JAMB UTME - Mathematics - 1988

Swali 1 Ripoti

If (IPO3)4 = 11510 find P

0

1

2

3

Maelezo ya Majibu

1 x 43 + P x 42 + 0 x 4 + 3 = 11510
16p + 67 = 115 p = $\frac{48}{16}$
= 3

Soma maelezo ya somo kwenye Number Bases (WAEC)

Number Bases

Tazama Jibu

Swali 2 Ripoti

If $ \frac{1}{p} = \frac{a^2+2ab+b^2}{a-b} $ and $ \frac{l}{q} = \frac{a+b}{a^2-2ab+b^2} $ Find $ \frac{p}{q} $

a + b

a - b

1

a² - b²

a - b

a + b

a2 - b2

Algebraic Expressions

Algebraic Fractions

Simple Operations On Algebraic Expressions

Quadratic Equations

Tazama Jibu

Swali 3 Ripoti

Find $m$ such that $(m + \sqrt{3})(1 - \sqrt{3})^2 = 6 - 2\sqrt{2}$

1

2

3

4

Maelezo ya Majibu

(m + $\sqrt{3}$ )(1 - $\sqrt{3}$ )2 = 6 - 2 $\sqrt{2}$
(m + $\sqrt{3}$ )(4 - 2 $\sqrt{3}$ ) = 6 - 2 $\sqrt{2}$
= 6 - 2 $\sqrt{3}$
4m - 6 + 4 - 2m $\sqrt{3}$ = 6 - 2 $\sqrt{3}$
comparing co-efficients,
4m - 6 = 6.......(i)
4 - 2m = -2.......(ii)
in both equations, m = 3

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

Soma maelezo ya somo kwenye Lengths And Perimeters (WAEC)

Surds (radicals)

Lengths And Perimeters

Tazama Jibu

Swali 4 Ripoti

Scores($x$)	0	1	2	3	4	5	6	7
Frequency($f$)	7	11	6	7	7	5	3

In the distribution above, the mode and median respectively are

1,3

1, 2

3, 3

0, 2

Maelezo ya Majibu

From the distribution, Mode = 1 and
Median = $\frac{2 + 2}{2}$
= 2
= 1, 2

Soma maelezo ya somo kwenye Representation Of Data (JAMB)

Soma maelezo ya somo kwenye Linear Inequalities (WAEC)

Representation Of Data

Linear Inequalities

Tazama Jibu

Swali 5 Ripoti

In the figure, PQ is a parallel to ST and QRS = $40^\circ$. Find the value of x.

55

^{\circ}

60

^{\circ}

65

^{\circ}

75

^{\circ}

Maelezo ya Majibu

From the figure, 3x + x - 40 $^{\circ}$ = 180 $^{\circ}$

4x = 180 $^{\circ}$ + 40 $^{\circ}$

4x = 220 $^{\circ}$

x = $\frac{220}{4}$

= 55 $^{\circ}$

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

Soma maelezo ya somo kwenye Angles (WAEC)

Angles And Intercepts On Parallel Lines

Angles

Tazama Jibu

Swali 6 Ripoti

In the figure, a solid consists of a hemisphere surmounted by a right circular cone, with radius 3.0cm and height 6.0cm. Find the volume of the solid

36

π

cm 3

54

π

cm 2

18

π

cm 2

108

π

cm 2

Maelezo ya Majibu

The volume of the solid = vol. of cone + vol. of hemisphere

volume of cone = $\frac{1}{2} π^{2} h$

= $\frac{1 π}{3} \times (3)^{2} x 6 = 18 π c m^{2}$

vol. of hemisphere = $\frac{4 π r^{3}}{6} = \frac{2 π r^{3}}{3}$

= $\frac{2 π}{3} \times (3)^{3} = 18 π c m^{3}$

vol. of solid = 18 $π$ + 18 $π$

= 36 $π$ cm3

Soma maelezo ya somo kwenye Volumes (WAEC)

Soma maelezo ya somo kwenye Euclidean Geometry (JAMB)

Volumes

Euclidean Geometry

Tazama Jibu

Swali 7 Ripoti

If log102 = 0.3010 and log103 = 0.4771, evaluate; without using logarithm tables, log104.5

