JAMB UTME - Mathematics - 1986

If x varies directly as y3 and x = 2 when y = 1, find x when y = 5

2

10

125

250

Awọn alaye Idahun

x

α

y3
x = ky3
k =

\frac{x}{y^{3}}

when x = 2, y = 1
k = 2
Thus x = 2y3 - equation of variation
= 2(5)3
= 250

Ka ìwé ẹ̀kọ́ nípa Variation (JAMB)

Variation

Wo Idahun

Ibeere 2 Ìròyìn

Find n if log24 + log27 - log2n = 1

10

14

27

28

Awọn alaye Idahun

log24 + log27 - log2n = 1
= log2(4 x 7) - log2n = 1
= log228 - log2n
= log

\frac{28}{2 n}

\frac{28}{2 n}

= 21
= 2
2n = 28
∴ n = 14

Ka ìwé ẹ̀kọ́ nípa Logarithms (WAEC)

Logarithms

Wo Idahun

Ibeere 3 Ìròyìn

Simplify $ \frac{0.0324 \times 0.00064}{0.48 \times 0.012} $

3.6 x 102

3.6 x 10-2

3.6 x 10-3

3.6 x 10-4

Awọn alaye Idahun

\frac{0.0324 \times 0.00064}{0.48 \times 0.012}

=

\frac{324 \times 10^{- 4} \times 10^{- 5}}{48 x 10^{- 2} x 12 x 10^{- 3}}

\frac{324 \times 64 \times 1 0^{- 9}}{48 \times 12 \times 10^{- 5}}

= 36 x 10-4
= 3.6 x 10-3

Wo Idahun

Ibeere 4 Ìròyìn

Simplify $\left(\frac{1}{\sqrt{5}+\sqrt{3}}-\frac{1}{\sqrt{5}-\sqrt{3}}\right)x\frac{1}{\sqrt{3}}$

√3

√5

2√3

7

-2

-1

Awọn alaye Idahun

(

\frac{1}{\sqrt{5} + \sqrt{3}} - \frac{1}{\sqrt{5} - \sqrt{3}}

x

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

)

\frac{1}{\sqrt{5} + \sqrt{3}} - \frac{1}{\sqrt{5} - \sqrt{3}}

=

\frac{\sqrt{5} - \sqrt{3} - (\sqrt{5} + \sqrt{3})}{(\sqrt{5} + \sqrt{3}) (5 \sqrt{3})}

=

\frac{- 2 \sqrt{3}}{5 - 3}

=

\frac{- 2 \sqrt{3}}{7}

Ka ìwé ẹ̀kọ́ nípa Number Bases (WAEC)

Ka ìwé ẹ̀kọ́ nípa Surds (radicals) (WAEC)

Number Bases

Surds (radicals)

Wo Idahun

Ibeere 5 Ìròyìn

Of the nine hundred students admitted in a university in 1979, the following was the distribution by state: Anambrs 185, Imo 135, Kaduna 90, Kwara 110, Ondo 155, Oyo 225. In a pie chart drawn to represent this distribution, The angle subtended at the centre by anambra is

50o

65o

74o

88o

Awọn alaye Idahun

Anambra =

\frac{185}{900}

x

\frac{360}{1}

= 74o

Ka ìwé ẹ̀kọ́ nípa Variation (JAMB)

Ka ìwé ẹ̀kọ́ nípa Euclidean Geometry (JAMB)

Ka ìwé ẹ̀kọ́ nípa Sets (JAMB)

Variation

Euclidean Geometry

Sets

Wo Idahun

Ibeere 6 Ìròyìn

The table below gives the scores of a group of students in a Mathematical test.

Scores	1	2	3	4	5	6	7	8
Frequency	2	4	7	14	12	6	4	1

If the mode in m and the number of students who scored 4 or less is s. What is (s, m)?

