JAMB UTME - Mathematics - 1983

Swali 1 Ripoti

The scores of set of final year students in the first semester examination in a paper are 41, 29, 55, 21, 47, 70, 70, 40, 43, 56, 73, 23, 50, 50. Find the median of the scores.

47

50

48

\frac{1}{2}

48

49

Maelezo ya Majibu

By re-arranging 21, 23, 29, 40, 41, 43| 47, 50| 50, 55, 56, 70, 70, 73
The median =

\frac{47 + 50}{2}

\frac{97}{2}

= 48

\frac{1}{2}

Tazama Jibu

Swali 2 Ripoti

In a sample survey of a University Community, the following table shows the percentage distribution of the number of members per household:

No. of members per household	1	2	3	4	5	6	7	8	Total
No. of households	3	12	15	28	21	10	7	4	100

What is the median?

4

3

5

4.5

none

Maelezo ya Majibu

\begin{array}{cc} x & f \\ 1 & 3 \\ 2 & 13 \\ 3 & 15 \\ 4 & 28 \\ 5 & 21 \\ 6 & 10 \\ 7 & 7 \\ 8 & 4 \end{array}

Median is half of total frequency = 50th term
4 falls in the range = 4

Tazama Jibu

Swali 3 Ripoti

The letters of the word MATRICULATION are cut and put into a box. One letter is drawn at random from the box. Find the probability of drawing a vowel

7

13

5

13

6

13

8

13

4

13

Maelezo ya Majibu

Vowels of letters are 6 in numbers
prob. of vowel =

\frac{6}{13}

Soma maelezo ya somo kwenye Probability (WAEC)

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

Probability

Surds (radicals)

Tazama Jibu

Swali 4 Ripoti

PQRS is a cyclic quadrilateral. If ∠QPS = 75o, what is the size of ∠QRS?

180o

150o

105o

75o

Circles

Tazama Jibu

Swali 5 Ripoti

y varies partly as the square of x and partly as the inverse of the square root of x. Write down the expression for y if y = 2 when x = 1 and y = 6 when x = 4.

y = $\frac{10 x^{2}}{31} + \frac{52}{31 \sqrt{x}}$

y = x2 + $\frac{1}{\sqrt{x}}$

y = x2 + $\frac{1}{x}$

y = $\frac{x^{2}}{31} + \frac{1}{31 \sqrt{x}}$

Maelezo ya Majibu

y = kx2 + $\frac{c}{\sqrt{x}}$
y = 2 when x = 1
2 = k + $\frac{c}{1}$
k + c = 2
y = 6 when x = 4
6 = 16k + $\frac{c}{2}$
12 = 32k + c
k + c = 2
32k + c = 12
= 31k + 10
k = $\frac{10}{31}$
c = 2 - $\frac{10}{31}$
= $\frac{62 - 10}{31}$
= $\frac{52}{31}$
y = $\frac{10 x^{2}}{31} + \frac{52}{31 \sqrt{x}}$

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Algebraic Expressions

Quadratic Equations

Tazama Jibu

Swali 6 Ripoti

Correct each of the numbers 59.81798 and 0.0746829 to three significant figures and multiply them, giving your answer to three significant figures

4.46

4.48

4.47

4.49

4.50

Maelezo ya Majibu

59.81798 = 59.8 (3 s.f)
0.0746829 = 0.0747
59.8 x 0.0747 = 4.46706
= 4.48 (3s.f)

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

Fractions, Decimals And Approximations

Tazama Jibu

Swali 7 Ripoti

If $ \left(\frac{2}{3}\right)^m \left(\frac{3}{4}\right)^n = \frac{252}{729} $, find the values of m and n

m = 4, n = 2

m = -4, n = -2

m = -4, n =2

m = 4, n = -2

m = -2, n = 4

Maelezo ya Majibu

(

\frac{2}{3}

)m (

\frac{3}{4}

)n =

\frac{252}{729}

\frac{2^{m}}{4^{n}}

x

\frac{3^{n}}{3^{m}}

= 283-6
2m - 2n x 3n - m = 28 x 3-6
m - 2n = 8........(i)
-m + n = -6........(ii)
Solving the equations simultaneously
m = 4, n = -2

Soma maelezo ya somo kwenye Number Bases (WAEC)

