JAMB Mathematics 2010 past questions and answers

Find r, if 6r7₈ = 511₉.

1. A.5
2. B.2
3. C.3
4. D.6

Simplify (3/4 of 4/9 ÷ 9½) ÷ 1 5/19.

1. A.1/25
2. B.1/4
3. C.1/5
4. D.1/36

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

1. A.0.40%
2. B.0.01%
3. C.0.25%
4. D.0.80%

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

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

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

1. A.9:10:15
2. B.12:15:16
3. C.12:15:10
4. D.10:15:24

Evaluate (81/16)^−¼ × 2⁻¹.

1. A.1/3
2. B.6
3. C.3
4. D.1/6

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

1. A.2.5441
2. B.2.0491
3. C.2.1461
4. D.3.1461

Rationalize (2√3 + √5)/(√5 − √3)

1. A.(3√15 + 11)/2
2. B.(3√15 − 11)/2
3. C.3√15 − 11
4. D.3√15 + 11

Express the product of 0.21 and 0.34 in standard form

1. A.7.14 × 10⁻³
2. B.7.14 × 10⁻¹
3. C.7.14 × 10⁻²
4. D.7.14 × 10⁻⁴

Which of the Venn diagrams below represents P'∩Q∩R'?

1. A.Diagram A
2. B.Diagram B
3. C.Diagram C
4. D.Diagram D

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

1. A.15
2. B.5
3. C.10
4. D.20

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

1. A.(5P + MX − 5)/M
2. B.(5P − MX − 5)/M
3. C.(5P − MX + 5)/M
4. D.(5P + MX + 5)/M

If 9x² + 6xy + 4y² is a factor of 27x³ − 8y³, find the other factor.

1. A.3x − 2y
2. B.2y − 3x
3. C.2y + 3x
4. D.3x + 2y

Factorize completely (x³ + 3x² − 10x)/(2x² − 8)

1. A.(x² + 5)/(2x + 4)
2. B.x(x + 5)/2(x + 2)
3. C.x(x − 5)/2(x + 2)
4. D.x(x − 5)/2(x − 2)

Solve for x and y if x − y = 2 and x² − y² = 8

1. A.(1, 3)
2. B.(3, 1)
3. C.(−1, 3)
4. D.(−3, 1)

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

1. A.5
2. B.12
3. C.6
4. D.3

If x is inversely proportional to y and x = 2½ when y = 2, find x if y = 4.

1. A.2¼
2. B.5
3. C.4
4. D.1¼

For what range of values of x is ½x + ¼ > ⅓x + ½?

1. A.x > −3/2
2. B.x > 3/2
3. C.x < 3/2
4. D.x < −3/2

Solve the inequalities −6 ≤ 4 − 2x < 5 − x.

1. A.−1 ≤ x < 6
2. B.−1 < x ≤ 5
3. C.−1 < x < 5
4. D.−1 ≤ x ≤ 6

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

1. A.5/9
2. B.5/7
3. C.5/8
4. D.5/11

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

1. A.44
2. B.−165
3. C.−44
4. D.165

If x * y = x + y², find the value of (2*3)*5.

1. A.36
2. B.11
3. C.25
4. D.55

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

1. A.q = 18
2. B.p = 18
3. C.p<1
4. D.q<1

If |x 3; 2 7| = 15, find the value of x. (Determinant written row by row.)

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

Evaluate |2 0 5; 4 6 3; 8 9 1| (determinant written row by row)

1. A.−42
2. B.102
3. C.18
4. D.−102

If P = (2 −3; 1 1), what is P⁻¹? (Matrices written row by row.)

1. A.(1/5 3/5; 1/5 2/5)
2. B.(1/5 3/5; −1/5 2/5)
3. C.(−1/5 3/5; −1/5 2/5)
4. D.(−1/5 −3/5; −1/5 −2/5)

From the diagram above, find x.

1. A.65°
2. B.50°
3. C.55°
4. D.75°

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

1. A.102°
2. B.52°
3. C.82°
4. D.112°

From the cyclic quadrilateral TUVW above, find the value of x.

1. A.23°
2. B.26°
3. C.24°
4. D.20°

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

1. A.10 cm²
2. B.6 cm²
3. C.8 cm²
4. D.24 cm²

An arc subtends an angle of 50° at the centre of circle of radius 6 cm. Calculate the area of the sector formed. (π = 22/7)

1. A.90/7 cm²
2. B.110/7 cm²
3. C.100/7 cm²
4. D.80/7 cm²

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

1. A.700π m²
2. B.98π m²
3. C.350π m²
4. D.749π m²

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

1. A.y = −x + 6
2. B.y = x + 6
3. C.y = −x − 6
4. D.y = x − 6

Find the distance between the points (½, ½) and (−½, −½).

1. A.√2
2. B.0
3. C.1
4. D.√3

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

1. A.y − 4x + 11 = 0
2. B.y − 4x − 11 = 0
3. C.y + 4x + 11 = 0
4. D.y + 4x − 11 = 0

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

1. A.13/15
2. B.15/17
3. C.8/17
4. D.16/17

If the area of ΔPQR above is 12√3 cm², find the value of q?

1. A.6 cm
2. B.8 cm
3. C.7 cm
4. D.5 cm

If y = (2x + 1)³, find dy/dx.

1. A.3(2x + 1)²
2. B.3(2x + 1)
3. C.6(2x + 1)
4. D.6(2x + 1)²

At what value of x does the function y = −3 − 2x + x² attain a minimum value?

1. A.1
2. B.−4
3. C.−1
4. D.4

Evaluate ∫₀² (x³ + x²) dx.

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

Find ∫(sin x + 2)dx.

1. A.cos x + x² + k
2. B.cos x + 2x + k
3. C.−cos x + 2x + k
4. D.−cos x + x² + k

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

1. A.7
2. B.2
3. C.6
4. D.9

Marks: 1, 2, 3, 4, 5
Frequencies: 2, 2, 8, 4, 4
The table above shows the marks obtained in a given test. How many students took the test?

1. A.15
2. B.20
3. C.16
4. D.13

Marks: 1, 2, 3, 4, 5
Frequencies: 2, 2, 8, 4, 4
The table above shows the marks obtained in a given test. Find the mean mark.

1. A.3.2
2. B.3.0
3. C.3.1
4. D.3.3

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

1. A.√(5/2)
2. B.√10
3. C.√6
4. D.√(2/5)

In how many ways can a committee of 2 women and 3 men be chosen from 6 men and 5 women?

1. A.50
2. B.200
3. C.100
4. D.30

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

1. A.1/8
2. B.1/3
3. C.1/6
4. D.1/9