(27, 4)

(14,4)

(13,4)

(4,4)

Awọn alaye Idahun

M = mode = the number having the highest frequency = 4
S = Number of students with 4 or less marks
= 14 + 7 + 4 + 2
= 27
∴ (M,S) = (27, 4)

Ka ìwé ẹ̀kọ́ nípa Representation Of Data (JAMB)

Ka ìwé ẹ̀kọ́ nípa Number Bases (WAEC)

Representation Of Data

Number Bases

Wo Idahun

Ibeere 7 Ìròyìn

If $ \frac{a}{c} = \frac{c}{d} = k $, find the value of $ \frac{3a^2-ac+c^2}{3b^2-bd+d^2} $

3k2

2k - k2

\frac{3 b^{2} k^{2} - b k^{2} d + d k^{2}}{3 b^{2} - b d + d^{2}}

k2

Awọn alaye Idahun

\frac{a}{c}

=

\frac{c}{d}

= k
∴

\frac{a}{b}

= bk

\frac{c}{d}

= k
∴ c = dk
=

\frac{3 a^{2} - a c + c^{2}}{3 b^{2} - b d + d^{2}}

=

\frac{3 (b k)^{2} - (b k) (d k) + d k^{2}}{3 b^{2} - b d + a^{2}}

=

\frac{3 b^{2} k^{2} - b k^{2} d + d k^{2}}{3 b^{2} - b d + d^{2}}

k =

\frac{3 b^{2} k^{2} - b k^{2} d + d k^{2}}{3 b^{2} - b d + d^{2}}

Ka ìwé ẹ̀kọ́ nípa Circles (WAEC)

Ka ìwé ẹ̀kọ́ nípa Algebraic Expressions (WAEC)

Ka ìwé ẹ̀kọ́ nípa Quadratic Equations (WAEC)

Ka ìwé ẹ̀kọ́ nípa Graphs Of Linear And Quadratic Functions (WAEC)

Circles

Algebraic Expressions

Quadratic Equations

Graphs Of Linear And Quadratic Functions

Wo Idahun

Ibeere 8 Ìròyìn

A girl walks 45 meters in the direction 050o from a point Q to a point X. She then walks 24 meters in the direction 140o from X to a point Y. How far is she then from Q?

69m

57m

51m

21m

Awọn alaye Idahun

QY = 452 + 242 = 2025 + 576
= 2601
QY =

\sqrt{2601}

= 51

Ka ìwé ẹ̀kọ́ nípa Euclidean Geometry (JAMB)

Euclidean Geometry

Wo Idahun

Ibeere 9 Ìròyìn

If P = 18, Q = 21, R = -6 and S = -4, Calculate $ \frac{(P-Q)^3+S^2}{R^3} + S^2 $

-11

216

11

216

-43

116

43

116

Awọn alaye Idahun

\frac{(P - Q)^{3} + S^{2}}{R^{3}}

=

\frac{(18 - 21)^{3} + (- 4)^{2}}{(- 6)^{3}}

=

\frac{- 27 + 16}{R^{3}}

=

\frac{- 11}{- 216}

=

\frac{11}{216}

Ka ìwé ẹ̀kọ́ nípa Algebraic Expressions (WAEC)

Algebraic Expressions

Wo Idahun

Ibeere 10 Ìròyìn

In the figure, $ \triangle $PQT is isosceles. PQ = QT, SRQ = $35^\circ$, TPQ = $20^\circ$ and PQR is a straight line.Calculate TSR

20

^{\circ}

55

^{\circ}

75

^{\circ}

140

^{\circ}

Awọn alaye Idahun

Given

△

isosceles PQ = QT, SRQ = 35

^{\circ}

TPQ = 20 $^{\circ}$

PQR = is a straight line

Since PQ = QT, angle P = angle T = 20 $^{\circ}$

Angle PQR = 180 $^{\circ}$ - (20 + 20) = 140 $^{\circ}$

TQR = 180 $^{\circ}$ - 140 $^{\circ}$ = 40 $^{\circ}$ < on a straight line

QSR = 180 $^{\circ}$ - (40 + 35) $^{\circ}$ = 105 $^{\circ}$

TSR = 180 $^{\circ}$ - 105 $^{\circ}$

= 75 $^{\circ}$

Wo Idahun

Ibeere 11 Ìròyìn

Find the reciprocal of $ \frac{\frac{2}{3}}{\frac{1}{2}+\frac{1}{3}} $

4

5

4

2

5

6

7

Awọn alaye Idahun

\frac{2}{3}

=

\frac{2}{3}

=

\frac{2}{3}

x

\frac{6}{5}

=

\frac{4}{5}

reciprocal of

\frac{4}{5}

=

\frac{1}{\frac{4}{5}}

=

\frac{5}{4}

Ka ìwé ẹ̀kọ́ nípa Fractions, Decimals And Approximations (WAEC)

