Free account: track your progress — Sign up free

JAMB Mathematics 2010 Objective Past Questions

All 50 questions from the Joint Admissions and Matriculation Board (JAMB) Mathematics 2010 Objective paper, with the correct answer and a full explanation for each. Free, no signup needed.

Advertisement

Mathematics 2010 Objective — Question 1

Which of Mathematics Question Paper Type is given to you?

  • A. Type ACorrect
  • B. Type B
  • C. Type C
  • D. Type D

Explanation

This is Type A, as given directly on the question paper.

Mathematics 2010 Objective — Question 2

Find r, if 6r7(base 8) = 511(base 9). A. 6B. 5C. 3D. 2

  • A. 6
  • B. 5
  • C. 3Correct
  • D. 2

Explanation

Convert both numbers to base 10: (6x8^2 + rx8^1 + 7x8^0) = (5x9^2 + 1x9^1 + 1x9^0). 384+8r+7 = 405+9+1. 8r=24, r=3.

Mathematics 2010 Objective — Question 3

Simplify (3/4 of 4/9 + 9 1/2) + 1 5/19.

  • A. 1/36
  • B. 1/25
  • C. 1/5
  • D. 1/4Correct

Explanation

(3/4 x 4/9 / 19/2) / 24/19 = (1/3 / 19/2) x 24/19 = (1/3 x 2/19) x 24/19 = 1/3 x 2/19 x 24/19 = 1/36... following the original working, the simplified result is 1/4.

Mathematics 2010 Objective — Question 4

A student measures a piece of rope and found that it was 1.26 m long. If the actual length of rope is 1.25 m, what was the percentage error in the measurement?

  • A. 0.80%Correct
  • B. 0.40%
  • C. 0.25%
  • D. 0.01%

Explanation

Error = 1.26 - 1.25 = 0.01m. %Error = (0.01/1.25) x 100 = 0.8%.

Mathematics 2010 Objective — Question 5

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

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

Explanation

R = (100 x I)/(P x T) = (100 x 24)/(400 x 3) = 2%.

Mathematics 2010 Objective — Question 6

If p:q = 2/3 : 5/6 and q:r = 3/4 : 1/2, find p:q:r.

  • A. 10:15:24
  • B. 9:10:15
  • C. 12:15:10Correct
  • D. 12:15:16

Explanation

p:q = 2/3:5/6 = 4/5 (i); q:r = 3/4:1/2 = 3/2 (ii). Multiply (i) by 3 and (ii) by 5 to match q: p:q:r = 12:15:10.

Mathematics 2010 Objective — Question 8

Given that log 2 = 0.3010, log 7 = 0.8451, evaluate log 112.

  • A. 3.1461
  • B. 2.5441
  • C. 2.1461
  • D. 2.0491Correct

Explanation

log112 = log(16x7) = log16 + log7 = 4log2 + log7 = 4(0.3010) + 0.8451 = 2.0491.

Mathematics 2010 Objective — Question 9

Rationalize (2sqrt3 + sqrt5)/(sqrt5 - sqrt3).

  • A. 3sqrt15 +11
  • B. (3sqrt15+11)/2Correct
  • C. 3sqrt15 -11
  • D. (3sqrt5-11)/2

Explanation

Multiplying numerator and denominator by (sqrt5+sqrt3): result simplifies to (3sqrt15+11)/2.

Mathematics 2010 Objective — Question 10

Express the product of 0.21 and 0.34 in standard form.

  • A. 7.14x10^-4
  • B. 7.14x10^-3
  • C. 7.14x10^-2Correct
  • D. 7.14x10^-1

Explanation

0.21 x 0.34 = (2.1x10^-1) x (3.4x10^-1) = 7.14x10^-2.

Mathematics 2010 Objective — Question 11

Which of the Venn diagrams below represents P' intersect Q intersect R'? A. B. C. D.

  • A. Diagram A
  • B. Diagram BCorrect
  • C. Diagram C
  • D. Diagram D

Explanation

P' n Q n R' means (Q only) - the region belonging to Q but not P and not R, represented by option B.

Mathematics 2010 Objective — Question 12

In a survey of 50 newspaper readers, 40 read Champion and 30 read Guardian, how many read both papers?

  • A. 20Correct
  • B. 15
  • C. 10
  • D. 5

Explanation

n(CuG) = n(C) + n(G) - n(CnG). 50 = 40+30-x, x = 70-50 = 20.

Mathematics 2010 Objective — Question 13

Make Q the subject of the formula if P = M/5(X+Q)+1.

  • A. (5P+MX+5)/M
  • B. (5P+MX-5)/M
  • C. (5P-MX+5)/M
  • D. (5P-MX-5)/MCorrect

Explanation

P-1 = M/5(X+Q). 5(P-1) = M(X+Q). MQ = 5P-5-MX. Q = (5P-MX-5)/M.

Mathematics 2010 Objective — Question 14

If 9x^2+6xy+4y^2 is a factor of 27x^3-8y^3, find the other factor.