0.3010

0.4771

0.6532

0.9542

Maelezo ya Majibu

If log102 = 0.3010 and log103 = 0.4771,
log104.5 = log10 $\frac{(3 \times 3)}{2}$
log103 + log103 - log102 = 0.4771 + 0.4771 - 0.0310
= 0.6532

Soma maelezo ya somo kwenye Logarithms (WAEC)

Logarithms

Tazama Jibu

Swali 8 Ripoti

In the figure, STQ = SRP, PT = TQ = 6cm and QS = 5cm. Find SR

47

5

32

5

22

5

Maelezo ya Majibu

From similar triangle, $\frac{Q S}{Q P} = \frac{T Q}{Q R} = \frac{5}{12} = \frac{6}{Q R}$

QT = $\frac{6 \times 12}{5} = \frac{72}{5} = S R = Q R - Q S$

= $\frac{72}{5} - 5 = \frac{72 - 25}{5}$

= $\frac{47}{5}$

Tazama Jibu

Swali 9 Ripoti

If the sum of the 8th and 9th terms of an arithmetic progression is 72 and the 4th term is -6, find the common difference

4

8

6

\frac{2}{3}

9

\frac{1}{3}

Surds (radicals)

Tazama Jibu

Swali 10 Ripoti

Simplify $ \frac{x-7}{x^2-9} \, x \, \frac{x^2-3x}{x^2-49} $

x

(x - 3) (x - 7)

x

(x + 3) (x - 7)

x

(x + 3) (x + 7)

x

(x - 3) (x + 7)

Maelezo ya Majibu

$\frac{x - 7}{x^{2} - 9}$ x $\frac{x^{2} - 3 x}{x^{2} - 49}$
= $\frac{x - 7}{(x - 3) (x + 3)}$ x $\frac{x (x - 3)}{(x - 7) (x + 7)}$
= $\frac{x}{(x + 3) (x + 7)}$

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Algebraic Expressions

Tazama Jibu

Swali 11 Ripoti

For what values of x is the curve $y = \frac{x^2 + 3}{x + 4}$ decreasing?

-3 < x

\leq

0

-3

\geq

x < 0

0 < x < 3

0

\leq

x

\leq

3

Quadratic Equations

Graphs Of Linear And Quadratic Functions

Tazama Jibu

Swali 12 Ripoti

if x is the addition of the prime numbers between 1 and 6; and y the H.C.F. of 6, 9, 15. Find the product of x and y

27

30

33

90

Probability

Number Bases

Sets

Tazama Jibu

Swali 13 Ripoti

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

3

x + 1

3x + 1

(x + 1) (x + 2)

5x + 1

(x + 1) (x + 2)

2x²+ 5x + 2

(x + 1) (x + 2)

Maelezo ya Majibu

$\frac{x + 2}{x + 1}$ - $\frac{x - 2}{x + 2}$ = $\frac{(x + 2) (x + 2) - (x - 2) - (x - 2) (x + 1)}{(x + 1) (x + 2)}$
= $\frac{(x^{2} + 4 x + 4) - (x^{2} - x - 2)}{(x + 1) (x + 2)}$ = $\frac{x^{2} + 4 x + 4 - x^{2} + x + 2}{(x + 1) (x + 2)}$
= $\frac{5 x + 6}{(x + 1) (x + 2)}$

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Algebraic Expressions

Quadratic Equations

Tazama Jibu

Swali 14 Ripoti

If $ g(y) = \frac{y - 3}{11} + \frac{11}{y^2 - 9} $. what is $ g(y + 3) $?

\frac{y}{11} + \frac{11}{y (y + 6)}

\frac{y}{11} + \frac{11}{y (y + 6)}

\frac{y}{11} + \frac{11}{y (y + 6)}

\frac{y}{11} + \frac{11}{y (y + 6)}

Solution Of Linear Equations

Algebraic Expressions

Number Bases

Tazama Jibu

Swali 15 Ripoti

The solution of the quadratic equation px2 + qx + b = 0 is

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

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

\frac{- q \pm \sqrt{q^{2} - 4 b p}}{2 p}

\frac{- q \pm \sqrt{p^{2} - 4 b p}}{2 p}

Maelezo ya Majibu

px2 + qx + b = 0
Using almighty formula
$\frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ .........(i)
Where a = p, b = q and c = b
substitute for this value in equation (i)
= $\frac{- q \pm \sqrt{q^{2} - 4 b p}}{2 p}$