Ka ìwé ẹ̀kọ́ nípa Positive And Negative Integers, Rational Numbers (WAEC)

Fractions, Decimals And Approximations

Positive And Negative Integers, Rational Numbers

Wo Idahun

Ibeere 12 Ìròyìn

The figure is a solid with the trapezium PQRS as its uniform cross-section. Find its volume

120m2

576m3

816m3

1056m3

Awọn alaye Idahun

Volume of solid = cross section x H

Since the cross section is a trapezium

= $\frac{1}{2} (6 + 11) \times 12 \times 8$

= 6 x 17 x 8 = 816m3

Ka ìwé ẹ̀kọ́ nípa Volumes (WAEC)

Volumes

Wo Idahun

Ibeere 13 Ìròyìn

An open rectangular box externally measures 4m x 3m x 4m. Find the total cost of painting the box externally if it costs ₦2.00 to paint one square meter

₦96.00

₦112.00

₦136.00

₦160.00

Awọn alaye Idahun

Total surface area(s) = 2(4 x 3) + 2(4 x 4)
= 2(12) + 2(16)
= 24 + 32
= 56cm2
1m2 costs ₦2.00
∴ 56m∴ will cost 56 x ₦2.00
= ₦112.00

Wo Idahun

Ibeere 14 Ìròyìn

Factorize x2 + 2a + ax + 2x

(x + 2a)(x + 1)

(x + 2a)(x - 1)

(x2 - 1)(x - a)

(x + 2)(x + a)

Algebraic Expressions

Wo Idahun

Ibeere 15 Ìròyìn

Find the total surface area of solid cone of radius $2\sqrt{3}$ cm and slanting side $4\sqrt{3}$

8

\sqrt{3} π

cm2

24

π

cm2

15

\sqrt{3} π

cm2

36

π

cm2

Awọn alaye Idahun

Total surface area of a solid cone
r = 2

\sqrt{3}

=

π r^{2}

+

π

rH
H = 4

\sqrt{3}

,

π

r(r + H)
∴ Area =

π

2

\sqrt{3}

[2

\sqrt{3}

+ 4

\sqrt{3}

]
=

π

2

\sqrt{3}

(6

\sqrt{3}

)
= 12

π

x 3
= 36

π

cm2

Ka ìwé ẹ̀kọ́ nípa Circles (WAEC)

Circles

Wo Idahun

Ibeere 16 Ìròyìn

make U the subject of the formula $S = \sqrt{\frac{6}{u} - \frac{w}{2}}$

u =

\frac{12}{2 s^{2}}

u =

\frac{12}{2 s + w}

u =	12
	2s²−w

u =

\frac{12}{2 s^{2}}

+ w

Awọn alaye Idahun

S =

\sqrt{\frac{6}{u} - \frac{w}{2}}

S =

\frac{12 - u w}{2 u}

2us2 = 12 - uw
u(2s2 + w) = 12
u =

\frac{12}{2 s^{2} + w}

Ka ìwé ẹ̀kọ́ nípa Change Of Subject Of A Formula/Relation (WAEC)

Ka ìwé ẹ̀kọ́ nípa Quadratic Equations (WAEC)

Change Of Subject Of A Formula/Relation

Quadratic Equations

Wo Idahun

Ibeere 17 Ìròyìn

Find the median of the numbers 89, 141, 130, 161, 120, 131, 131, 100, 108 and 119

131

125

123

120

Awọn alaye Idahun

Arrange in ascending order
89, 100, 108, 119, |120, 130|, 131, 131, 141, 161
Median =

\frac{120 + 130}{2}

= 125

Ka ìwé ẹ̀kọ́ nípa Measures Of Location (JAMB)

Measures Of Location

Wo Idahun

Ibeere 18 Ìròyìn

If U and V are two distinct fixed points and W is a variable points such that UWV is a right angle, what is the locus of W?

