JAMB UTME - Mathematics - 1985

Swali 1 Ripoti

What is the probability that a number chosen at random from the intergers between 1 and 10 inclusive is either a prime or a multiple of 3?

\frac{7}{10}

\frac{3}{5}

\frac{4}{5}

\frac{3}{10}

Maelezo ya Majibu

Simple Space: (1, 2, 3, 4, 5, 6, 7, 8, 9, 10 = 10)
Prime: (2, 3, 5, 7)
multiples of 3: (3, 6, 9)
Prime or multiples of 3: (2, 3, 5, 6, 7, 9 = 6)
Probability =

\frac{6}{10}

=

\frac{3}{5}

Soma maelezo ya somo kwenye Probability (WAEC)

Probability

Tazama Jibu

Swali 2 Ripoti

Write h in terms of a, b, c, d if $a = \frac{b(1-ch)}{a-dh}$

h = $\frac{a - b}{a d}$

h = $\frac{1 - b}{a d - b c}$

h = $\frac{(a - b)^{2}}{a d - b c}$

h =

\frac{a - b}{a d - b c}

h = $\frac{b - a}{a b - d c}$

Maelezo ya Majibu

a = $\frac{b (1 - c h)}{a - d h}$
a = $\frac{b - b c h}{1 - d h}$
= a - adh
= b - bch
a - b = bch + adn
a - b = adh
a - b = h(ad - bc)
h = $\frac{a - b}{a d - b c}$

Tazama Jibu

Swali 3 Ripoti

In a class of 120 students, 18 of them scored an A grade in mathematics. If the section representing the A grade students on a pie chart has angle Zo at the centre of the circle, what is Z?

15

27

50

52

54

Maelezo ya Majibu

Total students = 120
grade = 18
Zo = $\frac{18}{120}$ x $\frac{360}{1}$
= 54o

Tazama Jibu

Swali 4 Ripoti

In $ \triangle $ XYZ, XY = 13cm, YZ = 9cm, XZ = 11cm and XYZ = $ \theta $. Find cos$ \theta $^o

\frac{4}{39}

\frac{43}{39}

\frac{209}{3}

\frac{43}{78}

Maelezo ya Majibu

cos

θ

=

\frac{13^{2} + 9^{2} - 11^{2}}{2 (13) (9)}

=

\frac{169 + 81 - 21}{26 \times 9}

cos

θ

=

\frac{129}{26 \times 9}

=

\frac{43}{78}

Soma maelezo ya somo kwenye Introductory Calculus (WAEC)

Soma maelezo ya somo kwenye Trigonometry (JAMB)

Introductory Calculus

Trigonometry

Tazama Jibu

Swali 5 Ripoti

22$ \frac{1}{2} $% of the Nigerian Naira is equal to 17$ \frac{1}{10} $% of a foreign currency M. What is the conversion rate of the M to the Naira?

1M = 1

\frac{15}{57}

N

1M = 38

\frac{1}{4}

N

1M = 1

\frac{18}{57}

N

1M = 384

\frac{3}{4}

N

Maelezo ya Majibu

N = 22

\frac{1}{2}

%, M = 17

\frac{1}{10}

%
M =

\frac{171}{10}

%, N =

\frac{45}{2}

\frac{45}{2}

x

\frac{10}{171}

=

\frac{225}{171}

= 1

\frac{54}{171}

= 1

\frac{18}{57}

Soma maelezo ya somo kwenye Percentages (WAEC)

Soma maelezo ya somo kwenye Financial Arithmetic (WAEC)

Percentages

Financial Arithmetic

Tazama Jibu

Swali 6 Ripoti

In the figure, the area of the shaded segment is

3

π

9

\frac{\sqrt{3}}{4}

3

π - 3 \frac{\sqrt{3}}{4}

\frac{(\sqrt{3 - π)}}{4}

π + \frac{9 \sqrt{3}}{4}

Maelezo ya Majibu

Area of sector =

\frac{120}{360} \times π \times (3)^{2} = 3 π

Area of triangle = $\frac{1}{2} \times 3 \times 3 \times \sin 120^{o}$

= $\frac{9}{2} \times \frac{\sqrt{3}}{2} = \frac{9 \sqrt{3}}{4}$

Area of shaded portion = 3 $π - \frac{9 \sqrt{3}}{4}$

= 3 $π - 3 \frac{\sqrt{3}}{4}$

Soma maelezo ya somo kwenye Volumes (WAEC)