Number Bases

Tazama Jibu

Swali 8 Ripoti

Make T the subject of the equation $ \frac{av}{1-v} = \sqrt{\frac{2v+T}{a+2T}} $

T = $\frac{3 a v}{1 - v}$

T = $\frac{1 + v}{2 a^{2} v^{3}}$

T = $\frac{2 v (1 - v)^{3} - a^{4} v^{3}}{2 a^{3} v^{3} + (1 - v)^{2}}$

\frac{2 v (1 - v)^{3} - a^{4} v^{3}}{2 a^{3} v^{3} - (1 - v)^{3}}

Maelezo ya Majibu

$\frac{a v}{1 - v}$ = $\sqrt{\frac{2 v + T}{a + 2 T}}$
$\frac{(a v)^{3}}{(1 - v)^{3}}$ = $\frac{2 v + T}{a + 2 T}$
$\frac{a^{3} v^{3}}{(1^{3} - v)^{3}}$ = $\frac{2 v + T}{a + 2 T}$
= $\frac{2 v (1 - v)^{3} - a^{4} v^{3}}{2 a^{3} v^{3} - (1 - v)^{3}}$

Soma maelezo ya somo kwenye Variation (WAEC)

Soma maelezo ya somo kwenye Change Of Subject Of A Formula/Relation (WAEC)

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

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Variation

Change Of Subject Of A Formula/Relation

Solution Of Linear Equations

Quadratic Equations

Tazama Jibu

Swali 9 Ripoti

Without using tables find the numerical value of $ \log_{7} 49 + \log_{7}\left(\frac{1}{7}\right) $

1

2

3

7

9

Maelezo ya Majibu

log749 + log7

\frac{1}{7}

= log77
= 1

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

Soma maelezo ya somo kwenye Logarithms (WAEC)

Positive And Negative Integers, Rational Numbers

Logarithms

Tazama Jibu

Swali 10 Ripoti

If O is the centre of the circle in the figure, find the value of x

50

260

100

65

130

Maelezo ya Majibu

From the diagram; The value of x = 360

^{\circ}

- 2(130

^{\circ}

)

= 360 - 260

= 100 $^{\circ}$

Soma maelezo ya somo kwenye Circles (WAEC)

Circles

Tazama Jibu

Swali 11 Ripoti

PQR is the diagram of a semicircle RSP with centre at Q and radius of length 3.5cm. If QPT = 60^o. Find the perimeter of the figure PTRS. $ \pi = \frac{22}{7} $

25cm

18cm

36cm

29cm

25.5cm

Maelezo ya Majibu

Circumference of PRS =

\frac{π}{2}

=

\frac{22}{7}

x

\frac{7}{1}

x

\frac{1}{2}

= 11cm
Side PT = 7cm, Side TR = 7cm
Perimeter(PTRS) = 11cm + 7cm + 7cm
= 25cm

Tazama Jibu

Swali 12 Ripoti

Simplify $ \log_{10} a^{\frac{1}{3}} + \frac{1}{4}\log_{10} a - \frac{1}{12}\log_{10} a^{7} $

1

\frac{7}{6}

log10 a

zero

10

Maelezo ya Majibu

log10 a

\frac{1}{3}

+

\frac{1}{4}

log10 a -

\frac{1}{12}

log10a7 = log10 a

\frac{1}{3}

+ log10

\frac{1}{4}

- log10 a

\frac{7}{12}

= log10 a

\frac{7}{12}

- log10 a

\frac{7}{12}

= log10 1 = 0

Soma maelezo ya somo kwenye Logarithms (WAEC)

Logarithms

Tazama Jibu

Swali 13 Ripoti

In the figure, PQR is a straight line. Find the values of x and y.

^{\circ}

x = 15

^{\circ}

, y = 52.5

^{\circ}

x = 22.5

^{\circ}

, y = 45.0

^{\circ}

x = 56.25

^{\circ}

, y = 11.5

^{\circ}

Maelezo ya Majibu

\frac{2}{3}

+ 3y + 45

^{\circ}

= 180

^{\circ}

3x + 6y + 90 $^{\circ}$ = 360 $^{\circ}$

3x + 67 = 270.......(i) x 2, 5x + y + y = 180 $^{\circ}$

5x + 2y = 180 $^{\circ}$ .......(ii) x 6

6 x 12y = 540..........(iii)

30x + 12y = 1080.........(iv)

egn(iv) - eqn(iii)

24x = 540

x = 22.5 and y = 33.75 $^{\circ}$

Tazama Jibu

Swali 14 Ripoti

The value of $ (0.303)^3 - (0.02)^3 $ is

0.019

0.0019

0.00019

0.000019

0.0278

Tazama Jibu

Swali 15 Ripoti

On a square paper of length 2.524375cm is inscribed square diagram of length 0.524375cm. Find the area of the paper not covered by the diagram. correct to 3 significant figures.