The perpendicular bisector of UV

A circle with UV as radius

A line parallel to the line UV

A circle with the line UV as the diameter

Loci

Statistics

Wo Idahun

Ibeere 19 Ìròyìn

A regular polygon of n sides has 160o as the size of each interior angle. Find n

18

14

16

12

Awọn alaye Idahun

Interior + exterior = 360
160 + exterior = 360
Exterior = 360 - 160
Exterior = 20
n = 360/exterior
n = 360/20
n = 18

Ka ìwé ẹ̀kọ́ nípa Polynomials (JAMB)

Ka ìwé ẹ̀kọ́ nípa Triangles And Polygons (WAEC)

Polynomials

Triangles And Polygons

Wo Idahun

Ibeere 20 Ìròyìn

Factorize completely 8a + 125ax3

(2a + 5x2)(4 + 26ax)

a(2 + 5x)(4 - 10x + 25x2)

(2a + 5x)(4 - 10ax + 25x2)

a(2 + 5x)(4 + 10ax + 25x2)

Awọn alaye Idahun

8a + 125ax3 = 23a + 53ax3
= a(23 + 53x3)
∴a[23 + (5x)3]
a3 + b3 = (a + b)(a2 - ab + b2)
∴ a(23 + (5x)3)
= a(2 + 5x)(4 - 10x + 25x2)

Ka ìwé ẹ̀kọ́ nípa Algebraic Expressions (WAEC)

Algebraic Expressions

Wo Idahun

Ibeere 21 Ìròyìn

The ages of Tosan and Isa differ by 6 and the product of their ages is 187. Write their ages in the form (x, y), where x > y.

(12, 6)

(23, 17)

(17, 11)

(18, 12)

Awọn alaye Idahun

x - y = 6.......(i)
xy = 187.......(ii)
From equation (i), x(6 + y)
sub. for x in equation (ii) = y(6 + y)
= 187
y2 + 6y = 187
y2 + 6y - 187 = 0
(y + 17)(y - 11) = 0
y = -17 or y = 11
y cannot be negative, y = 11
Sub. for y in equation(i) = x - 11
= 16
x = 6 + 11
= 17
∴(x, y) = (17, 11)

Ka ìwé ẹ̀kọ́ nípa Solution Of Linear Equations (WAEC)

Solution Of Linear Equations

Wo Idahun

Ibeere 22 Ìròyìn

Evaluate (212)3 - (121)3 + (222)3

(313)3

(1020)3

(1222)3

(1002) 3

Number Bases

Wo Idahun

Ibeere 23 Ìròyìn

Solve the equation 3x2 + 6x - 2 = 0

x = -1

\pm

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

x = -1

\pm

\frac{\sqrt{15}}{3}

x = -2

\pm

2

x = 3

\pm

\frac{\sqrt{3}}{15}

Awọn alaye Idahun

3x2 + 6x - 2 = 0
Using almighty formula i.e. x =

\frac{b \pm \sqrt{b^{2} - 4 a c}}{2 a}

a = 3, b = 6, c = -2
x =

\frac{- 6 \pm \sqrt{6^{2} - 4 (3) (- 2)}}{2 (3)}

x =

\frac{6 \pm \sqrt{36 - 24}}{6}

x =

\frac{6 \pm \sqrt{60}}{6}

x =

\frac{- 6 \pm \sqrt{4 \times 15}}{6}

x =

\frac{- 1 \pm \sqrt{15}}{3}

Ka ìwé ẹ̀kọ́ nípa Quadratic Equations (WAEC)

Quadratic Equations

Wo Idahun

Ibeere 24 Ìròyìn

In the diagram, PQ and RS are chords of a circle centre O which meet at T outside the circle. If TP = 24cm. TQ = 8cm and TS = 12cm, find TR.