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Quadratic Equations

Tazama Jibu

Swali 16 Ripoti

For which of the following exterior angles is a regular polygon possible? i. 36o ii. 18o iii. 15o

i and ii

ii only

ii and iii

iii only

Maelezo ya Majibu

for a regular polygon to be possible, it must have all sides angles equal. $\frac{360}{18}$ = 20 sides and $\frac{360}{15}$ = 24 sides
(ii) and (iii) are right

Soma maelezo ya somo kwenye Polynomials (JAMB)

Polynomials

Tazama Jibu

Swali 17 Ripoti

In the figure, XR and YQ are tangents to the circle YZXP if ZXR = 45o and YZX = 55o, Find ZYQ

135o

125o

100o

90o

Circles

Tazama Jibu

Swali 18 Ripoti

if a = -3, b = 2, c = 4, evaluate $ \frac{a^3-b^3-c^{\frac{1}{2}}}{b-a-c} $

37

-37

5

37

5

-37

Tazama Jibu

Swali 19 Ripoti

Four interior angles of a pentagon are 90o - xo, 90o + xo, 110o - 2xo, 110o + 2xo. Find the fifth interior angle

110o

120o

130o

140o

Tazama Jibu

Swali 20 Ripoti

If $ \cos^2 \theta + \frac{1}{8} = \sin^2 \theta $, find $ \tan \theta $

3

\frac{3 \sqrt{7}}{7}

3

\sqrt{7}

\sqrt{7}

Maelezo ya Majibu

cos2 $θ$ + $\frac{1}{8}$ = sin2 $θ$ ..........(i)
from trigometric ratios for an acute angle, where cos $θ$ + sin2 $θ$ = 1 - cos $θ$ ........(ii)
Substitute for equation (i) in (i) = cos2 $θ$ + $\frac{1}{8}$ = 1 - cos2 $θ$
= cos2 $θ$ + cos2 $θ$ = 1 - $\frac{1}{8}$
2 cos2 $θ$ = $\frac{7}{8}$
cos2 $θ$ = $\frac{7}{2 \times 3}$
$\frac{7}{16}$ = cos $θ$
$\sqrt{\frac{7}{16}}$ = $\frac{\sqrt{7}}{4}$
but cos $θ$ = $\frac{adj}{hyp}$
opp2 = hyp2 - adj2
opp2 = 42 ( $\sqrt{7}$ )2
= 16 - 7
opp = $\sqrt{9}$ = 3
than $θ$ = $\frac{opp}{hyp}$
= $\frac{3}{\sqrt{7}}$
$\frac{3}{\sqrt{7}}$ x $\frac{7}{\sqrt{7}}$ = $\frac{3 \sqrt{7}}{7}$

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

Soma maelezo ya somo kwenye Trigonometry (JAMB)

Soma maelezo ya somo kwenye Modular Arithmetic (WAEC)

Sine, Cosine And Tangent Of An Angle

Trigonometry

Modular Arithmetic

Tazama Jibu

Swali 21 Ripoti

A tax player is allowed $ \frac{1}{8} $th of his income tax-free, and pays 20% on the remainder. If he pays ₦490.00 tax, what is his income?

₦560.00

₦2,450.00

₦2,800.00

₦3,920.00

Maelezo ya Majibu

He pays tax on 1 - $\frac{7}{8}$ = $\frac{1}{7}$ th of his income
20% is 490, 100% is $\frac{1000}{20}$ x 490, ₦2,450.00
= $\frac{7}{8}$ of his income = ₦2,450.00

$\frac{1}{\frac{7}{8}}$ x 2450
= $\frac{8 \times 2450}{7}$
= $\frac{19600}{7}$
= ₦2800.00

Tazama Jibu

Swali 22 Ripoti

Two sisters, Taiwo and Keyinde, own a store. The ratio of Taiwo's share to Kehinde's is 11:9. Later, Keyinde sells $ \frac{2}{3} $ of her share to Taiwo for ₦720.00. Find the value of the store.

