Mathematics 2017 Past Questions | JAMB
Study the following Mathematics past questions and answers for JAMB, WAEC NECO and Post-JAMB. Get prepared with official past questions and answers for upcoming examinations.
31. In how many ways can the word MATHEMATICS be arranged?
- A. \(\frac{11!}{9!2!}\)
- B. \(\frac{11!}{9!2!2!}\)
- C. \(\frac{11!}{2!2!2!}\)
- D. \(\frac{11!}{2!2!}\)
Correct Option: Answer is C
MATHEMATICS is an eleven letter word = 11!
There are 2Ms and 2As and 2Es
Divide the number of repeating letters
= \(\frac{11!}{2!2!2!}\)
32. In how many ways can the word MACICITA be arranged?
- A. \(\frac{8!}{2!}\)
- B. \(\frac{8!}{3! 2!}\)
- C. \(\frac{8!}{2! 2! 2!}\)
- D. 8!
Correct Option: Answer is C
MACICITA is an eight letter word = 8!
Since we have repeating letters, we have to divide to remove duplicates accordingly. There are 2A, 2C, 2I
∴ \(\frac{8!}{2! 2! 2!}\)
33. y is inversely proportional to x and y and 6 when x = 7. Find the constant of the variation
- A. 47
- B. 42
- C. 54
- D. 46
Correct Option: Answer is B
Y ∝ \(\frac{1}{2}\)
Y = 6, X = 7
Y = \(\frac{k}{x}\) where k is constant
6 = \(\frac{k}{7}\)
k = 42
34.
- A. 123o
- B. 170o
- C. 117o
- D. 137o
Correct Option: Answer is C
MN || PQ || RS
MN = PQ = RS (parallel lines)
Label the angle in the lines
a = i (corresponding angles are equal)
b = x (corresponding angles are equal)
If |MN| = |RS|
If a = i
and a = 63 = i
a + b = 180 (Adjacent interior angles are supplementary i.e add to 180)
∴ i + x = 180
63 + x = 180
x = 180 – 63
x = 117°
35. Find the equation of the locus of a point p (x, y) such that pv = pw, where v= (1, 1) and w = (3, 5)
- A. 2x + 2y = 9
- B. 2x + 3y = 8
- C. 2x + y = 9
- D. x + 2y = 8
Correct Option: Answer is D
The locus of a point p(x, y) such that pv = pw where v = (1, 1)
and w = (3, 5). This means that the point p moves so that its distance from v and w are equidistance
\(\sqrt{(x − x_1)^2 + (y − y_1)^2}\) = \(\sqrt{(x − x_2)^2 + (y − y_2)^2}\)
\(\sqrt{(x -1)^2 + (y – 1)^2}\) = \(\sqrt{(x – 3)^2 + (y – 5)^2}\)
square both sides
(x – 1)2 + (y – 1)2 = (x – 3)2 + (y – 5)2
x2 – 2x + 1 + y2 – 2y + 1 = x2 – 6x + 9 + y2 – 10y + 25
x2 + y2 -2x -2y + 2 = x2 + y2 – 6x – 10y + 34
Collecting like terms
x2 – x2 + y2 – y2 – 2x + 6x -2y + 10y = 34 – 2
4x + 8y = 32
Divide through by 4
36. Find ∫(x2 + 3x − 5)dx
- A. \(\frac{x_3}{3}\) – \(\frac{3x_2}{2}\) – 5x + k
- B. \(\frac{x_3}{3}\) – \(\frac{3x_2}{2}\) + 5x + k
- C. \(\frac{x_3}{3}\) + \(\frac{3x_2}{2}\) – 5x + k
- D. \(\frac{x_3}{3}\) + \(\frac{3x_2}{2}\) + 5x + k
Correct Option: Answer is A
∫xndx = \(\frac{x_{n + 1}}{n + 1}\)
∫dx = x + k
where k is constant
∫(x2 + 3x − 5)dx
∫x2 dx + ∫3xdx − ∫5dx
\(\frac{2_{2 + 1}}{2 + 1}\) + \(\frac{3x^{1 + 1}}{1 + 1}\) − 5x + k
\(\frac{x_3}{3}\) + \(\frac{3x_2}{2}\) − 5x + k
37.
In the diagram above MN is a chord of a circle KMN centre O and radius 10cm. If < MON = 140°, find, to the nearest cm, the length of the chord MN.
- A. 10cm
- B. 18cm
- C. 17cm
- D. 12cm
Correct Option: Answer is
From the diagram
Sin 70°
x = 10 Sin 70°
= 9.3969
Hence, length of chord MN = 2x
= 2 × 9.3969
= 18.79
= 19cm (nearest cm)
38. If m * n = [mn − nm] for m, n belong to R, evaluate − 3 * 4
- A. 3
- B. 4
- C. 5
- D. 6
Correct Option: Answer is C
39. Factorize completely x2 + 12xy + y2 + 3x + 3y – 18
- A. (x + y + 6)(x + y -3)
- B. (x – y – 6)(x – y + 3)
- C. (x – y + 6)(x – y – 3)
- D. (x + y – 6)(x + y + 3)
Correct Option: Answer is A
\(x^{2} + 2xy + y^{2} + 3x + 3y – 18\)
\(x^{2} + 2xy + 3x + y^{2} + 3y -18\)
\(x^{2} + 2xy – 3x + 6x + y^{2} -3y + 6y -18\)
\(x^{2} + 2xy -3x + y^{2} -3y + 6x + 6y -18\)
\(x^{2} + xy -3x + xy + y^{2} – 3y + 6x + 6y -18\)
x(x + y – 3) + y(x + y – 3) + 6(x + y – 3)
= (x + y – 3)(x + y + 6)
= (x + y + 6)(x + y -3)
40. Make S the subject of the relation
p = s + \(\frac{sm^2}{nr}\)
- A. s = \(\frac{nrp}{nr + m^2}\)
- B. s = nr + \(\frac{m^2}{mrp}\)
- C. s = \(\frac{nrp}{mr}\) + m2
- D. s = \(\frac{nrp}{nr}\) + m2
Correct Option: Answer is A
Explanation
p = s + \(\frac{sm^2}{nr}\)
p = s + ( 1 + \(\frac{m^2}{nr}\))
p = s (1 + \(\frac{nr + m^2}{nr}\))
nr × p = s (nr + m2)
s = \(\frac{nrp}{nr + m^2}\)