16cm

14cm

12cm

8cm

Awọn alaye Idahun

PT x QT = TR x TS

24 x 8 = TR x 12

TR = $\frac{24 \times 8}{12}$

= = 16cm

Ka ìwé ẹ̀kọ́ nípa Introductory Calculus (WAEC)

Ka ìwé ẹ̀kọ́ nípa Loci (JAMB)

Ka ìwé ẹ̀kọ́ nípa Inequalities (JAMB)

Introductory Calculus

Loci

Inequalities

Wo Idahun

Ibeere 25 Ìròyìn

A man kept 6 black, 5 brown and 7 purple shirts in a drawer. What is the probability of his picking a purple shirt with his eyes closed?

\frac{1}{7}

\frac{11}{18}

\frac{7}{18}

\frac{7}{11}

Awọn alaye Idahun

Prob. of purple shirt is

\frac{7}{18}

Ka ìwé ẹ̀kọ́ nípa Probability (WAEC)

Probability

Wo Idahun

Ibeere 26 Ìròyìn

Simplify $ \frac{1}{x-2} + \frac{1}{x+2} + \frac{2x}{x^2-4} $

2x

(x−2)(x+2)(x²−4)

2x

x²−4

x

x²−4

4x

x²−4

Awọn alaye Idahun

\frac{1}{x - 2}

+

\frac{1}{x + 2}

+

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

=

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

=

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

Ka ìwé ẹ̀kọ́ nípa Algebraic Expressions (WAEC)

Ka ìwé ẹ̀kọ́ nípa Algebraic Fractions (WAEC)

Algebraic Expressions

Algebraic Fractions

Wo Idahun

Ibeere 27 Ìròyìn

A number of pencils were shared out among Bisi, Sola and Tunde in the ratio of 2 : 3 : 5 respectively. If Bisi got 5, how many were share out?

15

25

30

50

Awọn alaye Idahun

Let x r3epresent total number of pencils shared

B : S : T = 2 + 3 + 5 = 10

2 : 3 : 5

= $\frac{2}{10}$ x y

= 5

2y =5

2y = 50

∴ y = $\frac{50}{2}$

= 25

Ka ìwé ẹ̀kọ́ nípa Sine, Cosine And Tangent Of An Angle (WAEC)

Ka ìwé ẹ̀kọ́ nípa Financial Arithmetic (WAEC)

Sine, Cosine And Tangent Of An Angle

Financial Arithmetic

Wo Idahun

Ibeere 28 Ìròyìn

Two chords QR and NP of a circle intersect inside the circle at x. If RQP = 37o, RQN = 49o and QPN = 35o, find PRQ

35o

37o

49o

59o

Awọn alaye Idahun

In PNO, ONP
= 180 - (35 + 86)
= 180 - 121
= 59
PRQ = QNP = 59(angles in the same segment of a circle are equal)

Ka ìwé ẹ̀kọ́ nípa Polynomials (JAMB)

Ka ìwé ẹ̀kọ́ nípa Euclidean Geometry (JAMB)

Polynomials

Euclidean Geometry

Wo Idahun

Ibeere 29 Ìròyìn

If $ y = \frac{x}{x - 3} + \frac{x}{x + 4} $ find y when $ x = -2 $

-

\frac{3}{5}

\frac{3}{5}

-

\frac{7}{5}

\frac{3}{5}

Awọn alaye Idahun

y =

\frac{x}{x - 3}

+

\frac{x}{x + 4}

when x = -2
y =

\frac{- 2}{- 5}

+

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

=

\frac{- 2}{5}

+

\frac{- 2}{2}

=

\frac{4 + - 10}{10}

=

\frac{- 14}{10}

= -

\frac{7}{5}

Ka ìwé ẹ̀kọ́ nípa Algebraic Expressions (WAEC)

Ka ìwé ẹ̀kọ́ nípa Measures Of Location (JAMB)

Ka ìwé ẹ̀kọ́ nípa Quadratic Equations (WAEC)

