JAMB UTME - Mathematics - 1981

Swali 1 Ripoti

If b = a + cp and r = ab + $\frac{1}{2}$cp², express b² in terms of a, c, r.

b² = aV + 2cr

b² = ar + 2c²r

b² = a² = $\frac{1}{2}$ cr²

b² = $\frac{1}{2}$ar² + c

b² = 2cr - a² Jibu sahihi

Maelezo ya Majibu

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Algebraic Expressions

Tazama Jibu

Swali 2 Ripoti

Marks scored by some children in an arithmetic test are:5, 3, 6, 9, 4, 7, 8, 6, 2, 7, 8, 4, 5, 2, 1, 0, 6, 9, 0, 8.
The arithmetic mean of the marks is

5 Jibu sahihi

Maelezo ya Majibu

Soma maelezo ya somo kwenye Integration (JAMB)

Soma maelezo ya somo kwenye Euclidean Geometry (JAMB)

Soma maelezo ya somo kwenye Statistics (WAEC)

Integration

Euclidean Geometry

Statistics

Tazama Jibu

Swali 3 Ripoti

If $\sin x° = \frac{a}{b}$, what is $\sin (90 - x)°$?

$\frac{\sqrt{b^2 - a^2}}{b}$ Jibu sahihi

1$\frac{-a}{b}$

$\frac{b^2 - a^2}{b}$

$\frac{a^2 - b^2}{b}$

$\sqrt{b^2 - a^3}$

Maelezo ya Majibu

Tazama Jibu

Swali 4 Ripoti

In $\bigtriangleup$XYZ, XY = 3cm, XZ = 5cm and YZ = 7cm. If the bisector of XYZ meets XZ at W, what is the length of XW?

1.5cm Jibu sahihi

2.5cm

3cm

4cm

None of the above

Maelezo ya Majibu

Soma maelezo ya somo kwenye Number Bases (WAEC)

Soma maelezo ya somo kwenye Triangles And Polygons (WAEC)

Number Bases

Triangles And Polygons

Tazama Jibu

Swali 5 Ripoti

The area of a circular plate is one-sixteenth the surface area of a ball of a ball, If the area of the plate is given as P cm², then the radius of the ball is

$\frac{2P}{\pi}$

$\frac{P}{\sqrt{\pi}}$

$\frac{P}{\sqrt{2\pi}}$

2$\frac{P}{\pi}$ Jibu sahihi

Maelezo ya Majibu

Soma maelezo ya somo kwenye Circles (WAEC)

Circles

Tazama Jibu

Swali 6 Ripoti

A micrometer is defined as one millionth of a millimeter. A length of 12,000 micrometres may be represented as

0.00012m

0.0000012m

0.000012m Jibu sahihi

0.00000012m

0.000000012m

Maelezo ya Majibu

Soma maelezo ya somo kwenye Positive And Negative Integers, Rational Numbers (WAEC)

Soma maelezo ya somo kwenye Number Bases (WAEC)

Positive And Negative Integers, Rational Numbers

Number Bases

Tazama Jibu

Swali 7 Ripoti

In the figure, the chords XY and ZW are produced to meet at T such that YT = WT, ZYW = 40o and YTW = 30o. What is YXW?

50^o

75^o

35^o Jibu sahihi

115^o

30^o

Maelezo ya Majibu

Soma maelezo ya somo kwenye Circles (WAEC)

Soma maelezo ya somo kwenye Euclidean Geometry (JAMB)

Soma maelezo ya somo kwenye Triangles And Polygons (WAEC)

Circles

Euclidean Geometry

Triangles And Polygons

Tazama Jibu

Swali 8 Ripoti

Solve the given equation $(\log_{3} x)^{2} - 6(\log_{3} x) + 9 = 0$

27 Jibu sahihi

$\frac{1}{27}$

Maelezo ya Majibu

Soma maelezo ya somo kwenye Logarithms (WAEC)

Logarithms

Tazama Jibu

Swali 9 Ripoti

The first term of an Arithmetic progression is 3 and the fifth term is 9. Find the number of terms in the progression if the sum is 81

9 Jibu sahihi

Maelezo ya Majibu

Soma maelezo ya somo kwenye Sequence And Series (WAEC)

Sequence And Series

Tazama Jibu

Swali 10 Ripoti

In one and a half hours, the minute hand of a clock rotates through an angle of

90^o

180^o

640^o

450^o

540^o Jibu sahihi

Maelezo ya Majibu

Soma maelezo ya somo kwenye Indices (WAEC)

Indices

Tazama Jibu

Swali 11 Ripoti

If $\log_{2} y = 3 - \log_{2} x^{\frac{3}{2}}$, find y when x = 4.