₦1,080.00

₦2,400.00

₦3,000.00

₦3,600.00

Maelezo ya Majibu

Let value of store = X
Ratio of Taiwo's share to kehine's is 11:9 Keyinde sells $\frac{2}{3}$ of her share to Taiwo for ₦720
$\frac{2}{3}$ of 9 = 6
∴ Sum of the ratio = 11 + 9 = 20
$\frac{6}{20}$ of x = ₦720
$\frac{6 x}{20}$ = 720
∴ x = $\frac{720 \times 20}{6}$
x = ₦24,000

Tazama Jibu

Swali 23 Ripoti

Solve the following equation equation for $x$

\[ x^2 + \frac{2x}{r^2} + \frac{1}{r^4} = 0 \]

r2

1

r⁴

-

\frac{1}{r^{2}}

1 - r

Maelezo ya Majibu

x2 + $\frac{2 x}{r^{2}}$ + $\frac{1}{r^{4}}$ = 0
(x + $\frac{1}{r^{2}}$ ) = 0
x + $\frac{1}{r^{2}}$ = 0
x = $\frac{- 1}{r^{2}}$

Soma maelezo ya somo kwenye Number Bases (WAEC)

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Number Bases

Quadratic Equations

Tazama Jibu

Swali 24 Ripoti

A 5.0g of salt was weighted by Tunde as 5.1g. What is the percentage error?

20

2

1.1

0.2

Maelezo ya Majibu

% error = $\frac{actual error}{true value}$ x 100
Where actual error = 5.1 - 5.0 = 0.1
true value = 5.0g
% error = $\frac{0.1}{5.0}$ x 100
= $\frac{10}{5}$
= 2

Soma maelezo ya somo kwenye Percentages (WAEC)

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

Percentages

Fractions, Decimals, Approximations And Percentage

Tazama Jibu

Swali 25 Ripoti

In the figure, PS = 7cm and RY = 9cm. IF the area of parallelogram PQRS is 56cm2. Find the area of trapezium PQTS

56cm2

112cm2

120cm2

176cm2

Maelezo ya Majibu

From the figure, PS = QR = YT = 7cm

Area of parallelogram PQRS = 56cm

56 = base x height, where base = 7

7 x h = 56cm,

h = $\frac{56}{7}$

= 8cm

Area of trapezium $\frac{1}{2}$ (sum of two sides)x height where two sides are QT and PS but QT = QR + RY + YT = 7 +9 + 7 = 23cm

Area of trapezium PQTS = $\frac{1}{2}$ (23 + 7) x 8

$\frac{1}{2}$ x 30 x 8 = 120cmsq

Tazama Jibu

Swali 26 Ripoti

In the figure, PS = RS = QS and QRS = 50o. Find QPR

25o

40o

50o

65o

Maelezo ya Majibu

In the figure PS = RS = QS, they will have equal base QR = RP

In angle SQR, angle S = 50O

In angle QRP, 65 + 65 = 130O

Since RQP = angle RPQ = $\frac{180 - 130}{2}$

= $\frac{50}{2} = 25^{o}$

QPR = 25O

Soma maelezo ya somo kwenye Polynomials (JAMB)

Polynomials

Tazama Jibu

Swali 27 Ripoti

If $ \cos \theta = \frac{x}{y} $, find $ \cosec \theta $

\frac{1}{y}

(x2 + y2)

\frac{x}{y}

\frac{1}{y}

\sqrt{x^{2} + y^{2}}

\frac{x - y}{y}

Maelezo ya Majibu

Cos $θ$ = $\frac{x}{y}$ = $\frac{adj}{opp}$
(hyp2) = opp2 + adj2
(hyp2) = x2 + y2
hyp = $\sqrt{x^{2} + y^{2}}$
Cosec $θ$ = hyp
= x2 + y2
= $\frac{1}{y}$ $\sqrt{x^{2} + y^{2}}$

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

Soma maelezo ya somo kwenye Angles Of Elevation And Depression (WAEC)

Sine, Cosine And Tangent Of An Angle

Angles Of Elevation And Depression

Tazama Jibu

Swali 28 Ripoti

If x and y represent the mean and the median respectively of the following set of numbers 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, find the $ \frac{x}{y} $ correct to one decimal place

