How good are you with figures and formulas? Find out with these Mathematics past questions and answers. This Test is useful for both job aptitude test candidates and students preparing for JAMB, WAEC, NECO or Post UTME.
Simplify \(3\sqrt{12} + 10\sqrt{3} - \frac{6}{\sqrt{3}}\)
10\(\sqrt{3}\)
18\(\sqrt{3}\)
14\(\sqrt{3}\)
7\(\sqrt{3}\)
Correct answer is C
\(3\sqrt{12} + 10\sqrt{3} - \frac{6}{\sqrt{3}}\)
= \(3\sqrt{4\times3} + 10\sqrt{3} - \frac{6}{\sqrt{3}}\)
= \(6\sqrt{3} + 10\sqrt{3} - \frac{6}{\sqrt{3}}\)
treating like a fraction, then
= \(\frac{18 + 30 - 6}{\sqrt{3}}\)
= \(\frac{42}{\sqrt{3}}\)
rationalizing
= \(14\sqrt{3}\)
\(58^0\)
\(64^0\)
\(48^0\)
\(76^0\)
Correct answer is D
Reflex ∠MOR = 2 × 124° = 248° (angle at the centre is twice the angle at the circumference)
∠MOR = 360° - 248° = 112° (sum of angle at a point is 360°)
∠OMN = 360° - (124°+ 48° + 112°) (sum of angles in a quadrilateral is 360°)
= 360° - 284°
∴ ∠OMN = 76°
One-third of the sum of two numbers is 12, twice their difference is 12. Find the numbers.
22 and 14
20 and 16
21 and 15
23 and 13
Correct answer is C
Let the two numbers be x and y
\(\frac{1}{3}( x + y) = 12\)
then x + y = 36 ..........i
2( x - y) = 12
x - y = 6 ............ii
add equations i and ii
2x = 42
x = 21, put x = 21 into equation i
x + y = 36
21 + y = 36
y = 36 - 21 = 15
therefore the numbers are 21 and 15
Mr Manu is 4 times as old as his son, Adu. 7 years ago the sum of their ages was 76. How old is Adu?
22years
12years
18years
15 years
Correct answer is C
Let Mr Manu be x years old and Adu be y years old.
But Mr Manu is four times as old as Adu then, x = 4y.
7 years ago, the sum of their ages was 76.
( x - 7) + ( y - 7) = 76
x + y - 14 = 76
x + y = 76 + 14 = 90
But x = 4y
Therefore, 4y + y = 90
5y = 90
y = \(\frac{90}{5}\)
y = 18
Therefore Adu is 18 years old.
13
11
5
9
Correct answer is B
Using the venn diagram above
μ = 30
n(W) = 15
n(M) = 13
\(n(W ∪ M)^1 = 6\)
Let x = number of students that study both woodwork and metalwork
i.e. n(W ∩ M) = x
Number of students that study only woodwork,\(n(W ∩ M^1)\) = \(15 - x\)
Number of students that study only metalwork, \(n(W^1 ∩ M)\) = \(13 - x \)
Bringing all together,
\(n(W ∩ M^1)\) +\( n(W^1 ∩ M)\) + \(n(W ∩ M)\) + \(n(W ∪ M)^1\) = \(μ\)
∴ (15 - x) + (13 - x) + x + 6 = 30
⇒ 34 - x = 30
⇒ 34 - 30 = x
∴ x = 4
\(n(W ∩ M^1)\) = \(15 - 4 = 11\)
∴ The number of students that study woodwork but not metalwork is 11.
The angle of a sector of a circle of radius 3.4 cm is 115°. Find the area of the sector.
\((Take \pi = \frac{22}{7})\)
\(11.6cm^2\)
\(12.7cm^2\)
\(10.2cm^2\)
\(9.4cm^2\)
Correct answer is A
\(\theta = 115° , radius = 3.4cm^2\)
Area of a sector = \(\frac{\theta}{360} \times \pi r^2\)
= \(\frac{115}{360} \times \frac{22}{7} \times 3.4\times 3.4\)
= \(\frac{29246.4}{2520}\)
= \(11.6cm^2\)
Solve \(1 + \sqrt[3]{ x - 3} = 4\)
30
6
12
66
Correct answer is A
\(1 + \sqrt [3]{x-3} = 4\)
= \(\sqrt[3]{x - 3} = 4 - 1\)
\(\sqrt[3]{x - 3} = 3 \)
take the cube of both sides
= x - 3 = 27
x = 27 + 3
∴ x = 30
In the diagram, O is the center of the circle QRS and ∠SQR = 28°. Find ∠ORS.
\(56^0\)
\(28^0\)
\(76^0\)
\(62^0\)
Correct answer is D
∠SOR = 2 × 28° = 56° (angle at the centre is twice the angle at the circumference)
From ∆SOR
|OS| = |OR| (radii)
So, ∆SOR is isosceles.
∠ORS = \(\frac{180^0 - 56^0}{2} = \frac{124^0}{2}\) ( base angles of isosceles triangle are equal)
∴ ∠ORS = 62°
6 days
8 days
10 days
12 days
Correct answer is A
12 men working 8 hours a day can complete the work in 4 days
12 men working 1 hour a day will complete the same work in (8 x 4) days [working less hours a day means they have to work for more days]
1 man working 1 hour a day will complete same work in (8 x 4 x 12) days [fewer number of men working means the remaining ones will have to work for more days ]
So, it will take 1 man working 1 hour a day to complete a piece of work in (8 x 4 x 12) days = 384 days
Now,
1 man working 16 hours a day will complete the piece of work in (384/16) days = 24 days [working more hours a day means less days to complete the work]
∴ 4 men working 16 hours a day will complete the piece of work in (24/4) days = 6 days [more men working means fewer days to complete the work]
ALTERNATIVELY
12 x 8 x 4 = 4 x 16 x d
⇒ d = \(\frac{12 \times 8 \times 4}{4 \times 16}\)
⇒ d = \(\frac{384}{64}\)
⇒ d = 6
∴ 4 men working 16 hours a day will complete the piece of work in 6 days
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