Algebraic Expressions

Measures Of Location

Quadratic Equations

Wo Idahun

Ibeere 30 Ìròyìn

Find the values of x which satisfy the equation 16x - 5 x 4x + 4 = 0

1 and 4

-2 and 2

0 and 1

-1 and 0

Awọn alaye Idahun

16x - 5 x 4x + 4 = 0
(4x)2 - 5(4x) + 4 = 0
let 4x = y
y2 - 5y + 4 = 0
(y - 4)(y - 1) = 0
y = 4 or 1
4x = 4
x = 1
4x = 1
i.e. 4x = 4o, x = 0
∴ x = 1 or 0

Ka ìwé ẹ̀kọ́ nípa Solution Of Linear Equations (WAEC)

Solution Of Linear Equations

Wo Idahun

Ibeere 31 Ìròyìn

Simplify $ \frac{9^{\frac{1}{3}} \times 27^{-\frac{1}{3}}}{3^{-\frac{1}{6}} \times 3^{\frac{2}{3}}} $

1

3

1

3

9

Awọn alaye Idahun

\frac{9^{\frac{1}{3}} \times 27^{- \frac{1}{3}}}{3^{- \frac{1}{6}} \times 3^{\frac{2}{3}}}

=

\frac{(3^{2})^{\frac{1}{3}} \times (3^{3})^{- \frac{1}{3}}}{3^{- \frac{1}{6}} \times 3^{\frac{2}{3}}}

=

\frac{3^{\frac{2}{3}} \times 3^{\frac{2}{3}}}{3^{- \frac{1}{6}} \times 3^{\frac{2}{3}}}

=

\frac{3^{\frac{5}{6}}}{3^{- \frac{5}{6}}}

= 1

Ka ìwé ẹ̀kọ́ nípa Representation Of Data (JAMB)

Ka ìwé ẹ̀kọ́ nípa Probability (WAEC)

Ka ìwé ẹ̀kọ́ nípa Number Bases (WAEC)

Representation Of Data

Probability

Number Bases

Wo Idahun

Ibeere 32 Ìròyìn

In 1984, Ike was 24 yrs old and his father was 45 yrs old. In what year was Ike exactly half his father's age?

1981

1979

1982

1978

Awọn alaye Idahun

Let the no. of years be y
24 - y =

\frac{1}{2}

(45 - y)
45 - y = 2(24 - y)
45 - y = 48 - 2y
2y - y = 48 - 45
∴ y = 3
The exact year = 1984
1984 - 3 = 1981

Wo Idahun

Ibeere 33 Ìròyìn

In $ \triangle $XYZ, determine the cosine of angle Z.

3

39

29

36

14

5

7

5

Awọn alaye Idahun

cos z =

\frac{y^{2} + x^{2} - z^{2}}{2 y x}

= $\frac{9 + 36 - 16}{2 (3) (6)}$

= $\frac{29}{36}$

Ka ìwé ẹ̀kọ́ nípa Circles (WAEC)

Circles

Wo Idahun

Ibeere 34 Ìròyìn

PQ and PR are tangents from P to a circle centre O as shown in the figure. If QRP = $34^\circ$, find the angle marked x

34

^{\circ}

56

^{\circ}

68

^{\circ}

112

^{\circ}

Awọn alaye Idahun

From the circle centre 0, if PQ & PR are tangents from P and QRP = 34

^{\circ}

Then the angle marked x i.e. QOP

34 $^{\circ}$ x 2 = 68 $^{\circ}$

Ka ìwé ẹ̀kọ́ nípa Circles (WAEC)

Ka ìwé ẹ̀kọ́ nípa Triangles And Polygons (WAEC)

Circles

Triangles And Polygons

Wo Idahun

Ibeere 35 Ìròyìn

If 5(x + 2y) = 5 and 4(x + 3y) = 16, find 3(x + y)