Soma maelezo ya somo kwenye Loci (WAEC)

Volumes

Loci

Tazama Jibu

Swali 7 Ripoti

Without using table, calculate the value of 1 + sec2 30o

2

\frac{1}{3}

\frac{2}{15}

\frac{5}{3}

3

\frac{1}{2}

Maelezo ya Majibu

1 + sec2 30o = sec 30o
=

\frac{2}{\sqrt{3}}

\frac{(2)^{2}}{3}

=

\frac{4}{3}

1 + sec2 30o = sec 30o
= 1 +

\frac{4}{\sqrt{3}}

= 2

\frac{1}{3}

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 Loci (JAMB)

Soma maelezo ya somo kwenye Matrices And Determinants (JAMB)

Sine, Cosine And Tangent Of An Angle

Introductory Calculus

Loci

Matrices And Determinants

Tazama Jibu

Swali 8 Ripoti

In the figure, GHIJKLMN is a cube of side a. Find the length of HN.

\sqrt{3 a}

3a

3a2

a

\sqrt{2}

a

\sqrt{3}

Maelezo ya Majibu

HJ2 = a2 + a2 = 2a2

HJ = $\sqrt{2 a^{2}} = a \sqrt{2}$

HN2 = a2 + (a $\sqrt{2}$ )2 = a2 + 2a2 = 3a2

HN = $\sqrt{3 a^{2}}$

= a $\sqrt{3}$ cm

Soma maelezo ya somo kwenye Polynomials (JAMB)

Soma maelezo ya somo kwenye Mensuration (JAMB)

Soma maelezo ya somo kwenye Inequalities (JAMB)

Polynomials

Mensuration

Inequalities

Tazama Jibu

Swali 9 Ripoti

A bag contains 4 white balls and 6 red balls. Two balls are taken from the bag without replacement. What is the probability that they are both red?

\frac{2}{3}

\frac{2}{15}

\frac{1}{2}

\frac{1}{3}

Maelezo ya Majibu

P(R1) =

\frac{6}{10}

=

\frac{2}{3}

P(R1 n R11) = P(both red)

\frac{3}{5}

x

\frac{5}{9}

=

\frac{1}{3}

Soma maelezo ya somo kwenye Probability (WAEC)

Soma maelezo ya somo kwenye Probability (JAMB)

Probability

Tazama Jibu

Swali 10 Ripoti

Find correct to two decimals places $100 + \frac{1}{100} + \frac{3}{1000} + \frac{27}{10000}$

100.02

1000.02

100.22

100.01

100.51

Maelezo ya Majibu

100 +

\frac{1}{100}

+

\frac{3}{1000}

+

\frac{27}{10000}

\frac{1000, 000 + 100 + 30 + 27}{10000}

=

\frac{1, 000.157}{10000}

= 100.02

Soma maelezo ya somo kwenye Number Bases (WAEC)

Soma maelezo ya somo kwenye Areas (WAEC)

Number Bases

Areas

Tazama Jibu

Swali 11 Ripoti

Two points X and Y both on latitude $60^\circ\text{S}$ have longitude $147^\circ\text{E}$ and $153^\circ\text{W}$ respectively. Find to the nearest kilometer the distance between X and Y measured along the parallel of latitude (Take $2\pi R = 4 \times 10^4\text{ km}$, where R is the radius of the earth)

16667km

28850km

8333km

2233km

Maelezo ya Majibu

Length of an area =

\frac{θ}{360}

× 2

π

r
Longitude difference = 147 + 153 = 300oN
distance between xy =

\frac{θ}{360}

× 2

π

R cos60o
=

\frac{300}{360}

× 4 × 104 ×

\frac{1}{2}

= 1.667 × 104km (1667 km)

Soma maelezo ya somo kwenye Circles (WAEC)

Circles

Tazama Jibu

Swali 12 Ripoti

List all integers satisfying the inequality $ -2 \le 2x - 6 < 4 $

2, 3, 4, 5

2, 3, 4

2, 5

3, 4, 5

4, 5

Maelezo ya Majibu

-2 $\leq$ 2x - 6 < 4 = 2x - 6 < 4

= 2x < 10

= x < 5

2x $\geq$ -2 + 6 $\geq$

= x $\geq$ 2

∴ 2 $\leq$ x < 5 [2, 3, 4]

Soma maelezo ya somo kwenye Inequalities (JAMB)

Inequalities

Tazama Jibu

Swali 13 Ripoti

At what real value of x do the curves whose equations are y = x3 + x and y = x2 + 1 intersect?