$\sqrt{65}$

4$\sqrt{2}$

1 Jibu sahihi

Maelezo ya Majibu

Soma maelezo ya somo kwenye Logarithms (WAEC)

Logarithms

Tazama Jibu

Swali 12 Ripoti

Multiply x² + x + 1 by x² - x + 1

x⁴ - x + x²

x⁴ - x² + x²

x⁴ + x² + 1 Jibu sahihi

x⁴ + x²

Maelezo ya Majibu

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Algebraic Expressions

Quadratic Equations

Tazama Jibu

Swali 13 Ripoti

The positive root of t in the following equation, 4t2 + 7t - 1 = 0, correct to 4 places of decimal, is

1.0622

10.6225

0.1328 Jibu sahihi

0.3218

2.0132

Maelezo ya Majibu

Soma maelezo ya somo kwenye Modular Arithmetic (WAEC)

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Modular Arithmetic

Quadratic Equations

Tazama Jibu

Swali 14 Ripoti

Given that 10x = 0.2 and log102 = 0.3010, find x

-1.3010

-0.6990 Jibu sahihi

0.6990

1.3010

0.02

Maelezo ya Majibu

Soma maelezo ya somo kwenye Number Bases (WAEC)

Soma maelezo ya somo kwenye Logarithms (WAEC)

Number Bases

Logarithms

Tazama Jibu

Swali 15 Ripoti

Simplify $\frac{\sqrt{2}}{\sqrt{3} - \sqrt{2}}$ - $\frac{3 - 2}{\sqrt{3} + \sqrt{2}}$

2$\sqrt{2} - \sqrt{3}$

3($\sqrt{6}$ - 1) Jibu sahihi

$\sqrt{6}$ - 3

-$\frac{1}{2}$

$\frac{-\sqrt{3}}{\sqrt{2} - \sqrt{2}}$

Maelezo ya Majibu

Tazama Jibu

Swali 16 Ripoti

Show that $\frac{\sin 2x}{1 + \cos x}$ + $\frac{sin2 x}{1 - cos x}$ is

sin x

cos²x

2 Jibu sahihi

Maelezo ya Majibu

Soma maelezo ya somo kwenye Sine, Cosine And Tangent Of An Angle (WAEC)

Soma maelezo ya somo kwenye Introductory Calculus (WAEC)

Soma maelezo ya somo kwenye Surds (radicals) (WAEC)

Sine, Cosine And Tangent Of An Angle

Introductory Calculus

Surds (radicals)

Tazama Jibu

Swali 17 Ripoti

An isosceles triangle of sides 13cm, 13cm, 10cm is inscribed in a circle. What is the radius of the circle?

7cm Jibu sahihi

12cm

8cm

6.5cm

69cm

Maelezo ya Majibu

Soma maelezo ya somo kwenye Circles (WAEC)

Circles

Tazama Jibu

Swali 18 Ripoti

In the figure, find x in terms of a, b and c.

a + b + c Jibu sahihi

180^o - (a + b + c)

a - b - c

a + b

a + c

Maelezo ya Majibu

Soma maelezo ya somo kwenye Polynomials (JAMB)

Soma maelezo ya somo kwenye Euclidean Geometry (JAMB)

Polynomials

Euclidean Geometry

Tazama Jibu

Swali 19 Ripoti

simplify $\frac{6^{2n + 1} \times 9^n \times 4^{2n}}{18^n \times 2^n \times 12^{2n}}$

3²ⁿ

3 x 2^{3n - 1}

2ⁿ

6 Jibu sahihi

Maelezo ya Majibu

Soma maelezo ya somo kwenye Indices (WAEC)

Soma maelezo ya somo kwenye Modular Arithmetic (WAEC)

Indices

Modular Arithmetic

Tazama Jibu

Swali 20 Ripoti

A group of 14 children children received the following scores in a reading test: 35, 35, 26, 26, 26, 29, 29, 29, 12, 25, 25, 25, 25, 17. What was the median score?

26 Jibu sahihi

Maelezo ya Majibu

Soma maelezo ya somo kwenye Sets (JAMB)

Sets

Tazama Jibu

Swali 21 Ripoti

In the figure, WU//YZ, WY//YZ = 12cm, VZ = 6cm, XU = 8cm. Determine the length of WU.

