JAMB UTME - Mathematics - 1988

Tambaya 1 Rahoto

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

Bayanin Amsa

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

Duba Amsa

Tambaya 2 Rahoto

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

Bayanin Amsa

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

Duba Amsa

Tambaya 3 Rahoto

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

Duba Amsa

Tambaya 4 Rahoto

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)

Duba Amsa

Tambaya 5 Rahoto

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

Bayanin Amsa

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)

Karanta bayanin darasi akan Surds (radicals) (WAEC)

Surds (radicals)

Duba Amsa

Tambaya 6 Rahoto

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

Bayanin Amsa

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

Duba Amsa

Tambaya 7 Rahoto

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

Duba Amsa

Tambaya 8 Rahoto

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

Duba Amsa

Tambaya 9 Rahoto

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

Duba Amsa

Tambaya 10 Rahoto

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

110o

120o

130o

140o

Duba Amsa

Tambaya 11 Rahoto

$\begin{array}{cc} S c o r e s (x) & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ F r e q u e n c y (f) & 7 & 11 & 6 & 7 & 7 & 5 & 3 \end{array}$

In the distribution above, the mode and median respectively are

1,3

1, 2

3, 3

0, 2

Bayanin Amsa

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

Karanta bayanin darasi akan Representation Of Data (JAMB)

Karanta bayanin darasi akan Linear Inequalities (WAEC)

Representation Of Data

Linear Inequalities

Duba Amsa

Tambaya 12 Rahoto

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

0.3010

0.4771

0.6532

0.9542

Bayanin Amsa

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

Karanta bayanin darasi akan Logarithms (WAEC)

Logarithms

Duba Amsa

Tambaya 13 Rahoto

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

20

2

1.1

0.2

Bayanin Amsa

% 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

Karanta bayanin darasi akan Percentages (WAEC)

Karanta bayanin darasi akan Fractions, Decimals, Approximations And Percentage (JAMB)

Percentages

Fractions, Decimals, Approximations And Percentage

Duba Amsa

Tambaya 14 Rahoto

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

Bayanin Amsa

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

Karanta bayanin darasi akan Volumes (WAEC)

Karanta bayanin darasi akan Indices, Logarithms And Surds (JAMB)

Karanta bayanin darasi akan Areas (WAEC)

Volumes

Indices, Logarithms And Surds

Areas

Duba Amsa

Tambaya 15 Rahoto

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

Bayanin Amsa

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

Karanta bayanin darasi akan Polynomials (JAMB)

Polynomials

Duba Amsa

Tambaya 16 Rahoto

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

Bayanin Amsa

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

Duba Amsa

Tambaya 17 Rahoto

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

Duba Amsa

Tambaya 18 Rahoto

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

30o

120o

150o

210o

300o

Logarithms

Duba Amsa

Tambaya 19 Rahoto

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

1

2

3

4

Bayanin Amsa

(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

Karanta bayanin darasi akan Surds (radicals) (WAEC)

Karanta bayanin darasi akan Lengths And Perimeters (WAEC)

Surds (radicals)

Lengths And Perimeters

Duba Amsa

Tambaya 20 Rahoto

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

Duba Amsa

Tambaya 21 Rahoto

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}

Bayanin Amsa

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

Karanta bayanin darasi akan Quadratic Equations (WAEC)

Quadratic Equations

Duba Amsa

Tambaya 22 Rahoto

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

\frac{1}{y}

(x2 + y2)

\frac{x}{y}

\frac{1}{y}

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

\frac{x - y}{y}

Bayanin Amsa

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
= $\frac{1}{y}$ $\sqrt{x^{2} + y^{2}}$

Karanta bayanin darasi akan Sine, Cosine And Tangent Of An Angle (WAEC)

Karanta bayanin darasi akan Angles Of Elevation And Depression (WAEC)

Sine, Cosine And Tangent Of An Angle

Angles Of Elevation And Depression

Duba Amsa

Tambaya 23 Rahoto

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

Duba Amsa

Tambaya 24 Rahoto

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}

Bayanin Amsa

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 $^{\circ}$

Karanta bayanin darasi akan Circles (WAEC)

Circles

Duba Amsa

Tambaya 25 Rahoto

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}

Bayanin Amsa

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

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

4x = 220 $^{\circ}$

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

= 55 $^{\circ}$

Karanta bayanin darasi akan Angles And Intercepts On Parallel Lines (WAEC)

Karanta bayanin darasi akan Angles (WAEC)

Angles And Intercepts On Parallel Lines

Angles

Duba Amsa

Tambaya 26 Rahoto

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)

Bayanin Amsa

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

Karanta bayanin darasi akan Algebraic Expressions (WAEC)

Karanta bayanin darasi akan Quadratic Equations (WAEC)

Algebraic Expressions

Quadratic Equations

Duba Amsa

Tambaya 27 Rahoto

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

Bayanin Amsa

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

Karanta bayanin darasi akan Variation (WAEC)