-2

2

-1

9

1

Maelezo ya Majibu

y = x3 + x and y = x2 + 1

\begin{array}{cc} x & - 2 & - 1 & 0 & 1 & 2 \\ Y = x^{3} + x & - 10 & - 2 & 0 & 2 & 10 \\ y = x^{2} + 1 & 5 & 2 & 1 & 2 & 5 \end{array}

The curves intersect at x = 1

Soma maelezo ya somo kwenye Coordinate Geometry (JAMB)

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Coordinate Geometry

Quadratic Equations

Tazama Jibu

Swali 14 Ripoti

In the figure, PQ is the tangent from P to the circle QRS with SR as its diameter. If QRS = $ \theta^\circ $ and RQP = $ \phi^\circ $, which of the following relationships between $ \theta^\circ $ and $ \phi^\circ $ is correct

θ

^{\circ}

+

ϕ

^{\circ}

= 902

ϕ

^{\circ}

= 902 - 2

θ

^{\circ}

θ

^{\circ}

=

ϕ

^{\circ}

ϕ

^{\circ}

= 2

θ

^{\circ}

θ

^{\circ}

+ 2

ϕ

^{\circ}

Maelezo ya Majibu

180 -

ϕ

^{\circ}

=

θ

^{\circ}

+

ϕ

^{\circ}

(Sum of opposite interior angle equal to its exterior angle)

180 = 2 $ϕ$ + $θ$ $^{\circ}$

Soma maelezo ya somo kwenye Introductory Calculus (WAEC)

Soma maelezo ya somo kwenye Trigonometry (JAMB)

Soma maelezo ya somo kwenye Circles (WAEC)

Introductory Calculus

Trigonometry

Circles

Tazama Jibu

Swali 15 Ripoti

The bearing of a bird on a tree from a hunter on the ground is ₦72oE. What is the bearing of the hunter from the birds?

S 18o W

S 72o W

S 72o E

S 27o E

S 27o W

Maelezo ya Majibu

Bearing of Hunter from Bird is
180 + 27 = 207o
Note that bearing is always taken from the north
207o = S 27o W

Soma maelezo ya somo kwenye Bearings (WAEC)

Bearings

Tazama Jibu

Swali 16 Ripoti

Solve the simultaneous equations 2x - 3y + 10 = 10x - 6y = 5

x = 2

\frac{1}{2}

, y = 3

\frac{1}{2}

x =

\frac{1}{2}

, y =

\frac{3}{2}

x = 2

\frac{1}{4}

, y = 3

\frac{1}{2}

x = 2

\frac{1}{3}

, y = 3

\frac{1}{2}

x = 2

\frac{1}{3}

, y = 2

\frac{1}{2}

Maelezo ya Majibu

2x - 3y = -10; 10x - 6y = -5
2x - 3y = -10 x 2
10x - 6y = 5
4x - 6y = -20 .......(i)
10x - 6y = 5.......(ii)
eqn(ii) - eqn(1)
6x = 15
x =

\frac{15}{6}

=

\frac{5}{2}

x = 2

\frac{1}{2}

Sub. for x in equ.(ii) 10(

\frac{5}{2}

) - 6y = 5
y = 3

\frac{1}{2}

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

Solution Of Linear Equations

Tazama Jibu

Swali 17 Ripoti

Make c the subject of formula $v = 1 - \frac{a}{5}\left(b + \frac{3c}{7}\right)$

[

\frac{7}{3}

+

\frac{5}{a}

(v - 1)] + b

[

\frac{7 b}{3}

+

\frac{5}{a}

(v - 1)]

\frac{7}{3}

[b +

\frac{5}{a}

(v - 1)]

\frac{7}{3}

[b +

\frac{5 v - 1}{a}

]

Change Of Subject Of A Formula/Relation

Solution Of Linear Equations

Tazama Jibu

Swali 18 Ripoti

a sum of money was invested at 8% per annum simple interest. If after 4 years the money amounts to N330.00. Find the amount originally invested