1cm``3cm

6cm

2cm

4cm Jibu sahihi

Maelezo ya Majibu

Tazama Jibu

Swali 22 Ripoti

Simplify T = $\frac{4R_2}{R_1^{-1} + R_2^{-1} + 4R_3^{-1}}$

$\frac{4R_1 \times R_2 R_3}{R_2R_3 + R_1R_3 + 4R_1 R_2}$ Jibu sahihi

$\frac{R_1 R_2 R_3}{R_2R_3 + R_1R_2 + 4R_1 R_2}$

$\frac{16R_1 R_2 R_3}{R_2R_3 + R_1R_2 + R_1 R_2}$

$\frac{4R_1 R_2 R_3}{4R_2R_3 + R_1R_2 + 4R_1 R_2}$

Maelezo ya Majibu

Soma maelezo ya somo kwenye Logical Reasoning (WAEC)

Soma maelezo ya somo kwenye Algebraic Fractions (WAEC)

Soma maelezo ya somo kwenye Simple Operations On Algebraic Expressions (WAEC)

Logical Reasoning

Algebraic Fractions

Simple Operations On Algebraic Expressions

Tazama Jibu

Swali 23 Ripoti

Suppose x varies inversely as y, y varies directly as the square of t and x = 1, when t = 3. Find x when t = $\frac{1}{3}$.

81 Jibu sahihi

$\frac{1}{9}$

$\frac{1}{27}$

$\frac{1}{81}$

Maelezo ya Majibu

Tazama Jibu

Swali 24 Ripoti

If sine x equals cosine x, what is x in radians?

$\frac{\pi}{2}$

$\frac{\pi}{3}$

$\frac{\pi}{4}$ Jibu sahihi

$\frac{\pi}{6}$

$\frac{\pi}{12}$

Maelezo ya Majibu

Soma maelezo ya somo kwenye Sine, Cosine And Tangent Of An Angle (WAEC)

Sine, Cosine And Tangent Of An Angle

Tazama Jibu

Swali 25 Ripoti

The ratio of the price of a loaf of bread to the price of a packet of sugar in 1975 was r : t. In 1980, the price of a loaf went up by 25% and that of a packet of sugar went up by 10%. Their new ratio is now

40r:50t

44r : 50t

50r : 44t Jibu sahihi

44r:55t

55r:44t

Maelezo ya Majibu

Soma maelezo ya somo kwenye Sine, Cosine And Tangent Of An Angle (WAEC)

Soma maelezo ya somo kwenye Variation (WAEC)

Soma maelezo ya somo kwenye Ratio, Proportions And Rates (WAEC)

Sine, Cosine And Tangent Of An Angle

Variation

Ratio, Proportions And Rates

Tazama Jibu

Swali 26 Ripoti

The number 25 when converted from the tens and units base to the binary base (base two) is one of the following

10011

111011

111000

11001 Jibu sahihi

110011

Maelezo ya Majibu

Soma maelezo ya somo kwenye Number Bases (WAEC)

Number Bases

Tazama Jibu

Swali 27 Ripoti

The difference between 4$\frac{5}{7}$ and 2$\frac{1}{4}$ greater by

$\frac{23}{28}$

$\frac{24}{28}$

$\frac{50}{56}$ Jibu sahihi

$\frac{27}{28}$

$\frac{48}{56}$

Maelezo ya Majibu

Soma maelezo ya somo kwenye Positive And Negative Integers, Rational Numbers (WAEC)

Soma maelezo ya somo kwenye Fractions, Decimals, Approximations And Percentage (JAMB)

Positive And Negative Integers, Rational Numbers

Fractions, Decimals, Approximations And Percentage

Tazama Jibu

Swali 28 Ripoti

The weights of 30 new-born babies are given as follow: 6, 9, 5, 7, 6, 7, 5, 8, 9, 5, 7, 5, 8, 7, 8, 7, 5, 6, 5, 7, 6, 9, 9, 7, 8, 8, 7, 8, 9, 8. The mode is

7 Jibu sahihi

Maelezo ya Majibu

Soma maelezo ya somo kwenye Linear Inequalities (WAEC)

Soma maelezo ya somo kwenye Algebraic Fractions (WAEC)

Soma maelezo ya somo kwenye Angles And Intercepts On Parallel Lines (WAEC)