7

1

3

27

Awọn alaye Idahun

5(x + 2y) = 5
∴ x + 2y = 1.....(i)
4(x + 3y) = 16 = 42
x + 3y = 2 .....(ii)
x + 2y = 1.....(i)
x + 3y = 2......(ii)
y = 1
Substitute y = 1 into equation (i) = x + 2y = 1
∴ x + 2(1) = 1
x + 2 = 1
∴ x = 1
∴ 3x + y = 3-1 + 1
= 3 = 1

Ka ìwé ẹ̀kọ́ nípa Algebraic Expressions (WAEC)

Algebraic Expressions

Wo Idahun

Ibeere 36 Ìròyìn

Find all real numbers $x$ which satisfy the inequality $\frac{1}{3}(x + 1) - 1 > \frac{1}{5}(x + 4)$

x < 11

x < -1

x > 6

x > 11

Awọn alaye Idahun

\frac{1}{3}

(x + 1) - 1 >

\frac{1}{5}

(x + 4)
=

\frac{x + 1}{3}

- 1 >

\frac{x + 4}{5}

\frac{x + 1}{3}

-

\frac{x + 4}{5}

- 1 > 0
=

\frac{5 x + 5 - 3 x - 12}{15}

= 2x - 7 > 15
= 2x > 12
= x > 11

Ka ìwé ẹ̀kọ́ nípa Inequalities (JAMB)

Inequalities

Wo Idahun

Ibeere 37 Ìròyìn

Factorize (4a + 3)2 - (3a - 2)2

(a + 1)(a + 5)

(a - 5)(7a - 1)

(a + 5)(7a + 1)

a(7a + 1)

Awọn alaye Idahun

(4a + 3)2 - (3a - 2)2 = a2 - b2
= (a + b)(a - b)
= [(4a + 3) + (3a - 2)][(4a + 3) + (3a - 2)]
= [(4a + 3 + 3a - 2)][(4a + 3 - 3a + 2)]
= (7a + 1)(a + 5)
∴ (a + 5)(7a + 1)

Ka ìwé ẹ̀kọ́ nípa Algebraic Expressions (WAEC)

Algebraic Expressions

Wo Idahun

Ibeere 38 Ìròyìn

Simplify $ \frac{1}{5x+5} + \frac{1}{7x+7} $

\frac{12}{35 x + 1}

\frac{1}{35 (x + 1)}

\frac{12 x}{35 (x + 7)}

\frac{12}{35 x + 35}

Awọn alaye Idahun

\frac{1}{5 x + 5}

+

\frac{1}{7 x + 7}

=

\frac{1}{5 (x + 1)}

+

\frac{1}{7 (x + 1)}

=

\frac{7 + 5}{35 (x + 1)}

=

\frac{12}{35 (x + 1)}

Ka ìwé ẹ̀kọ́ nípa Solution Of Linear Equations (WAEC)

Ka ìwé ẹ̀kọ́ nípa Algebraic Expressions (WAEC)

Solution Of Linear Equations

Algebraic Expressions

Wo Idahun

Ibeere 39 Ìròyìn

Find the probability that a number selected at random from 40 to 50 is a prime

2

11

5

11

3

11

4

11

Awọn alaye Idahun

From 40 to 50 = 11 & number are prime i.e. 41, 43, 47
prob. of selecting a prime No. is

\frac{3}{11}

Wo Idahun

Ibeere 40 Ìròyìn

If Musa scored 75 in biology instead of 57, his average mark in four subjects would have been 60. What was his total mark?

282

240

222

210

Awọn alaye Idahun

Let x represent Musa's total mark when he scores 57 in biology and Let Y represent Musa's total mark when he now scored 75 in biology, if he scored 75 in biology his new total mark will be

\frac{Y}{4}

= 60, y = 4 x 60 = 240
To get his total mark when he scored 57, subtract 57 from 75 to give 18, then subtract this 18 from the new total mark(ie. 240)
= 240 - 18
= 222