N180.00

n165.00

N150.00

N250.00

N200.00

Maelezo ya Majibu

S.I =

\frac{P T R}{100}

T = 4yrs, R = 8%, a = N330.00

330 - P =

\frac{P T R}{100}

, A = P + I

i.e. A = P +

\frac{P T R}{100}

330 = P +

\frac{P (4) (8)}{100}

33000 = 32P + 100p

132P = 33000

P = N250.00

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

Positive And Negative Integers, Rational Numbers

Tazama Jibu

Swali 19 Ripoti

If three numbers P, Q, R are in ratio 6 : 4 : 5, find the value of $ \frac{3p-q}{4q+r} $

3

2

3

2

3

18

Maelezo ya Majibu

P : Q : r = 6 : 4 : 5
5 = 6 + 4 + 5
= 15
P = $\frac{6}{15}$ , q = $\frac{4}{15}$ , r = $\frac{5}{15}$ = $\frac{1}{3}$
To find $\frac{3 p - q}{4 q + r}$
3p - q = 3 x $\frac{6}{15}$ - $\frac{4}{15}$
$\frac{18}{15}$ - $\frac{4}{15}$ = $\frac{14}{15}$
∴ 4q + r = 4 x $\frac{4}{15}$ + $\frac{5}{15}$
$\frac{16}{15}$ = $\frac{16}{15}$ + $\frac{5}{15}$
= $\frac{21}{15}$
$\frac{14}{15}$ x $\frac{15}{21}$ = $\frac{14}{21}$
= $\frac{2}{3}$

Tazama Jibu

Swali 20 Ripoti

Factorize abx2 + 8y - 4bx - 2axy

(ax - 4)(bx - 2y)

(ax + b)(x - 8y)

(ax - 2y)(bx - 4)

(bx - 4)(ax - 2y)

(abx - 4)(x - 2y)

Maelezo ya Majibu

abx2 + 8y - 4bx - 2axy = (abx2 - 4bx) + (8y - 2axy)
= bx(ax - 4) 2y(ax - 4) 2y(ax - 4)
= (bx - 2y)(ax - 4)

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Algebraic Expressions

Tazama Jibu

Swali 21 Ripoti

The number of goals scored by a football team in 20 matches is shown below:

No. of goals	0	1	2	3	4	5
No. of matches	3	5	7	3	1	0

What are the values of the mean and the mode respectively?

(1.75, 5)

(1.75, 2)

(1.75, 1)

(65, 74)

Maelezo ya Majibu

\begin{array}{cc} x & f & f x \\ 0 & 3 & 0 \\ 1 & 5 & 5 \\ 2 & 7 & 14 \\ 3 & 4 & 12 \\ 4 & 1 & 4 \\ 5 & 0 & 0 \end{array}

\sum f

= 20

\sum f x

= 35
Mean =

\frac{\sum f x}{\sum f}

=

\frac{35}{20}

=

\frac{7}{4}

= 1.75
Mode = 2
= 1.75, 2

Soma maelezo ya somo kwenye Probability (WAEC)

Soma maelezo ya somo kwenye Statistics (WAEC)

Probability

Statistics

Tazama Jibu

Swali 22 Ripoti

In the figure, MNQP is a cyclic quadrilateral. MN and Pq are produced to meet at X and NQ and MP are produced to meet at Y. If MNQ = $86^\circ$ and NQP = $122^\circ$ find ($x^\circ$, $y^\circ$)

28

^{\circ}

, 36

^{\circ}

36

^{\circ}

, 28

^{\circ}

43

^{\circ}

, 61

^{\circ}

61

^{\circ}

, 43

^{\circ}

36

^{\circ}

, 43

^{\circ}

Maelezo ya Majibu

y

^{\circ}

= 180

^{\circ}

- (86

^{\circ}

+ 58

^{\circ}

)

180 - 144 = 36 $^{\circ}$

x $^{\circ}$ = 180 - (94 + 58)

180 -152 = 28

(x $^{\circ}$ , y $^{\circ}$ ) = (28 $^{\circ}$ , 36 $^{\circ}$ )

Soma maelezo ya somo kwenye Polynomials (JAMB)

Soma maelezo ya somo kwenye Differentiation (JAMB)

Soma maelezo ya somo kwenye Inequalities (JAMB)

Polynomials

Differentiation

Inequalities

Tazama Jibu

Swali 23 Ripoti

Arrange the following numbers in ascending order of magnitude $ \frac{6}{7} $, $ \frac{13}{15} $, 0.8650