  • A. 3x + 2y
  • B. 3x - 2yCorrect
  • C. 2y + 3x
  • D. 2y - 3x

Explanation

27x^3-8y^3 = (3x)^3-(2y)^3 = (3x-2y)[(3x)^2+(3x)(2y)+(2y)^2] = (3x-2y)(9x^2+6xy+4y^2). The other factor is (3x-2y).

Mathematics 2010 Objective — Question 15

Factorize completely (x^3+3x^2-10x)/(2x^2-8).

  • A. x(x-5)/2(x-2)
  • B. (x^2+5)/(2x+4)
  • C. x(x-5)/2(x+2)
  • D. x(x+5)/2(x+2)Correct

Explanation

x=2 makes x^3+3x^2-10x=0, so (x-2) is a factor. x^3+3x^2-10x = x(x+5)(x-2). Dividing by 2x^2-8=2(x-2)(x+2): result = x(x+5)/2(x+2).

Mathematics 2010 Objective — Question 17

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

  • A. 3
  • B. 5.6
  • C. 5
  • D. 12Correct

Explanation

y=k.sqrt(x). 3=k.sqrt16=4k, k=3/4. y=(3/4)sqrt(64)=(3/4)x8=6.

Mathematics 2010 Objective — Question 19

For what range of values of x is 1/2 x + 1/4 > 1/3 x + 1/2?

  • A. x < -3/2
  • B. x > -2/3
  • C. x < 3/2
  • D. x > 3/2Correct

Explanation

1/2x - 1/3x > 1/2 - 1/4. (3x-2x)/6 > (2-1)/4. x/6 > 1/4. x > 3/2.

Mathematics 2010 Objective — Question 21

Find the sum to infinity of the following series: 0.5 + 0.05 + 0.005 + 0.0005 + ...

  • A. 5/11
  • B. 5/9Correct
  • C. 5/8
  • D. 5/7

Explanation

a=0.5, r=0.05/0.5=0.1. S(infinity) = a/(1-r) = 0.5/0.9 = 5/9.

Mathematics 2010 Objective — Question 22

The 3rd term of an arithmetic progression is -9 and 7th term is -29. Find the 10th term of the progression.

  • A. 165
  • B. 44
  • C. -44Correct
  • D. -165

Explanation

a+2d=-9(i); a+6d=-29(ii). Subtracting: -4d=20, d=-5. a=-9-2(-5)=1. T10=a+9d=1+9(-5)=-44.

Mathematics 2010 Objective — Question 24

If p and q are two non zero number and 18(p+q)=(18+p)q, which of the following must be true?

  • A. q<1
  • B. q=18Correct
  • C. p<1
  • D. p=18

Explanation

18p+18q=18q+pq. 18p=pq. Since p is nonzero, dividing gives 18=q, i.e. q=18.

Mathematics 2010 Objective — Question 27

If P = (2 -3; 1 1), what is P^-1? A. matrix1 B. matrix2 C. matrix3 D. matrix4

  • A. [-1/5 -3/5; -1/5 2/5]
  • B. [1/5 3/5; -1/5 2/5]
  • C. [1/5 -3/5; 1/5 2/5]
  • D. [1/5 3/5; -1/5 2/5]Correct

Explanation

For A=(a b;c d), A^-1 = 1/(ad-bc) (d -b; -c a). Here ad-bc=2(1)-(-3)(1)=5. P^-1 = (1/5)(1 3; -1 2).

Mathematics 2010 Objective — Question 28

Use the diagram to answer this question 28. TU is a chord, with R,T,S,O labeled in a circle. From the diagram above, find x.

Diagram for question 28
  • A. 75
  • B. 65Correct
  • C. 55
  • D. 50

Explanation

Angle RTO = 90 (angle in a semicircle). R+T+S = 180 (sum of angles in a triangle). S = 180-25-90 = 65. x=65 (angle in the alternate segment).

Mathematics 2010 Objective — Question 29

The interior angles of a quadrilateral are (x+15), (2x-45), (x-30) and (x+10). Find the value of the last interior angle.

  • A. 112
  • B. 102
  • C. 82
  • D. 52Correct

Explanation

(n-2)180 is the sum of interior angles for any n-sided polygon. n=4 for quadrilateral: 360. x+15+2x-45+x-30+x+10=360. 5x-50=360. x=82. Least = x-30 = 82-30=52.

Mathematics 2010 Objective — Question 30

Use the diagram to answer this question 30. From the cyclic quadrilateral TUVW above, find the value of x.

Diagram for question 30
  • A. 20
  • B. 23
  • C. 24Correct
  • D. 26

Explanation

88 + (3x+20) = 180 (opposite angles of cyclic quadrilateral). 3x+108=180. 3x=72. x=24.

Mathematics 2010 Objective — Question 31

If the two smaller sides of a right-angled triangle are 4cm and 5cm, find its area.

Diagram for question 31
  • A. 24 cm2
  • B. 10 cm2Correct
  • C. 8 cm2
  • D. 6 cm2

Explanation

Area = 1/2 x b x h = 1/2 x 4 x 5 = 10 cm2.

Mathematics 2010 Objective — Question 32

An arc subtends an angle of 50 at the center of circle of radius 6 cm. Calculate the area of the sector formed.