18

15

1.0

5

Maelezo ya Majibu

Mean $\bar{x}$ = $\frac{156}{10}$ = 15.6
Median = $\bar{y}$ = $\frac{15 + 16}{2}$
$\frac{31}{2}$ = 15.5
$\frac{x}{y}$ = $\frac{15.6}{15.5}$ = 1.0065
1.0(1 d.p)

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

Surds (radicals)

Tazama Jibu

Swali 29 Ripoti

Simplify $ \frac{x-y}{x^{\frac{1}{3}}-x^{\frac{1}{3}}} $

x2 + xy + y2

x

\frac{2}{3}

+ x

\frac{1}{3}

+ y

\frac{2}{3}

x

\frac{2}{3}

- x

\frac{1}{3}

y

\frac{2}{3}

y

\frac{2}{3}

Tazama Jibu

Swali 30 Ripoti

The thickness of an 800 pages of book is 18mm. Calculate the thickness of one leaf of the book giving your answer in meters and in standard form

2.25 x 10-4m

50 x 10-4m

2.25 x 10-5m

4.50 x 10-5m

Maelezo ya Majibu

Thickness of an 800 pages book = 18mm to meter
18 x 103m = 1.8 x 10-2m
One leaf = $\frac{1.8 \times 10^{- 2}}{800}$
= $\frac{1.8 \times 10^{- 2}}{8 \times 10^{2}}$
= $\frac{- 1.8}{8}$ x 10-4
= 0.225 x 10-4
= 2.25 x 10-5m

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

Fractions, Decimals And Approximations

Tazama Jibu

Swali 31 Ripoti

In triangle PQR, PQ = 1cm, QR = 2cm and PQR = 120o Find the longest side of the triangle

\sqrt{3}

cm

\sqrt{7}

cm

3cm

7cm

Maelezo ya Majibu

PR2 = PQ2 + QR2 - 2(QR)(PQ) COS 120o
PR2 = 12 + 22 - 2(1)(2) x - cos 60o
= 5 - 2(1)(2) x - $\frac{1}{2}$
= 5 + 2 = 7
PR = $\sqrt{7}$ cm

Tazama Jibu

Swali 32 Ripoti

The solutions of x2 - 2x - 1 = 0 are the points of intersection of two graphs. if one of the graphs is y = 2 + x - x2, find the second graph

y = 1 - x

y = 1 + x

y = x - 1

y = 3x + 3

Algebraic Expressions

Tazama Jibu

Swali 33 Ripoti

What is the solution of the equation x2 - x - 1 + 0?

x = 1.6 and x = -0.6

x = -1.6 and x = 0.6

x = 1.6 and x = 0.6

x = -1.6 and x = -0.6

Quadratic Equations

Tazama Jibu

Swali 34 Ripoti

Evaluate $ \frac{8^{\frac{1}{3}} \times 5^{\frac{2}{3}}}{10^{\frac{2}{3}}} $ = $ \frac{8^{\frac{1}{3}} \times 5^{\frac{2}{3}}}{10^{\frac{2}{3}}} $

2

5

3

3√5

3√2

Maelezo ya Majibu

$\frac{8^{\frac{1}{3}} \times 5^{\frac{3}{2}}}{\frac{2}{10^{3}}}$ = $\frac{(2^{3})^{\frac{1}{3}} \times 5^{\frac{3}{2}}}{(2 \times 5)^{\frac{2}{3}}}$
= $\frac{2 \times 5}{2^{\frac{2}{3}} \times 5^{\frac{3}{2}}}$
= 21 - $\frac{2}{3}$
= 2 $\frac{1}{3}$
= 3 $\sqrt{2}$

Soma maelezo ya somo kwenye Number Bases (WAEC)

Soma maelezo ya somo kwenye Modular Arithmetic (WAEC)

Number Bases

Modular Arithmetic

Tazama Jibu

Swali 35 Ripoti

PQR is a triangle in which PQ = 10cm and QPR = 60oS is a point equidistant from P and Q. Also S is a point equidistant from PQ and PR. If U is the foot of the perpendicular from S on PR, find the length SU in cm to one decimal place

2.7

4.33

3.1

3.3

Maelezo ya Majibu

$△$ PUS is right angled
$\frac{U S}{5}$ = sin60o
US = 5 x $\frac{\sqrt{3}}{2}$
= 2.5 $\sqrt{3}$
= 4.33cm

Tazama Jibu

Swali 36 Ripoti

In a class of 150 students, the sector in a pie chart representing the students offering Physics has angle 12o. How many students are offering Physics?