$\frac{6}{7}$ < 0.865 < $\frac{13}{15}$

$\frac{13}{15}$ < $\frac{6}{7}$ < 0.865

$\frac{6}{7}$ < $\frac{13}{15}$ < 0.865

0.865 < $\frac{6}{7}$ < $\frac{13}{15}$

Maelezo ya Majibu

$\frac{6}{7}$ , $\frac{13}{15}$ , 0.8650

In ascending order, we have 0.8571, 0.8650, 0.8666

i.e. $\frac{6}{7}$ < 0.8650 < $\frac{13}{15}$

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

Fractions, Decimals And Approximations

Tazama Jibu

Swali 24 Ripoti

The factors of 9 - (x2 - 3x - 1)2 are

-(x - 4)(x + 1) (x - 1)(x - 2)

(x - 4)(x - 2) (x - 1)(x + 1)

-(x - 2)(x + 1) (x - 2) (x - 1)

(x - 2)(x + 2) (x - 1)(x + 1)

Maelezo ya Majibu

9 - (x2 - 3x - 1)2 = [3 - (x2 - 3x - 1)] [3 + (x2 - 3x - 1)]
= (3 - x2 + 3x + 1)(3 + x2 - 3x - 1)
= (4 + 3x - x2)(x2 - 3x + 2)
= (4 - x)(1 + x)(x - 1)(x - 2)
= -(x - 4)(x + 1) (x - 1)(x - 2)

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Algebraic Expressions

Tazama Jibu

Swali 25 Ripoti

If $ \cos \theta = \frac{\sqrt{3}}{2} $ and $ \theta $ is less than 90^o. Calculate $ \cos \frac{90-\theta}{\sin^2\theta} $

\frac{4}{\sqrt{3}}

\sqrt{\frac{3}{2}}

\sqrt{\frac{76}{2}}

4

\sqrt{\frac{76}{2}}

Maelezo ya Majibu

cos

\frac{90 - θ}{s i n^{2} θ}

=

\frac{\tan θ}{s i n^{2} θ}

Sin2

θ

=

\frac{1}{4}

\frac{c o s (90 - θ)}{s i n^{2} θ}

=

\frac{1}{\sqrt{3}}

=

\frac{4}{\sqrt{3}}

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

Soma maelezo ya somo kwenye Trigonometry (JAMB)

Sine, Cosine And Tangent Of An Angle

Trigonometry

Tazama Jibu

Swali 26 Ripoti

In $ \triangle $ XYZ, XKZ = 90^O, XK = 15cm, XY = 35cm and YK = 8cm. Find the area of $ \triangle $ XYZ

190 sq.cm

20 sq.cm

210 sq.cm

160sq.cm

320sq.cm

Maelezo ya Majibu

By Pythagoras, KZ2 = 252 - 52

KZ2 = (25 + 15)(25 - 15) = 400

KZ = $\sqrt{400}$ = 20

area of XYZ = $\frac{1}{2} \times 28 \times 15$

= 210 sq. cm

Tazama Jibu

Swali 27 Ripoti

Find x if log9x = 1.5

72.0

27.0

36.0

3.5

24.5

Maelezo ya Majibu

If log9x = 1.5, 91.5 = x
∴ x = 27

Soma maelezo ya somo kwenye Logarithms (WAEC)

Logarithms

Tazama Jibu

Swali 28 Ripoti

If two fair coins are tossed, what is the probability of getting at least one head?

\frac{1}{4}

\frac{1}{2}

1

\frac{43}{78}

\frac{3}{4}

Maelezo ya Majibu

Prob. of getting at least one head
Prob. of getting one head + prob. of getting 2 heads
=

\frac{1}{4}

+

\frac{2}{4}

=

\frac{3}{4}

Tazama Jibu

Swali 29 Ripoti

If the hypotenuse of right angled isosceles triangle is 2, what is the length of each of the other sides?

\sqrt{2}

\frac{1}{2}

22

1

2 - 1

Maelezo ya Majibu

45o =

\frac{x}{2}

, Since 45o =

\frac{1}{\sqrt{2}}

x = 2 x

\frac{1}{\sqrt{2}}

=

\frac{2 \sqrt{2}}{2}

=

\sqrt{2}

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

Soma maelezo ya somo kwenye Statistics (WAEC)

Soma maelezo ya somo kwenye Angles (WAEC)

Angles And Intercepts On Parallel Lines

Statistics

Angles

Tazama Jibu

Swali 30 Ripoti

A solid sphere of radius 4cm has a mass of 64kg. What will be the mass of a shell of the same metal whose internal and external radii are 2cm and 3cm respectively?