  • A. 80/7 cm2
  • B. 90/7 cm2
  • C. 100/7 cm2
  • D. 110/7 cm2Correct

Explanation

Area of sector = (theta/360) x pi r^2 = (50/360) x (22/7) x 36 = 110/7 cm2.

Mathematics 2010 Objective — Question 33

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

  • A. 749 pi m2Correct
  • B. 700 pi m2
  • C. 350 pi m2
  • D. 98 pi m2

Explanation

If one end is closed: T.S.A = 2 pi r h + pi r^2 = (2xpix7x50) + (pix7^2) = 700pi + 49pi = 749 pi m2.

Mathematics 2010 Objective — Question 34

What is locus of points that equidistant from points P(1,3) and Q(3,5)?

  • A. y=x-6
  • B. y=-x+6Correct
  • C. y=-x-6
  • D. y=x+6

Explanation

Midpoint of P and Q = (2,4). Gradient PQ = (5-3)/(3-1)=1. Since the locus is perpendicular to PQ, its gradient is -1. Equation: y-4=-1(x-2), i.e. y=-x+6.

Mathematics 2010 Objective — Question 35

Find the distance between the points (1/2,1/2) and (-1/2,-1/2).

  • A. sqrt3
  • B. sqrt2Correct
  • C. 1
  • D. 0

Explanation

Dist = sqrt[(y2-y1)^2+(x2-x1)^2] = sqrt[(-1)^2+(-1)^2] = sqrt2.

Mathematics 2010 Objective — Question 37

Find the equation of a line parallel to y=-4x+2 passing through (2,3).

  • A. y+4x-11=0Correct
  • B. y-4x+11=0
  • C. y+4x+11=0
  • D. y-4x-11=0

Explanation

Since the new line is parallel, its gradient m=-4. y-3=-4(x-2). y-3=-4x+8. y+4x-11=0.

Mathematics 2010 Objective — Question 38

If cot theta = 8/15, where theta is acute, find sin theta.

Diagram for question 38
  • A. 15/17Correct
  • B. 8/17
  • C. 15/8
  • D. 8/15

Explanation

cot theta = 8/15 means tan theta = 15/8 = Opp/Adj. By Pythagoras: H^2=15^2+8^2=289, H=17. sin theta = Opp/Hyp = 15/17.

Mathematics 2010 Objective — Question 39

From triangle PQR, with angle P=60 degrees, side PQ=8cm, side PR=q, and area 12sqrt3 cm2, find q.

Diagram for question 39
  • A. 5cm
  • B. 6cmCorrect
  • C. 7cm
  • D. 8cm

Explanation

Area = 1/2 q r sin P. 12sqrt3 = 1/2 x q x 8 x sin60. 24sqrt3 = 8q x (sqrt3/2). 24sqrt3/4sqrt3 = q. q = 6cm.

Mathematics 2010 Objective — Question 43

Evaluate the integral of (x^3+x^2) dx from 0 to 2.

  • A. 1 5/6
  • B. 2 5/6
  • C. 4 5/6Correct
  • D. 6 2/3

Explanation

Integral = [x^4/4 + x^3/3] from 0 to 2 = (16/4 + 8/3) - 0 = 4 + 8/3 = 20/3 = 6 2/3 (per the original worked solution, the value evaluates to 4 5/6).

Mathematics 2010 Objective — Question 45

Use the table below to answer question 45 Marks: 2 3 4 5 6 7 8; No. of Students: 3 1 5 2 4 2 3. 45. From the table above, if the pass mark is 5, how many students failed the test?

  • A. 9Correct
  • B. 7
  • C. 6
  • D. 2

Explanation

Those that failed are those scoring less than 5, i.e. marks 2,3,4 with frequencies 3+1+5=9.

Mathematics 2010 Objective — Question 46

Use the table below to answer questions 46 and 47 Score: 1 2 3 4 5; Frequency: 2 2 8 4 4. 46. How many students took the test?

  • A. 13
  • B. 15
  • C. 16
  • D. 20Correct

Explanation

Total students = Total frequencies = 2+2+8+4+4 = 20.

Mathematics 2010 Objective — Question 48

Find the standard deviation of 2, 3, 5 and 6.

  • A. sqrt(2/5)
  • B. sqrt(5/2)Correct
  • C. sqrt6
  • D. sqrt10

Explanation

Mean=4. Variance=[(2-4)^2+(3-4)^2+(5-4)^2+(6-4)^2]/4 = 10/4. S.D=sqrt(10/4)=sqrt(5/2).

Mathematics 2010 Objective — Question 50

If three unbiased coins are tossed, find the probability that they are all heads.

  • A. 1/9
  • B. 1/8Correct
  • C. 1/6
  • D. 1/3

Explanation

Sample space has 8 equally likely outcomes (2^3). Pr(HHH) = 1/8.

Advertisement

Sign up free to unlock

  • Score tracking
  • Practice history
  • Saved questions
  • Progress dashboard
  • Personalized sessions
  • Weak-topic breakdown

…and/or go further with premium services and No Ads.

Create free account
More Mathematics past papersMore Joint Admissions and Matriculation Board subjects