JAMB Mathematics Past Questions 2010

10 questions from the JAMB 2010 Mathematics paper, with answers and explanations. Tap "Show answer" under each one when you are ready.

JAMB 2010Question 1 · Algebraic Processes

Factorize completely

\frac{x ^{3} + 3 x ^{2} - 10 x}{2 x ^{2} - 8}

A. $\frac{x ( x - 5 )}{2 ( x + 2 )}$
B. $\frac{x ( x - 5 )}{2 ( x - 2 )}$
C. $\frac{x ( x + 5 )}{2 ( x + 2 )}$
D. $\frac{x ^{2} + 5}{2 x + 4}$

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Answer: C. $\frac{x ( x + 5 )}{2 ( x + 2 )}$

Factorizing numerator and denominator and cancelling (x-2) gives x(x+5)/[2(x+2)].

JAMB 2010Question 2 · Algebraic Processes

Solve for x and y if x - y = 2 and

x^{2}

y^{2}

= 8

A.(-1, 3)
B.(3, 1)
C.(-3, 1)
D.(1, 3)

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Answer: B. (3, 1)

x-y=2, x+y=4 (from difference of squares), giving x=3, y=1.

JAMB 2010Question 3 · Calculus

Find ∫(sin x + 2)dx

A. $cos x + x^{2} + K$
B.cos x 2x + K
C. $- cos x + x^{2} + K$
D.-cos x + 2x + K

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Answer: D. -cos x + 2x + K

∫(sinx+2)dx = -cosx+2x+K.

JAMB 2010Question 4 · Commercial Arithmetic

At what rate will the interest on N400 increases to N24 in 3 years reckoning in simple interest?

A.3%
B.2%
C.5%
D.4%

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Answer: B. 2%

24 = 400xRx3/100 gives R=2%.

JAMB 2010Question 5 · Coordinate Geometry and Trigonometry

Find the gradient of the line passing through the points P(1, 1) and Q(2, 5).

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Answer: D. 4

Gradient = (5-1)/(2-1) = 4.

JAMB 2010Question 6 · Geometry and Mensuration

A cylindrical pipe 50m long with radius 7m has one end open. What is the total surface area of the pipe?

A.749pim 2
B.700pim 2
C.350pim 2
D.98pim 2

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Answer: A. 749pim 2

Total surface area = 2πrh + πr² = 700π+49π = 749π m².

JAMB 2010Question 7 · Inequalities, Permutation, and Combination

Determine the value of x for which (

x^{2}

- 1)>0

A.x 1
B.-1 < x < 1
C.x > 0
D.x < -1

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Answer: A. x 1

x²-1>0 gives x<-1 or x>1.

JAMB 2010Question 8 · Number, Fractions, and Approximation

Find r, if

6 r 7_{8}

51 1_{9}

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Answer: A. 3

391+8r=415 gives r=3.

JAMB 2010Question 9 · Sequences, Series, and Variation

If y varies directly as the square root of x and y = 3 when x = 16. Calculate y when x = 64

A.12
B.6
C.3
D.5

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Answer: B. 6

y=k $x$ ; 3=4k so k= $\frac{3}{4}$ ; at x=64, y=( $\frac{3}{4}$ )x8=6.

JAMB 2010Question 10 · Sequences, Series, and Variation

W is directly proportional to U. If W = 5 when U = 3, find U when W =

\frac{2}{7}

A. $\frac{6}{35}$
B. $\frac{10}{21}$
C. $\frac{21}{10}$
D. $\frac{35}{6}$

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Answer: A. $\frac{6}{35}$

U = ( $\frac{2}{7}$ ) x ( $\frac{3}{5}$ ) = 6/35.

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JAMB Mathematics Past Questions 2010

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