6.00cm2

6.10cm2

6cmv

6.09cm2

4.00cm2

Maelezo ya Majibu

Area of the paper = area of square = L x B or S2
where s = S x k
Area of the paper = (2.524)2
area of the diagram = (0.524)2
area not covered = (2.524)2 - (0.524)2
= 6.370576 - 0.274576
= 6.096
= 6.10cm2 (2 s.f)

Soma maelezo ya somo kwenye Coordinate Geometry (WAEC)

Coordinate Geometry

Tazama Jibu

Swali 16 Ripoti

In a triangle PQT, QR = $ \sqrt{3}\text{ cm} $, PR = 3cm, PQ = $ 2\sqrt{3} $cm and PQR = 30^o. Find angles P and R

P = 60o and R = 90o

P = 30o and R = 120o

P = 90o and R = 60o

P = 60o and R 60o

P = 45o and R = 105o

Maelezo ya Majibu

By using cosine formula, p2 = Q2 + R2 - 2QR cos p
Cos P =

\frac{Q^{2} + R^{2} - p^{2}}{2 Q R}

=

\frac{(3)^{2} + 2 (\sqrt{3})^{2} - 3^{2}}{2 \sqrt{3}}

=

\frac{3 + 12 - 9}{12}

=

\frac{6}{12}

=

\frac{1}{2}

= 0.5
Cos P = 0.5
p = cos-1 0.5 = 60

^{\circ}

= < P = 60

^{\circ}

If < P = 60

^{\circ}

and < Q = 30

< R = 180 $^{\circ}$ - 90 $^{\circ}$
angle P = 60 $^{\circ}$ and angle R is 90 $^{\circ}$

Tazama Jibu

Swali 17 Ripoti

The lengths of the sides of a right angled triangle are (3x + 1)cm, (3x - 1)cm and xcm. Find x

2

6

18

12

5

Maelezo ya Majibu

(3x + 1)2 = (3x - 1)2 + 2 (Pythagoras's theorem)
9x2 + 6x + 1 = 9x - 6x2 + 1 + x2
x2 - 12x = 0
x(x - 12) = 0
x = 0 or 12

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Algebraic Expressions

Tazama Jibu

Swali 18 Ripoti

The figure FGHK is a rhombus. What is the value of angle X?

30

^{\circ}

90

^{\circ}

150

^{\circ}

120

^{\circ}

60

^{\circ}

Maelezo ya Majibu

< HKF = 60

^{\circ}

, < KFG = 120

^{\circ}

< KFG = < KHG = x(opposite angles)

x = 120 $^{\circ}$

Soma maelezo ya somo kwenye Angles (WAEC)

Soma maelezo ya somo kwenye Triangles And Polygons (WAEC)

Angles

Triangles And Polygons

Tazama Jibu

Swali 19 Ripoti

Which of the following equations represents the graph above?

y = 2 + 7x + 4x2

y = 2 - 7x + 4x2

y = 2 + 7x - 4x2

y = 2 - 7x - 4x2

Maelezo ya Majibu

x = -2 or x =

\frac{1}{4}

(x + 2)(4x - 1) = 0

y = 2 - 7x - 4x2

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Algebraic Expressions

Tazama Jibu

Swali 20 Ripoti

If w varies inversely as V and U varies directly as w3, Find the relationship between u and v given that u = 1, when v = 2

u =

\frac{8}{v^{3}}

v =

\frac{8}{u^{2} v^{3}}

u = 8v3

v = 8u2

Maelezo ya Majibu

W

α

\frac{1}{v}

u

α

w3
w =

\frac{k_{1}}{v}

u = k2w3
u = k2(

\frac{k_{1}}{v}

)3
=

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

k = k2k1k2
u =

\frac{k}{v^{3}}

k = uv3
= (1)(2)3
= 8
u =

\frac{8}{v^{3}}

Soma maelezo ya somo kwenye Variation (WAEC)