5kg

16kg

19kg

6kg

Maelezo ya Majibu

$\frac{1 \sqrt{3}}{(\frac{1}{2})^{2}}$
= $\frac{4}{\sqrt{3}}$
= $\frac{\sqrt{3}}{\sqrt{3}}$
= $\frac{4 \sqrt{3}}{\sqrt{3}}$
m = 64kg, V = $\frac{4 π r^{3}}{3}$
= $\frac{4 π (4)^{3}}{3}$
= $\frac{256 π}{3}$ x 10-6m3
density(P) = $\frac{Mass}{Volume}$
= $\frac{64}{\frac{256 π}{3 \times 10^{- 6}}}$
= $\frac{64 \times 3 \times 10^{- 6}}{256}$
= $\frac{3}{4 \times 10^{- 6}}$
m = PV = $\frac{3}{4 π \times 10^{- 6}}$ x $\frac{4}{3}$ $π$ [32 - 22] x 10-6
$\frac{3}{4 \times 10^{- 6}}$ x $\frac{4}{3}$ x 5 x 10-6
= 5kg

Tazama Jibu

Swali 31 Ripoti

If $e^x = 1 + \frac{x}{2} + \frac{x^2}{1.2} + \frac{x^3}{1.2.3} + .....$ Find $\frac{1}{e^x}$

1 -

\frac{x}{2}

+

\frac{x^{2}}{{1.2}^{3}}

+

\frac{x^{3}}{2^{4} .3}

+ .........

1 -

\frac{x}{2}

+

\frac{x^{2}}{{1.2}^{3}}

+

\frac{x^{4}}{2.4.3}

+ ..

1 +

\frac{x}{2}

+

\frac{x^{2}}{1.2}

+

\frac{x^{3}}{1.2.3}

+

\frac{x^{4}}{1.23.4}

+ .........

1 - x +

\frac{x^{2}}{{1.2}^{3}}

+

\frac{x^{3}}{2^{4} .3}

+ .........

1 +

\frac{x}{2}

+

\frac{x^{2}}{{1.2}^{3}}

+

\frac{x^{4}}{1.2.6}

+ ........

Maelezo ya Majibu

ex = 1 +

\frac{x}{2}

+

\frac{x^{2}}{1.2}

+

\frac{x^{3}}{1.2.3}

+

\frac{x^{4}}{1.23.4}

Tazama Jibu

Swali 32 Ripoti

Find the area of a regular hexagon inscribed in a circle of radius 8cm

16

\sqrt{3}

cm2

96

\sqrt{3}

cm2

192

\sqrt{3}

cm2

16

\sqrt{3}

cm2

33cm2

Maelezo ya Majibu

Area of a regular hexagon = 8 x 8 x sin 60o
= 32 x

\frac{\sqrt{3}}{2}

=
Area = 16

\sqrt{3}

x 6 = 96

\sqrt{3}

cm2

Soma maelezo ya somo kwenye Areas (WAEC)

Areas

Tazama Jibu

Swali 33 Ripoti

Solve for (x, y) in the equation 2x + y = 4: x^2 + xy = -12

(6, -8): (-2, 8)

(3, -4): (-1, 4)

(8, -4): (-1, 4)

(-8, 6): (8, -2)

(-4, 3): (4, -1)

Maelezo ya Majibu

2x + y = 4......(i)
x^2 + xy = -12........(ii)
from eqn (i), y = 4 - 2x
= x2 + x(4 - 2x)
= -12
x2 + 4x - 2x2 = -12
4x - x2 = -12
x2 - 4x - 12 = 0
(x - 6)(x + 2) = 0
sub. for x = 6, in eqn (i) y = -8, 8
=(6,-8); (-2, 8)

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

Solution Of Linear Equations

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Swali 34 Ripoti

If 32y + 6(3y) = 27. Find y

3

-1

2

-3

1

Maelezo ya Majibu

32y + 6(3y) = 27
This can be rewritten as (3y)2 + 6(3y) = 27
Let 3y = x
x2 + 6x - 27 = 0
(x + 9)(x - 3) = 0
when x - 3 = 0, x = 3
sub. for x in 3y = x
3y = 3
log33 = y
y = 1

