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Mathematics
UTME / JAMB 2015
Coordinate Geometry
Solution
Find the equation of a line which is form origin and passes through the point (−3, −4)
A
y = \( \frac{3x}{4} \)
B
y = \( \frac{4x}{3} \)
C
y = \( \frac{2x}{3} \)
D
y = \( \frac{x}{2} \)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
The slope of the line from (0, 0) passing through (-3, -4) = \(\frac{-4 - 0}{-3 - 0}\)
= \(\frac{4}{3}\)
Equation of a line is given as \(y = mx + b\), where m = slope and b = intercept.
To get the value of b, we use a point on the line, say (0, 0).
\(y = \frac{4}{3} x + b\)
\(0 = \frac{4}{3}(0) + b\)
\(b = 0\)
The equation of the line is \(y = \frac{4}{3} x\)
Source: Myschool Past Questions Archive (Record #40636)
Mathematics
UTME / JAMB 2015
Fractions, Decimals, Percentages & Approximations
Solution
The amount A to which a principal P amounts at r% compound interest for n years is given by the formula A = P(1 + (r \div 100)\(^n\). Find A, if P = 126, r = 4 and n = 2.
A
N132.50K
B
N136.30K
C
N125.40K
D
N257.42K
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\( A = P \left(1 + \frac{r}{100}\right)^n \)
Where P = 126, r = 4,n = 2
A=126 \( \left(1 + \frac{4}{100}\right)^2 \text{Using LCM} \)
=126 \( \left(\frac{100+4}{100}\right)^2 = 126 \left(\frac{104}{100}\right)^2 \)
=126 \( \left(1.04^2 \right) \)
= 126 * 1.04 * 1.04
=136.28
A = 136.30 (approx.)
The Amount A, = N136.30k
Source: Myschool Past Questions Archive (Record #40642)
Mathematics
UTME / JAMB 2015
Plane Geometry, Polygons & Circle Theorems
Make x the subject of the equation
s = 2 + \(\frac{t}{5} \)(x + ⅗y)
A
x = 5[(s − 2) ÷ t] - 3/5y
B
x = 25[(s − 2) ÷ t] − 3ty
C
x = [1 ÷ (s − 2)3ty]
D
x = [5(s − 2) 2 ÷ 3ty] × t
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option A.
Source: Myschool Past Questions Archive (Record #40645)
Mathematics
UTME / JAMB 2015
Plane Geometry, Polygons & Circle Theorems
Solution
If log520 = x, find x
A
1.761
B
1.354
C
1.861
D
2.549
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
log520 = x
5x = 20(Take log10 of both sides)
log5x = log20
xlog5 = log20
x= [log20 ÷ log5]
[1.30103 ÷ 0.69897]
x = 1.861
Source: Myschool Past Questions Archive (Record #40647)
Mathematics
UTME / JAMB 2015
Fractions, Decimals, Percentages & Approximations
Solution
Find at which rate per annum simple interest N525 will amount to N588 in 3 years.
A
3%
B
2%
C
5%
D
4%
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
I = A − P
= N588 − N525
∴I = N63
I = PRT ÷ 100
R = [100I ÷PT]
R = [(100 × 63 ) ÷ (525 × 3)]
= (6300 ÷ 1575) = 4
∴ The rate = 4 %
Source: Myschool Past Questions Archive (Record #40649)
Mathematics
UTME / JAMB 2015
Sets, Logic & Venn Diagrams
Solution
Given that A = {1, 5, 7}
B = {3, 9, 12, 15}
C = {2, 4, 6, 8}
Find (A ∪ B) ∪ C
A
{1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 15}
B
{1, 2, 3, 5, 6, 8, 12, 15}
C
{2, 4, 5, 9, 12, 15}
D
{1, 5, 6, 7, 8, 9, 12, 15}
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
{A ∪ B ∪ C}
{A ∪ B} = {1, 3, 5, 7, 9, 12, 15}
∪ C={2,4,6,8}
{A ∪ B} ∪ C = {1, 3, 5, 7, 9, 12, 15} ∪ {2, 4, 6, 8}
= {1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 15}
{A ∪ B} ∪ C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 15}
Source: Myschool Past Questions Archive (Record #40654)
Mathematics
UTME / JAMB 2015
Variations
Solution
The extension of a stretched string is directly proportional to its tension. If the extension produced by a tension of 8 Newton’s is 2cm, find the extension produced by a tension of 12 newton’s.
A
2
B
1
C
0
D
3
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Let the extension be E and the tension be T.
Then \(E \propto T\)
\(E = kT\)
when T = 8N, E = 2cm
\(2 = k \times 8\)
\(k = \frac{2}{8} = 0.25\)
\(\therefore E = 0.25T\)
when T = 12N, \(E = 0.25 \times 12 = 3cm\)
Source: Myschool Past Questions Archive (Record #40657)
Mathematics
UTME / JAMB 2015
Algebraic Expressions, Polynomials & Factorisation
Solution
Factorize \( x^2 − 2x − 15 \)
A
(x + 3)2
B
(x + 5)(x − 3)
C
(x − 5)2
D
(x − 5)(x + 3)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
x2 − 2x − 15
(x2 − 5x) + (3x − 15)
x(x − 5)+ 3(x − 5)
(x − 5)(x + 3)
Source: Myschool Past Questions Archive (Record #40664)
Mathematics
UTME / JAMB 2015
Coordinate Geometry
Solution
If A = (−3,5) and B = (4,−1) find the co-ordinate of the mid point
A
2, ½
B
½ , 2
C
1, ½
D
0, 2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
The coordinate of the midpoint is \((\frac{-3 + 4}{2}, \frac{5 + (-1)}{2})\)
= \((\frac{1}{2}, 2)\)
Source: Myschool Past Questions Archive (Record #40667)
Mathematics
UTME / JAMB 2015
Fractions, Decimals, Percentages & Approximations
Solution
Find the simple interest on N325 in 5years at 3% per annum.