Soma maelezo ya somo kwenye Change Of Subject Of A Formula/Relation (WAEC)

Variation

Change Of Subject Of A Formula/Relation

Tazama Jibu

Swali 21 Ripoti

In the figure, find PRQ

66

\frac{1}{2}

^{\circ}

^{\circ}

125

^{\circ}

105

^{\circ}

65

^{\circ}

Maelezo ya Majibu

Angle subtended at any part of the circumference of the circle

\frac{125^{o}}{2}

at centre = 360

^{\circ}

- 235

^{\circ}

= 125

^{\circ}

$\bar{P Q R}$ = $\frac{125}{2}$

= 62 $\frac{1}{2}$ $^{\circ}$

Soma maelezo ya somo kwenye Representation Of Data (JAMB)

Soma maelezo ya somo kwenye Triangles And Polygons (WAEC)

Representation Of Data

Triangles And Polygons

Tazama Jibu

Swali 22 Ripoti

A ship H leaves a port P and sails 30 km due south. Then it sails 50km due west. What is the bearing of H from P

20o 34'

243o 26'

116o 34'

63o 26'

240o 56'

Bearings

Tazama Jibu

Swali 23 Ripoti

Given that cos z = L , whrere z is an acute angle, find an expression for $ \frac{\cot z - \cosec z}{\sec z + \tan z} $

1-L

1+L

L²√3

1+L

1+L³

L²

L(L−1)

1−L+1√1−L²

Maelezo ya Majibu

Given Cos z = L, z is an acute angle
$\frac{cot z - cosec z}{sec z + tan z}$ = cos z
= $\frac{cos z}{sin z}$
cosec z = $\frac{1}{sin z}$
cot z - cosec z = $\frac{cos z}{sin z}$ - $\frac{1}{sin z}$
cot z - cosec z = $\frac{L - 1}{sin z}$
sec z = $\frac{1}{cos z}$
tan z = $\frac{sin z}{cos z}$
sec z = $\frac{1}{cos z}$ + $\frac{sin z}{cos z}$
= $\frac{1}{l}$ + $\frac{sin z}{L}$
the original eqn. becomes
$\frac{cot z - cosec z}{sec z + tan z}$ = $\frac{L - \frac{1}{sin z}}{1 + s i n \frac{z}{L}}$
= $\frac{L (L - 1)}{sin z (1 + sin z)}$
= $\frac{L (L - 1)}{sin z + 1 - c o s^{2} z}$
= sin z + 1
= 1 + $\sqrt{1 - L^{2}}$
= $\frac{L (L - 1)}{1 - L + 1 \sqrt{1 - L^{2}}}$

Soma maelezo ya somo kwenye Matrices And Determinants (JAMB)

Soma maelezo ya somo kwenye Modular Arithmetic (WAEC)

Matrices And Determinants

Modular Arithmetic

Tazama Jibu

Swali 24 Ripoti

Solve the simultaneous equations for x in x2 + y - 8 = 0, y + 5x - 2 = 0

-28, 7

6, -28

6, -1

-1, 7

3, 2

Maelezo ya Majibu

x2 + y - 8 = 0, y + 5x - 2 = 0
Rearranging, x2 + y = 8.....(i)
5x + y = 2.......(ii)
Subtract eqn(ii) from eqn(i)
x2 - 5x - 6 = 0
(x - 6)(x + 1) = 0
x = 6, -1

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

Solution Of Linear Equations

Tazama Jibu

Swali 25 Ripoti

If x is jointly proportional to the cube of y and the fourth power of z. In what ratio is x increased or decreased when y is halved and z is doubled?

4:1 increase

2:1 increase

1:1 no change

1:4 decrease

3:4 decrease

Variation

Progression

Tazama Jibu

Swali 26 Ripoti

PQRS is a cyclic quadrilateral which PQ = PS. PT is a tangent to the circle and PQ makes an angle of $50^\circ$ with the tangent as shown in the figure. What is the size of QRS?