Wo Idahun

Ibeere 41 Ìròyìn

If $ \cos \theta = \frac{a}{b} $, find $ 1 + \tan^2 \theta $

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

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

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

\frac{2 a^{2} + b^{2}}{a^{2} + b^{2}}

Awọn alaye Idahun

cos

θ

=

\frac{a}{b}

, Sin

θ

=

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

Tan

θ

=

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

, Tan 2 =

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

1 + tan2

θ

= 1 +

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

=

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

=

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

Ka ìwé ẹ̀kọ́ nípa Sine, Cosine And Tangent Of An Angle (WAEC)

Ka ìwé ẹ̀kọ́ nípa Trigonometry (JAMB)

Sine, Cosine And Tangent Of An Angle

Trigonometry

Wo Idahun

Ibeere 42 Ìròyìn

At what points does the straight line y = 2x + 1 intersect the curve y = 2x2 + 5x - 1?

(-2, -3) and(

\frac{1}{2}

, 0)

(1, 0), (1, 3)

(4, 0) and (0,1)

(2, 0) and (0,1)

Graphs Of Linear And Quadratic Functions

Wo Idahun

Ibeere 43 Ìròyìn

Three boys shared some oranges. The first received 1/3 of the oranges and the second received 2/3 of the remaining. If the third boy received the remaining 12 oranges, how many oranges did they share

60

54

48

42

Awọn alaye Idahun

Let x = the number of oranges
The 1st received 1/3 of x = 1/3x
∴Remainder = x - 1/3x = 2x/3
The 2nd received 2/3 of 2x/3 = 2/3 * 2x/3 = 4x/3
The 3rd received 12 oranges
∴1/3x + 4x/9 + 12 = x
(3x + 4x + 108)/9 = x
3x + 4x + 108 = 9x
7x + 108 = 9x
9x - 7x = 108
2x = 108
x = 54 oranges

Ka ìwé ẹ̀kọ́ nípa Number Bases (WAEC)

Ka ìwé ẹ̀kọ́ nípa Modular Arithmetic (WAEC)

Number Bases

Modular Arithmetic

Wo Idahun

Ibeere 44 Ìròyìn

An arc of a circle of radius 6cm is 8cm long. Find the area of the sector

5

\frac{1}{3}

cm2

24cm2

36cm2

84cm2

Awọn alaye Idahun

Radius of the circle r = 6cm, Length of the arc = 8cm
Area of sector =

\frac{θ}{360}

x 2

π

r2........(i)
Length of arc =

\frac{θ}{360}

x 2

π

r........(ii)
from eqn. (ii)

θ

=

\frac{240}{π}

, subt. for

θ

in eqn (i)
Area x

\frac{240}{1}

x

\frac{1}{360}

x

\frac{π 6}{1}

= 24cm2

Ka ìwé ẹ̀kọ́ nípa Coordinate Geometry (WAEC)

Coordinate Geometry

Wo Idahun

Ibeere 45 Ìròyìn

The people in a city with a population of 0.9 million were grouped according to their ages. Use the diagram to determine the number of people in the 15 - 29 years group

29 x 104

26 x 104

16 x 104

13 x 104

Awọn alaye Idahun

15 - 29 years is represented by 104

^{\circ}

Number of people in the group is $\frac{104}{360}$ x 0.9m

= 260000 = 26 x 104

Ka ìwé ẹ̀kọ́ nípa Number Bases (WAEC)

Number Bases

Wo Idahun

Ibeere 46 Ìròyìn

Find the smallest number by which 252 can be multiplied to obtain a perfect square

2

3

5

7

Awọn alaye Idahun

Let the smallest number be x and the perfect square be y 252x = y.
By trial and error method, 252 x 9 = 1764
Check if y = 1764
y2 = 42
x = 7

Ka ìwé ẹ̀kọ́ nípa Introductory Calculus (WAEC)

Ka ìwé ẹ̀kọ́ nípa Number Bases (WAEC)

Ka ìwé ẹ̀kọ́ nípa Surds (radicals) (WAEC)

Introductory Calculus

Number Bases

Surds (radicals)

Wo Idahun

Ibeere 47 Ìròyìn

Udoh deposited ₦150.00 in the bank. At the end of 5 years the simple interest on the principal was ₦55.00. At what rate per annum was the interest paid?

11%

7