Soma maelezo ya somo kwenye Progression (JAMB)

Soma maelezo ya somo kwenye Areas (WAEC)

Linear Inequalities

Algebraic Fractions

Angles And Intercepts On Parallel Lines

Progression

Areas

Tazama Jibu

Swali 29 Ripoti

What is the length of an arc of a circle that substends 2$\frac{1}{2}$ radians at the centre when the raduis of the circle = $\frac{k}{k + 1}$ + $\frac{k + 1}{k}$ then

p< 0

p$\geq$ 0

p $\leq$ 0

p < 1

p > 0 Jibu sahihi

Maelezo ya Majibu

Soma maelezo ya somo kwenye Circles (WAEC)

Soma maelezo ya somo kwenye Surds (radicals) (WAEC)

Circles

Surds (radicals)

Tazama Jibu

Swali 30 Ripoti

The sum of the root of a quadratic equation is $\frac{5}{2}$ and the product of its root is 4. The quadratic equation is

x + 8x² - 5 = 0

2x² - 5x + 8 = 0 Jibu sahihi

2x² - 8x + 5 = 0

x² + 8x - 5 = 0

Maelezo ya Majibu

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Quadratic Equations

Tazama Jibu

Swali 31 Ripoti

What is the area between two concentric circles of diameters 26cm and 20cm?

100$\pi$

169$\pi$

69$\pi$ Jibu sahihi

9$\pi$

269$\pi$

Maelezo ya Majibu

Soma maelezo ya somo kwenye Volumes (WAEC)

Soma maelezo ya somo kwenye Areas (WAEC)

Volumes

Areas

Tazama Jibu

Swali 32 Ripoti

A sum of money invested at 5% per annum simple interest amounts to $285.20 after 3 years. How long will it take the same sum to amount to $434.00 at 7$\frac{1}{2}$% per annum simple interest?

7$\frac{1}{2}$ years

10 years Jibu sahihi

5 years

12 years

14 years

Maelezo ya Majibu

Soma maelezo ya somo kwenye Sine, Cosine And Tangent Of An Angle (WAEC)

Soma maelezo ya somo kwenye Ratio, Proportions And Rates (WAEC)

Sine, Cosine And Tangent Of An Angle

Ratio, Proportions And Rates

Tazama Jibu

Swali 33 Ripoti

Evaluate $\frac{6.3 \times 10^5}{8.1 \times 10^3}$ to 3 significant fiqures

77.80 Jibu sahihi

778.0

7.870

8.770

88.70

Maelezo ya Majibu

Soma maelezo ya somo kwenye Number Bases (WAEC)

Soma maelezo ya somo kwenye Indices (WAEC)

Number Bases

Indices

Tazama Jibu

Swali 34 Ripoti

What is the size of an exterior angle of a regular pentagon?

36^o

60^o

72^o Jibu sahihi

120^o

360^o

Maelezo ya Majibu

Tazama Jibu

Swali 35 Ripoti

In the figure, find the area of XYZW

60cm²

54cm²

27cm² Jibu sahihi

54$\sqrt{2}$cm²

27$\sqrt{2}$cm²

Maelezo ya Majibu

Soma maelezo ya somo kwenye Volumes (WAEC)

Soma maelezo ya somo kwenye Loci (JAMB)

Soma maelezo ya somo kwenye Coordinate Geometry (JAMB)

Soma maelezo ya somo kwenye Inequalities (JAMB)

Volumes

Loci

Coordinate Geometry

Inequalities

Tazama Jibu

Swali 36 Ripoti

In the diagram, XZ is the diameter of a circle's radius $\frac{5}{2}$. If XY is 4cm, then the area of the triangle XYZ is

12cm²

28$\frac{1}{2}$cm²

16cm²

10cm²

6cm² Jibu sahihi

Maelezo ya Majibu

Soma maelezo ya somo kwenye Circles (WAEC)

Circles

Tazama Jibu

Swali 37 Ripoti

Solve $\frac{1}{x + 1}$ - $\frac{1}{x + 3}$ = $\frac{1}{4}$

x = -1 or 3

x = 1 or 3

x = 1 or -5 Jibu sahihi

x = -1 or 5

x = -1 or -3

Maelezo ya Majibu

Soma maelezo ya somo kwenye Solution Of Linear Equations (WAEC)