50

^{\circ}

40

^{\circ}

110v

80

^{\circ}

^{\circ}

Maelezo ya Majibu

< SPQ = 80

^{\circ}

< SPQ + < SRQ = 180(Supplementary)

80 + < QRS = 180 $^{\circ}$ - 80 $^{\circ}$

= 100 $^{\circ}$

Soma maelezo ya somo kwenye Circles (WAEC)

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

Soma maelezo ya somo kwenye Triangles And Polygons (WAEC)

Circles

Indices, Logarithms And Surds

Triangles And Polygons

Tazama Jibu

Swali 27 Ripoti

Simplify $ \frac{3}{2x-1} + \frac{2-x}{x-2} $

2−x

(2x−1)(x−2)

5−x

(2x−1)(x−2)

4−2x

2x−1

6−3x

(2x−1)(x−2)

Maelezo ya Majibu

\frac{3}{2 x - 1}

+

\frac{2 - x}{x - 2}

=

\frac{3}{2 x - 1}

-

\frac{x - 2}{x - 2}

=

\frac{3}{2 x - 1}

- 1
=

\frac{3 - (2 x - 1)}{2 x - 1}

=

\frac{3 - 2 x + 1}{2 x - 1}

=

\frac{4 - 2 x}{2 x - 1}

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Algebraic Expressions

Tazama Jibu

Swali 28 Ripoti

Find the missing value in the following table:

$x$	$-2$	$-1$	$0$	$1$	$2$	$3$
$y=x^3-x+3$		$3$	$3$	$3$	$9$	$27$

-3

3

-9

13

9

Maelezo ya Majibu

When x = -2, y = x3 - x + 3
= -23 - (-2) + 3
= -8 + 2 + 3
= -3

Tazama Jibu

Swali 29 Ripoti

A construction company is owned by two partners X and Y and it is agreed that their profit will be divided in the ratio 4:5. At the end of the year, Y received ₦5,000 more than X. What is the total profit of the company for the year?

₦20, 000

₦25,000

₦30,000

₦15,000

₦45, 000

Maelezo ya Majibu

Total sharing ratio is 9
X has 4, Y has 4 + 1
If 1 is ₦5000
Total profit = 5000 x 9
= ₦45,000

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 30 Ripoti

PQRS is a desk of dimensions $2\text{m} \times 0.8$ which is inclined at $30^\circ$ to the horizontal. Find the inclination of the diagonal PR to the horizontal

30

^{\circ}

35'

30

^{\circ}

32'

15

^{\circ}

36'

10

^{\circ}

42'

Maelezo ya Majibu

tan

θ

=

\frac{0.8}{2}

= (0.4)

$θ$ = tan-1(0.4)

From the diagram, the inclination of the diagonal PR to the horizontal is 10 $^{\circ}$ 42'

Soma maelezo ya somo kwenye Measures Of Dispersion (JAMB)

Measures Of Dispersion

Tazama Jibu

Swali 31 Ripoti

If a rod of length 250cm is measured as 255cm long in error, what is the percentage error in the measurement?

55

10

5

4

2

Maelezo ya Majibu

% error =

\frac{Actual error}{real value}

x 100
=

\frac{5}{250}

x 100
= 2

Soma maelezo ya somo kwenye Percentages (WAEC)

Percentages

Tazama Jibu

Swali 32 Ripoti

A man drove for 4 hours at a certain speed, he then doubled his speed and drove for another 3 hours. Although he covered 600 kilometers. At what speed did he drive for the last 3 hours?

120km/hr

60km/hr

670km/hr

40km/hr

Maelezo ya Majibu

Speed =

\frac{d i s t a n c e}{t i m e}

let x represent the speed, d represent distance
x =

\frac{d}{4}

d = 4x
2x =

\frac{600 - d}{3}

6x = 600 - d
6x = 600 - 4x
10x = 600
x =

\frac{600}{10}

= 60km/hr

Tazama Jibu

Swali 33 Ripoti

The farm yield of four crops on a piece of land in Ondo are represented on the pie chart. what is the angle of the sector occupies by Okro in the chart?