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

Solution Of Linear Equations

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Swali 35 Ripoti

Solve the following equation $ \frac{2}{2r-1} - \frac{5}{3} = \frac{1}{r+2} $

(

\frac{5}{2}

, 1)

(5, -4)

(2, 1)

(1,

\frac{- 5}{2}

)

(

\frac{- 5}{2}

, 1)

Maelezo ya Majibu

\frac{2}{2 r - 1}

-

\frac{5}{3}

=

\frac{1}{r + 2}

\frac{2}{2 r - 1}

-

\frac{1}{r + 2}

=

\frac{5}{3}

\frac{2 r + 4 - 2 r + 1}{2 r - 1 (r + 2)}

=

\frac{5}{3}

\frac{5}{(2 r + 1) (r + 2)}

=

\frac{5}{3}

5(2r - 1)(r + 2) = 15
(10r - 5)(r + 2) = 15
10r2 + 20r - 5r - 10 = 15
10r2 + 15r = 25
10r2 + 15r - 25 = 0
2r2 + 3r - 5 = 0
(2r2 + 5r)(2r + 5) = r(2r + 5) - 1(2r + 5)
(r - 1)(2r + 5) = 0
r = 1 or

\frac{- 5}{2}

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

Solution Of Linear Equations

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Swali 36 Ripoti

If $a\left\{\frac{x+1}{x-2}-\frac{x-1}{x+2}\right\}=6x$. Find a in its simplest form

x2 - 1

x2 + 1

x2 + 4

x2 - 4

1

Maelezo ya Majibu

a{

\frac{x + 1}{x - 2} - \frac{x - 1}{x + 2}

} = a{

\frac{(x + 1) (x + 2) - (x - 1) (x - 2)}{(x - 2) (x + 2)}

}
= 6

\frac{6 x}{x^{2} - 4}

= 6x
a = x2 - 4

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Algebraic Expressions

Tazama Jibu

Swali 37 Ripoti

Which of these angles can be constructed using ruler and a pair of compasses only?

115o

125o

135o

145o

Volumes

Angles

Tazama Jibu

Swali 38 Ripoti

The ratio of the length of two similar rectangular blocks is 2 : 3. If the volume of the larger block is 351cm3, then the volume of the other block is

234.00 cm3

526.50 cm3

166.00 cm3

687cm3

Maelezo ya Majibu

Let x represent total vol. 2 : 3 = 2 + 3 = 5

\frac{3}{5}

x = 351
x =

\frac{351 \times 5}{3}

= 585
Volume of smaller block =

\frac{2}{3}

x 585
= 234.00

Soma maelezo ya somo kwenye Polynomials (JAMB)

Polynomials

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Swali 39 Ripoti

If the quadratic function 3x2 - 7x + R is a perfect square, find R

\frac{49}{24}

\frac{49}{12}

\frac{49}{13}

\frac{49}{3}

\frac{49}{36}

Maelezo ya Majibu

3x2 - 7x + R. Computing the square, we have
x2 -

\frac{7}{3}

= -

\frac{R}{3}

(

\frac{x}{1} - \frac{7}{6}

)2 = -

\frac{R}{3}

+

\frac{49}{36}

\frac{- R}{3}

+

\frac{49}{36}

= 0
R =

\frac{49}{36}

x

\frac{3}{1}

=

\frac{49}{12}

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

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Fractions, Decimals, Approximations And Percentage

Quadratic Equations

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Swali 40 Ripoti

In the equation below, Solve for x if all the numbers are in base 2: $\frac{11}{x} = \frac{1000}{x+101}$

101

11

110

111

10

Maelezo ya Majibu

\frac{11}{x}

=

\frac{1000}{x + 101}

= 11(x + 101)
1000x = 11x + 1111
1000x - 11x = 1111
101x = 1111
x =

\frac{1111}{101}

x = 11

Soma maelezo ya somo kwenye Number Bases (WAEC)

Number Bases

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Swali 41 Ripoti

If f(x - 2) = 4x2 + x + 7, find f(1)

12

27

7

46

17

Maelezo ya Majibu

f(x - 2) = 4x2 + x + 7
x - 2 = 1, x = 3
f(x - 2) = f(1)
= 4(3)2 + 3 + 7
= 36 + 10
= 46