Karanta bayanin darasi akan Positive And Negative Integers, Rational Numbers (WAEC)

Karanta bayanin darasi akan Ratio, Proportions And Rates (WAEC)

Variation

Positive And Negative Integers, Rational Numbers

Ratio, Proportions And Rates

Duba Amsa

Tambaya 28 Rahoto

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

Bayanin Amsa

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

Duba Amsa

Tambaya 29 Rahoto

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

Bayanin Amsa

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

Karanta bayanin darasi akan Volumes (WAEC)

Karanta bayanin darasi akan Euclidean Geometry (JAMB)

Volumes

Euclidean Geometry

Duba Amsa

Tambaya 30 Rahoto

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}

)

Bayanin Amsa

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) = ( $\frac{19}{24}, \frac{- 1}{8}$ )

Karanta bayanin darasi akan Algebraic Expressions (WAEC)

Algebraic Expressions

Duba Amsa

Tambaya 31 Rahoto

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}

Duba Amsa

Tambaya 32 Rahoto

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

Duba Amsa

Tambaya 33 Rahoto

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

a - b

2a + b

2a + 7b

a - b

2a - 7b

a + b

2a - 7b

a - b

Bayanin Amsa

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

Karanta bayanin darasi akan Solution Of Linear Equations (WAEC)

Karanta bayanin darasi akan Algebraic Expressions (WAEC)

Solution Of Linear Equations

Algebraic Expressions

Duba Amsa

Tambaya 34 Rahoto

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

3

256

3

32

6

85

Bayanin Amsa

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

Karanta bayanin darasi akan Number Bases (WAEC)

Karanta bayanin darasi akan Number Bases (JAMB)

Number Bases

Duba Amsa

Tambaya 35 Rahoto

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

Bayanin Amsa

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

Duba Amsa

Tambaya 36 Rahoto

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

Bayanin Amsa

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) = $\frac{6}{36}$
= $\frac{1}{6}$

Karanta bayanin darasi akan Probability (WAEC)

Probability

Duba Amsa

Tambaya 37 Rahoto

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

Bayanin Amsa

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

Karanta bayanin darasi akan Number Bases (WAEC)

Karanta bayanin darasi akan Modular Arithmetic (WAEC)

Number Bases

Modular Arithmetic

Duba Amsa

Tambaya 38 Rahoto

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

25o

40o

50o

65o

Bayanin Amsa

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

Karanta bayanin darasi akan Polynomials (JAMB)

Polynomials

Duba Amsa

Tambaya 39 Rahoto

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

Duba Amsa

Tambaya 40 Rahoto

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

47

5

32

5

22

5

Bayanin Amsa

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

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

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

= $\frac{47}{5}$

Duba Amsa

Tambaya 41 Rahoto

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)

Duba Amsa

Tambaya 42 Rahoto

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

Duba Amsa

Tambaya 43 Rahoto

Solve the following equation equation for x2 + $\frac{2 x}{r^{2}}$ + $\frac{1}{r^{4}}$ = 0

r2

1

r⁴

-

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

1 - r

Bayanin Amsa

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

Karanta bayanin darasi akan Number Bases (WAEC)

Karanta bayanin darasi akan Quadratic Equations (WAEC)

Number Bases

Quadratic Equations

Duba Amsa

Tambaya 44 Rahoto

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

x

(x - 3) (x - 7)

x

(x + 3) (x - 7)

x

(x + 3) (x + 7)

x

(x - 3) (x + 7)

Bayanin Amsa

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

Karanta bayanin darasi akan Algebraic Expressions (WAEC)

Algebraic Expressions

Duba Amsa

Tambaya 45 Rahoto

If cos2 $θ$ + $\frac{1}{8}$ = sin2 $θ$ , find tan $θ$

3

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

3

\sqrt{7}

\sqrt{7}

Bayanin Amsa

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 $\frac{7}{\sqrt{7}}$ = $\frac{3 \sqrt{7}}{7}$

Karanta bayanin darasi akan Sine, Cosine And Tangent Of An Angle (WAEC)

Karanta bayanin darasi akan Trigonometry (JAMB)

Karanta bayanin darasi akan Modular Arithmetic (WAEC)

Sine, Cosine And Tangent Of An Angle

Trigonometry

Modular Arithmetic

Duba Amsa

Tambaya 46 Rahoto

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

0.8

1.8

8.0

8.1

Bayanin Amsa

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

Karanta bayanin darasi akan Fractions, Decimals And Approximations (WAEC)

Fractions, Decimals And Approximations

Duba Amsa

Tambaya 47 Rahoto

If (IPO3)4 = 11510 find P

0

1

2

3

Bayanin Amsa

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

Karanta bayanin darasi akan Number Bases (WAEC)

Number Bases

Duba Amsa

Tambaya 48 Rahoto

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

Duba Amsa

Tambaya 49 Rahoto

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

Bayanin Amsa

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

Karanta bayanin darasi akan Fractions, Decimals And Approximations (WAEC)

Fractions, Decimals And Approximations

Duba Amsa






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