18

15

10

5

Maelezo ya Majibu

No of students offering Physics are $\frac{12}{360}$ x 150
= 5

Tazama Jibu

Swali 37 Ripoti

If cos 60o = 1/2, which of the following angle has cosine of -1/2?

30o

120o

150o

210o

300o

Logarithms

Tazama Jibu

Swali 38 Ripoti

Find correct to one decimal place, $0.24633 \div 0.0306$

0.8

1.8

8.0

8.1

Maelezo ya Majibu

$\frac{0.24633}{0.03060}$ multiplying throughout by 100,000
= $\frac{24633}{3060}$
= 8.05
= 8.1

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

Fractions, Decimals And Approximations

Tazama Jibu

Swali 39 Ripoti

Factorize completely (x2 + x)2 - (2x + 2)2

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

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

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

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

Tazama Jibu

Swali 40 Ripoti

If 7 and 189 are the first and fourth terms of a geometric progression respectively find the sum for the first
three terms of the progression

182

180

91

63

28

Sequence And Series

Tazama Jibu

Swali 41 Ripoti

Tope bought X oranges at N5.00 each and some mangoes at N4.00 each. if she bought twice as many mangoes as oranges and spent at least N65.00 and at most N130.00, find the range of values of X.

4≤X≤5

5≤X≤8

5≤X≤10

8≤X≤10

Number Bases

Tazama Jibu

Swali 42 Ripoti

Given that 3x - 5y - 3 = 0, 2y - 6x + 5 = 0 the value of (x, y) is

(

\frac{- 1}{8}, \frac{19}{24}

)

8,

\frac{24}{19}

-8,

\frac{24}{19}

(

\frac{19}{24}, \frac{- 1}{8}

)

Maelezo ya Majibu

3x - 5y = 3, 2y - 6x = -5
-5y + 3x = 3........{i} x 2
2y - 6x = -5.........{ii} x 5
Substituting for x in equation (i)
-5y + 3( $\frac{19}{24}$ ) = 3
-5y + 3 x $\frac{19}{24}$ = 3
-5y = $\frac{3 - 19}{8}$
-5 = $\frac{24 - 19}{8}$
= $\frac{5}{8}$
y = $\frac{5}{8 \times 5}$
y = $\frac{- 1}{8}$
(x, y) = ( $\frac{19}{24}, \frac{- 1}{8}$ )

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Algebraic Expressions

Tazama Jibu

Swali 43 Ripoti

In the figure, PQRS is a circle. If chords QR and RS are equal, calculate the value of x.

80

^{\circ}

60

^{\circ}

45

^{\circ}

40

^{\circ}

Maelezo ya Majibu

SRT is a straight line, where QRT = 120

SRQ = 180 $^{\circ}$ - 120 $^{\circ}$ = 60 $^{\circ}$ - (angle on a straight line)

also angle QRS = 180 $^{\circ}$ - 100 $^{\circ}$ (angle on a straight line) . In angles where QR = SR and angle SRQ = 60 $^{\circ}$

x = 100 - 60 = 40 $^{\circ}$

Soma maelezo ya somo kwenye Circles (WAEC)

Circles

Tazama Jibu

Swali 44 Ripoti

Simplify $ \frac{4a^2 - 49b^2}{2a^2 - 5ab - 7b^2} $

a - b

2a + b

2a + 7b

a - b

2a - 7b

a + b

2a - 7b

a - b

Maelezo ya Majibu

$\frac{4 a^{2} - 49 b^{2}}{2 a^{2} - 5 a b - 7 b^{2}}$ = $\frac{(2 a)^{2} - (7 b)^{2}}{(a - b) (2 a + 7 b)}$
= $\frac{(2 a + 7 b) (2 a - 7 b)}{(a - b) (2 a + 7 b)}$
= $\frac{2 a - 7 b}{a - b}$

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

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Solution Of Linear Equations