Solution Of Linear Equations

Tazama Jibu

Swali 38 Ripoti

Find a two-digit number such that three times the tens digit is 2 less than twice the units digit and twice the number is 20 greater than the number obtained by reversing the digits

47 Jibu sahihi

Maelezo ya Majibu

Soma maelezo ya somo kwenye Number Bases (WAEC)

Soma maelezo ya somo kwenye Modular Arithmetic (WAEC)

Number Bases

Modular Arithmetic

Tazama Jibu

Swali 39 Ripoti

Find the value of x satisfying $\frac{x}{2}$ - $\frac{1}{3}$ < $\frac{2x}{5}$ + $\frac{1}{6}$

x < 5 Jibu sahihi

x < 7$\frac{1}{2}$

x > 5

x > 7$\frac{1}{2}$

Maelezo ya Majibu

Soma maelezo ya somo kwenye Solution Of Linear Equations (WAEC)

Solution Of Linear Equations

Tazama Jibu

Swali 40 Ripoti

Which of the following fractions is less than one-third?

$\frac{22}{63}$

$\frac{4}{11}$

$\frac{15}{46}$ Jibu sahihi

$\frac{33}{98}$

$\frac{122}{303}$

Maelezo ya Majibu

Soma maelezo ya somo kwenye Positive And Negative Integers, Rational Numbers (WAEC)

Soma maelezo ya somo kwenye Number Bases (WAEC)

Positive And Negative Integers, Rational Numbers

Number Bases

Tazama Jibu

Swali 41 Ripoti

7 pupils of average age 12 years leave a class of 25 pupils of average age 14 years. If 6 new pupils of average age 11years join the class, what is the average age of the pupils now in the class?

13years

12 years 7$\frac{1}{2}$ months

13 years 5 months

13 years 10 months Jibu sahihi

11 years

Maelezo ya Majibu

Soma maelezo ya somo kwenye Modular Arithmetic (WAEC)

Soma maelezo ya somo kwenye Lengths And Perimeters (WAEC)

Modular Arithmetic

Lengths And Perimeters

Tazama Jibu

Swali 42 Ripoti

The difference between the length and width of a rectangle is 6cm and the area is 135cm2. What is the length?

25cm

18cm

15cm Jibu sahihi

24cm

27cm

Maelezo ya Majibu

Soma maelezo ya somo kwenye Volumes (WAEC)

Soma maelezo ya somo kwenye Lengths And Perimeters (WAEC)

Volumes

Lengths And Perimeters

Tazama Jibu

Swali 43 Ripoti

Evaluate correct to 4 decimal places 827.51 x 0.015

8.8415

12.4127 Jibu sahihi

124.1265

12.4120

114.1265

Maelezo ya Majibu

Soma maelezo ya somo kwenye Fractions, Decimals And Approximations (WAEC)

Fractions, Decimals And Approximations

Tazama Jibu

Swali 44 Ripoti

By selling an article for N45.00 a man makes a profit of 80%. For how much should he have sold it in order to make a profit of 32%?

N180.00

N59.00

N63.00

N58.00

N55.00 Jibu sahihi

Maelezo ya Majibu

Soma maelezo ya somo kwenye Sine, Cosine And Tangent Of An Angle (WAEC)

Soma maelezo ya somo kwenye Modular Arithmetic (WAEC)

Soma maelezo ya somo kwenye Number Bases (JAMB)

Sine, Cosine And Tangent Of An Angle

Modular Arithmetic

Number Bases

Tazama Jibu

Swali 45 Ripoti

Two cars X and Y start at the same point and travel towards a point P which is 150km away. If the average speed of Y is 60km per hour and x arrives at P 25 minutes earlier than Y. What is the average speed of X?

51$\frac{3}{7}$km per hour

72km per hour Jibu sahihi

37$\frac{1}{2}$ km per hour

66km per hour

75km per hour

Maelezo ya Majibu

Tazama Jibu

Swali 46 Ripoti

A baking recipe calls for 2.5kg of sugar and 4.5kg of flour. With this recipe some cakes were baked using 24.5kg of a mixture of sugar and flour. How much sugar was used?

12.25kg

6.75kg

8.75kg Jibu sahihi

15.75kg

8.25kg

Maelezo ya Majibu

Soma maelezo ya somo kwenye Modular Arithmetic (WAEC)

Soma maelezo ya somo kwenye Number Bases (JAMB)

Modular Arithmetic

Number Bases

Tazama Jibu

Swali 47 Ripoti