 3, 5, 4, 5, 5, 3, 1, 2, 4 and 4. Find the average grade point for
this student.

A. 4.0

B. 4.05

C. 4.50

D. 3.50

**ANSWER: A**

28. Find the geometric mean of the numbers 3, 9 and 1.

A. 5

B. 2

C. 4

D. 3

**ANSWER: D**

29. Find the harmonic mean of the numbers :3, 4, 5, 6
correct to 2 d.p.

A. 4.21

B. 4.28

C. 4.12

D. 4.82

**ANSWER: A**

30. A cadet jogged at 20km/h from Old Site to New Site
and on his return, he jogged at 15km/h. Find his average speed for the jogging exercise.

A. 17^{2}/_{9} km/h

B. 17 ^{1}/_{7 }km/h

C. 17^{3}/_{9} km/h

D. 17 km/h

**ANSWER: B**

31. The points of intersection between 3x -y =7 and x
+ 2y -4 = 0 is

A. (3, 5)

B. (1/, 18/7)

C. (7/18, 14/10)

D. (^{18}/_{7}, ^{10}/_{14})

**ANSWER: D**

32. The slope of vertical line is given as

A. undefined

B. Ꚙ

C. -Ꚙ

D. none

**ANSWER: A**

33. The equation of the line AB passing through A(1,
-1) and B (-1, -1) is

A. 2y + 8x =5

B. y + x =7

C. y=4x-5

D. 8x + y = 10

**ANSWER: C**

34. The equation of a circle with centre C (2, 1) and
radius r = 6 is

A. x^{2} + y^{2} – 4x -2y = 31

B. 2x^{2} + y^{2} – 4x = 8

C. x^{2} – y^{2} - 8x – 2y = 31

D. x^{2} + y^{2} -8x - 4y = 16

**ANSWER: A**

35. Which of the following statement is correct in Mathematics?

A. ^{a}/_{0}

B. ^{0}/_{0}

C. ^{a}/_{b}. ^{1}/_{0}

D. ^{0}/_{a}

**ANSWER: D**

_{}

36. The equation ax5 + ax3 + b is called

A. polynomial

B. binomial

C. trinomial

D. All of the above

**ANSWER: A**

37. In the figure below PQ and QR are chords of the
circle PQR. QRS is a straight line and PR equals to RS. <PSR is 20˚. What is
the size of <POQ ?

A. 70 ˚

B. 90 ˚

C. 80 ˚

D. 60 ˚

**ANSWER: C**

38. Find the gradient ( or slope) of the line passing
through the given points (3, -5) and (8, 15)

A. 4

B. 5

C. 6

D. 3

**ANSWER: A**

39. A pole of height 6m casts a shadow 4.5m long, find
the height of a crane whose shadow is 75m long.

A. 80m

B. 90m

C. 100m

D. 110m

**ANSWER: C**

40. Find the area of the sector of a circle of radius
8cm subtending an angle of 60 ˚ at the centre.

A. 33.52 cm^{2}

B. 35.60 cm^{2}

C. 30.50 cm^{2}

D. 40 cm^{2}

**ANSWER: A**

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