11

^{\circ}

19

\frac{1}{3}

^{\circ}

33

\frac{1}{3}

^{\circ}

91

\frac{1}{3}

^{\circ}

91

^{\circ}

Maelezo ya Majibu

Adding the values of all the items together, it gives 70

Okro sector = $\frac{145}{270}$ x $\frac{360^{o}}{1}$

= 19.33 $^{\circ}$

= 19 $\frac{1}{3}$ $^{\circ}$

Soma maelezo ya somo kwenye Angles (WAEC)

Angles

Tazama Jibu

Swali 34 Ripoti

Find the mean of the following 24.57, 25.63, 24.32, 26.01, 25.77

25.12

25.30

25.26

25.50

25.75

Maelezo ya Majibu

\frac{24.57 + 25.63 + 24.32 + 26.01 + 25.77}{5}

mean =

\frac{126.3}{5}

= 25.26

Soma maelezo ya somo kwenye Integration (JAMB)

Soma maelezo ya somo kwenye Statistics (WAEC)

Integration

Statistics

Tazama Jibu

Swali 35 Ripoti

Find the angle of the sectors representing each item in pie chart of the following data 6, 10, 14, 16, 26

15o, 25o, 35o, 40o, 65o

60o, 100o, 140o, 160o, 260o

6o, 10o, 14o, 16o, 26o

30o, 50o, 70o, 80o, 130o

none of the above

Maelezo ya Majibu

6 + 10 + 14 + 16 + 26 = 72

\frac{6}{72}

x 360
= 30o
Similarly others give 30o, 50o, 70o, 80o and 130o respectively

Soma maelezo ya somo kwenye Polynomials (JAMB)

Soma maelezo ya somo kwenye Measures Of Dispersion (JAMB)

Polynomials

Measures Of Dispersion

Tazama Jibu

Swali 36 Ripoti

In a class of 60 pupils, the statistical distribution of the numbers of pupils offering Biology, History, French, Geography and Additional mathematics is as shown in the pie chart. How many pupils offer Additional Mathematics?

15

10

18

12

20

Maelezo ya Majibu

2x - 24)

^{\circ}

+ (3x - 18)

^{\circ}

+ (2x + 12)

^{\circ}

+ (x + 12)

^{\circ}

+ x

^{\circ}

= 360

^{\circ}

9x = 360 $^{\circ}$ + 18 $^{\circ}$

x = $\frac{378}{9}$

= 42 $^{\circ}$ , if x = 42 $^{\circ}$ , then add maths = $\frac{2 x - 42}{360}$ x 60

= $\frac{2 \times 42 - 24}{360}$ x 60

= $\frac{84 - 24}{6}$

= 10

Soma maelezo ya somo kwenye Statistics (WAEC)

Statistics

Tazama Jibu

Swali 37 Ripoti

If M represents the median and D the mode of the measurements 5, 9, 3, 5, 7, 5, 8, then (M, D) is

(6, 5)

(5, 8)

(5, 7)

(5, 5)

(7, 5)

Probability

Linear Inequalities

Tazama Jibu

Swali 38 Ripoti

Simplify $ \frac{3\sqrt{27a^{-9}}}{8} $

9a²

2a³

3

2a³

2

3a²

2

Maelezo ya Majibu

\frac{3 \sqrt{27 a^{- 9}}}{8}

=

\frac{3 a^{- 3}}{2}

=

\frac{3}{2}

x

\frac{1}{a^{3}}

=

\frac{3}{2 a^{3}}

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

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

Fractions, Decimals And Approximations

Surds (radicals)

Tazama Jibu

Swali 39 Ripoti

If x + 2 and x - 1 are factors of the expression 1x3 + 2kx2 + 24, find the values of 1 and K

1 = -6, k = -9

1 = -2, k = 1

k = -1, 1 = -2

1 = 0, k = 1

k = 0,1 = 6

Maelezo ya Majibu

f(x) = Lx3 + 2kx2 + 24
f(-2) = -8L + 8k = -24
4L - 4k = 12
f(1):L + 2k = -24
L - 4k = 3
3k = -27
k = -9
1 = -6

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Algebraic Expressions

Tazama Jibu

Swali 40 Ripoti

In the figure PT is a tangent to the circle with centre at O. If PQT = $30^\circ$, find the value of PTO

30

^{\circ}

50

^{\circ}

24

^{\circ}

12

^{\circ}

60

^{\circ}

Maelezo ya Majibu

FROM the diagram, PQT = 50

^{\circ}

PTQ = 50 $^{\circ}$ (opposite angles are supplementary)

Soma maelezo ya somo kwenye Circles (WAEC)

Circles

Tazama Jibu

Swali 41 Ripoti

Find x if (xbase4)2 = 100100base2

6

12

100

210

110

Maelezo ya Majibu

(x2)4 to base10 gives (1 x 25) + (1 x 25) + (1 x 2)
32 + 4 = 36
x2 = 36, x = 6
610 to base 4 =

\begin{array}{cc} 4 & 6 \\ 1 r 2 \end{array}

= 124

Soma maelezo ya somo kwenye Number Bases (WAEC)