A
N48.75K
B
N50.10K
C
N75.50K
D
N15.75K
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
I =[ PRT ÷ 100]
[(325 × 5 × 3) ÷ (100)]
N(195 ÷ 4)
N48.75K
Source: Myschool Past Questions Archive (Record #40669)
Mathematics
UTME / JAMB 2015
Fractions, Decimals, Percentages & Approximations
Solution
Simplify (0.09)2 and give your answer correct to 4 significant figures
A
0.81
B
0.081
C
0.0081
D
8.0001
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
(0.09)2 = 0.09 × 0.09
= 0.0081
= 0.008100 to 4 significant figures
Please, start counting first from the non-zero digits i.e. 8
Source: Myschool Past Questions Archive (Record #40676)
Mathematics
UTME / JAMB 2015
Linear, Simultaneous & Quadratic Equations
Solution
Simplify \( [1 ÷ (x^2 + 3x + 2)] + [1 ÷ (x^2 + 5x + 6)] \)
A
\( \frac{2}{(x + 1)^2} \)
B
\( \frac{2}{(x + 1)(x + 2} \)
C
\( \frac{2}{(x + 1)(x + 2} \)
D
\( \frac{2}{(x + 1)(x + 3} \)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\( [1 ÷ (x^2 + 3x + 2)] + [1 ÷ (x^2 + 5x + 6)] \)
= \( 1 ÷ (x^2 + 3x + 2) + [1 ÷ (x^2 +5x + 6)]\)
= \( [1 ÷ ((x^2 + x) + (2x + 2) )] + [1 ÷ ((x^2 + 3x) + (2x + 6) )] \)
= [1 ÷ (x(x + 2) + 2(x +1))] + [1 ÷ (x(x + 3) +2(x + 3) )]
= [1 ÷ (x + 1)(x + 2)] + [1 ÷ ((x + 3) + (x + 2))]
=((x + 3) + (x + 1)) ÷ (x + 1)(x + 2)(x + 3)
Using the L.C.M
=((x + x + 3 + 1)) ÷ (x + 1)(x + 2)(x + 3)
=(2x+4)/(x+1)(x+2)(x+3) =2(x+2)/(x+1)(x+2)(x+3)
= \( \frac{2 }{(x + 1)(x + 3)} \)
Source: Myschool Past Questions Archive (Record #40682)
Mathematics
UTME / JAMB 2015
Permutations, Combinations & Probability
Solution
One bag contain 3 blue and 5 red balls, another bag contain 2 blue and 4 red balls respectively. One ball is drawn for each bag. What is the probability both balls are blue
A
\( \frac{2}{15} \)
B
\( \frac{3}{24} \)
C
\( \frac{3}{21} \)
D
\( \frac{3}{28} \)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
The probability of drawing a blue ball from the first bag is \( \frac{3}{8} \), since there are 3 blue balls out of 8 total balls.
The probability of drawing a blue ball from the second bag is \( \frac{2}{6} = \frac{1}{3} \), since there are 2 blue balls out of 6 total balls.
Since the draws from each bag are independent, the probability that both balls are blue is the product of the individual probabilities:
\( \frac{3}{8} \times \frac{2}{6} = \frac{3 \times 2}{8 \times 6} = \frac{6}{48} = \frac{1}{8}. \)
Source: Myschool Past Questions Archive (Record #40685)
Mathematics
UTME / JAMB 2015
Sets, Logic & Venn Diagrams
Solution
Given that A = {3, 4, 1, 10, ⅓ }
B = {4, 3,⅓, ⅓, 7}.
Find A∩B
A
{}
B
{⅓, 1, 2}
C
{3, 4, ⅓}
D
{1, 3, ⅓}
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
A ∩ B = {3, 4, ⅓}
Source: Myschool Past Questions Archive (Record #40686)
Mathematics
UTME / JAMB 2015
Linear, Simultaneous & Quadratic Equations
Solution
Find x if 132x = 70 eight.
A
5
B
3
C
6
D
1
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
132x = 708
\( 1 × x^2 + 3 × x^1 + 2 × x^0 \)
\( 7 × 8^1 + 0 × 8^0 \)
\( x^2 + 3x + 2 − 56 = 0 \)
\( x^2 + 3x − 54 = 0 \)
x(x + 9)−6(x + 9) = 0
(x + 9)(x − 6) = 0
Either (x + 9) = 0 or (x − 6) = 0
x = − 9 or +6
The positive values for x = 6
The base number for 132x = 1326
Source: Myschool Past Questions Archive (Record #40687)