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

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Solution Of Linear Equations

Algebraic Expressions

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Swali 42 Ripoti

PRSQ is a trapezium of area 14cm2 in which PQ||RS. If PQ = 4cm and SR = 3cm, Find the area of SQR in cm2

7.0

6.0

5.2

5.0

Maelezo ya Majibu

Area of trapezium = 14cm2
Area of trapezium =

\frac{1}{2}

(a + b)h
14 =

\frac{1}{2}

(4 + 3)h
14 =

\frac{7}{2}

h
h =

\frac{14 \times 2}{7}

= 4
Area of SQR =

\frac{1}{2}

(3 x 4)
=

\frac{12}{2}

= 6.0

Tazama Jibu

Swali 43 Ripoti

Find the values of p for which the equation x2 - (p - 2)x + 2p + 1 = 0

(21, 0)

(0, 12)

(1, 2)

(3, 4)

(4, 5)

Maelezo ya Majibu

Equal roots implies b2 - 4ac = 0
a = 1b = - (p - 2), c = 2p + 1
[-(p - 2)]2 - 4 x 1 x (2p + 1) = 0
p2 - 4p + 4 - 4(2p + 1) = 0
p2 - 4p = 4 - 8p - 4 = 0
p2 - 12p = 0
p(p - 12) = 0
p = 0 or 12

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Quadratic Equations

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Swali 44 Ripoti

In a restaurant, the cost of providing a particular type of food is partly constant and partially inversely proportional to the number of people. If cost per head for 100 people is 30k and the cost for 40 people is 60k, Find the cost for 50 people?

15k

20k

50k

40k

45k

Maelezo ya Majibu

C = a + k

\frac{1}{N}

= c
=

\frac{a N + k}{N}

CN = aN + K
30(100) = a(100) + k
3000 = 100a + k.......(i)
60(40) = a(40) + k
2400 = 40a + k.......(ii)
eqn (i) - eqn (ii)
600 = 60a
a = 10
subt. for a in eqn (i) 3000 = 100(10) + K
3000 - 1000 = k
k = 2000
CN = 10N + 2000. when N = 50,
50C = 10(50) + 2000
50C = 500 + 2000
C =

\frac{2500}{50}

= 50k

Soma maelezo ya somo kwenye Variation (WAEC)

Soma maelezo ya somo kwenye Linear Inequalities (WAEC)

Variation

Linear Inequalities

Tazama Jibu

Swali 45 Ripoti

John gives one-third of his money to Janet who has ₦105.00. He then finds that his money is reduced to one-fourth of what Janet now has. Find how much money john has at first

₦45.00

₦48.00

₦52.00

₦60.00

₦53.00

Maelezo ya Majibu

Let x be John's money, Janet already had ₦105,

\frac{1}{3}

of x was given to Janet
Janet now has

\frac{1}{3^{2}}

x + 105 =

\frac{x + 315}{3}

John's money left =

\frac{2}{3}

x
=

\frac{\frac{1}{4} (x + 315)}{3}

=

\frac{2}{3}

24x = 3x + 945
∴ x = 45

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

Fractions, Decimals And Approximations

Tazama Jibu

Swali 46 Ripoti

$(\sqrt{2} + 4\sqrt{2})(\sqrt{3} + \sqrt{2})(\sqrt{3} + \sqrt{2})$ is equal to

1

(

\sqrt{2} + 4 \sqrt{2}

)

(6

\sqrt{2}

8

Maelezo ya Majibu

(

\sqrt{2} + 4 \sqrt{2}

) (

\sqrt{3} + \sqrt{2}

) (

\sqrt{3} + \sqrt{2}

)
(

\sqrt{3} + \sqrt{2}

+ (

\sqrt{3} + \sqrt{2}

) = 3 + (

\sqrt{6} - \sqrt{6}

) - 2
= 1

Tazama Jibu

Swali 47 Ripoti

Find the missing value in the table below

x	-4	-3	-2	-1	0	1	2	3
y=4?3x?x^3	80		18	8	4	0	-10	-32

-32

-14

40

22

37

Maelezo ya Majibu

When x = -3, y = 4 - 3(3) - (-3)3

= 4 + 9 + 27

= 13 + 27

= 40

Tazama Jibu






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