Algebraic Expressions

Tazama Jibu

Swali 45 Ripoti

A basket contain green, black and blue balls in the ratio 5 : 2 : 1. If there are 10 blue balls. Find the corresponding new ratio when 10 green and 10 black balls are removed from the basket

1 : 1 : 1

4 : 2 : 1

5 : 1 : 1

4 : 1 : 1

Maelezo ya Majibu

Let x represent total number of balls in the basket.
If there are 10 blue balls, $\frac{1}{8}$ of x = 10
x = 10 x 8 = 80 balls
Green balls will be $\frac{5}{8}$ x 80 = 50 and black balls = $\frac{2}{8}$ x 80 = 20
Ratio = Green : black : blue
50 : 20 : 10
-10 : 10 : -
------------------
New Ratio 40 : 10 : 10
4 : 1 : 1

Soma maelezo ya somo kwenye Variation (WAEC)

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

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

Variation

Positive And Negative Integers, Rational Numbers

Ratio, Proportions And Rates

Tazama Jibu

Swali 46 Ripoti

If a metal pipe 10cm long has an external diameter of 12cm and a thickness of 1cm find the volume of the metal used in making the pipe

120

π

cm3

110

π

cm3

60

π

cm3

50

π

cm3

Maelezo ya Majibu

The volume of the pipe is equal to the area of the cross section and length.
let outer and inner radii be R and r respectively.
Area of the cross section = (R2 - r2)
where R = 6 and r = 6 - 1
= 5cm
Area of the cross section = (62 - 52) $π$ = (36 - 25) $π$ cm sq
vol. of the pipe = $π$ (R2 - r2)L where length (L) = 10
volume = 11 $π$ x 10
= 110 $π$ cm3

Soma maelezo ya somo kwenye Volumes (WAEC)

Soma maelezo ya somo kwenye Indices, Logarithms And Surds (JAMB)

Soma maelezo ya somo kwenye Areas (WAEC)

Volumes

Indices, Logarithms And Surds

Areas

Tazama Jibu

Swali 47 Ripoti

Simplify $ \frac{1\frac{1}{2}}{2+\frac{1}{4}\text{ of }32} $

3

256

3

32

6

85

Maelezo ya Majibu

$\frac{1 \frac{1}{2}}{2 + \frac{1}{4} of 32}$
= $\frac{\frac{3}{2}}{2 + \frac{1}{4} \times 32}$
$\frac{3}{2}$ x 4 = 6

Soma maelezo ya somo kwenye Number Bases (WAEC)

Soma maelezo ya somo kwenye Number Bases (JAMB)

Number Bases

Tazama Jibu

Swali 48 Ripoti

If two dice are thrown together, what is the probability of obtaining at least a score of 10?

1

6

1

12

5

6

11

12

Maelezo ya Majibu

The total sample space when two dice are thrown together is 6 x 6 = 36
$\begin{matrix} 1 & 2 & 3 & 4 & 5 & 6 \\ 1. & 1.1 & 1.2 & 1.3 & 1.4 & 1.5 & 1.6 \\ 2 & 2.1 & 2.2 & 2.3 & 2.4 & 2.5 & 2.6 \\ 3 & 3.1 & 3.2 & 3.3 & 3.4 & 3.5 & 3.6 \\ 4 & 4.1 & 4.2 & 4.3 & 4.4 & 4.5 & 4.6 \\ 5 & 5.1 & 5.2 & 5.3 & 5.4 & 5.5 & 5.6 \\ 6 & 6.1 & 6.2 & 6.3 & 6.4 & 6.5 & 6.6 \end{matrix}$
At least 10 means 10 and above
P(at least 10) = $\frac{6}{36}$
= $\frac{1}{6}$

Soma maelezo ya somo kwenye Probability (WAEC)

Probability

Tazama Jibu

Swali 49 Ripoti

If x varies inversely as the cube root of y and x = 1 when y = 8, find y when x = 3

1

3

2

3

8

27

4

9

Variation

Tazama Jibu






Bonyeza na Ushikilie kuvuta kuzunguka
Bonyeza Hapa Kufunga

Scores(\(x\))	0	1	2	3	4	5	6	7
Frequency(\(f\))	7	11	6	7	7	5	3