Number Bases

Tazama Jibu

Swali 42 Ripoti

Given a regular hexagon, calculate each interior angle of the hexagon

60o

30o

120o

45o

135o

Maelezo ya Majibu

Sum of interior angles of polygon = (2n - 4)rt < s

sum of interior angles of an hexagon
(2 x 6 - 4) x 90o = (12 - 4) x 90o
= 8 x 90o
= 720o
each interior angle will have $\frac{720^{o}}{6}$
= 120o

Soma maelezo ya somo kwenye Angles (WAEC)

Angles

Tazama Jibu

Swali 43 Ripoti

One interior angle of a convex hexagon is 170o and each of the remaining interior angles is equal to xo. Find x

120o

110o

105o

102o

100o

Maelezo ya Majibu

An hexagon polygon is a six sided polygon
n = 6
sum of all interior angles of hexagon polygon will be (2n - 4) x 90o
= [2 x 6 - 4] x 90
= 720o
If one angle is 170o and each of the remaining five angles is 5xo
5xo + 170o = 720o
= 5x + 550
x =

\frac{550}{5}

= 110o

Soma maelezo ya somo kwenye Polynomials (JAMB)

Polynomials

Tazama Jibu

Swali 44 Ripoti

Factorize completely 81a4 - 16b4

(3a + 2b)(2a - 3b)(9a2 + 4b2)

(3a - 2b)(2a - 3b)(4a2 - 9b2)

(3a - 2b)(3a - 2b)(9a2 - 4b2)

(6a - 2b)(8a - 3b)(4a3 - 9b2)

Maelezo ya Majibu

81a4 - 16b4 = (9a2)2 - (4b2)2
= (9a2 + 4b2)(9a2 - 4b2)
N:B 9a2 + 4b2 = (3a - 2b)(3a - 2b)

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Algebraic Expressions

Tazama Jibu

Swali 45 Ripoti

Solve the following equations 4x - 3 = 3x + y = x - y = 3, 3x + y = 2y + 5x - 12

x = 5, y = 2

x = 2, y = 5

x = 5, y = -2

x = -2, y = -5

x = -5, y = -2

Maelezo ya Majibu

4x - 3 = 3x + y = x - y = 3.......(i)
3x + y = 2y + 5x - 12.........(ii)
eqn(ii) + eqn(i)
3x = 15
x = 5
substitute for x in equation (i)
5 - y = 3
y = 2

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 46 Ripoti

In a figure, PQR = 60o, PRS = 90o, RPS = 45o, QR = 8cm. Determine PS

2

\sqrt{3}

cm

4

\sqrt{6}

cm

2

\sqrt{6}

cm

8

\sqrt{6}

cm

8cm

Maelezo ya Majibu

From the diagram, sin 60o =

\frac{P R}{8}

PR = 8 sin 60 =

\frac{8 \sqrt{3}}{2}

= 4

\sqrt{3}

Cos 45o =

\frac{P R}{P S}

=

\frac{4 \sqrt{3}}{P S}

PS Cos45o = 4

\sqrt{3}

PS = 4

\sqrt{3}

x 2
= 4

\sqrt{6}

Soma maelezo ya somo kwenye Circles (WAEC)

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

Soma maelezo ya somo kwenye Areas (WAEC)

Soma maelezo ya somo kwenye Angles (WAEC)

Circles

Angles Of Elevation And Depression

Areas

Angles

Tazama Jibu

Swali 47 Ripoti

If $0.0000152 \times 0.042 = A \times 10^8$, where $1 \le A < 10$, find A and B

A = 9, B = 6.38

A = 6.38, B = -9

A = -6.38, B = -9

A = -9, B = -6.38

Maelezo ya Majibu

0.0000152 x 0.042 = A x 108

1 $\leq$ A < 10, it means values of A includes 1 - 9

0.0000152 = 1.52 x 10-5

0.00042 = 4.2 x 10-4

1.52 x 4.2 = 6.384

10-5 x 10-4

= 10-5-4

= 10-9

= 6.38 x 10-9

A = 6.38, B = -9

Soma maelezo ya somo kwenye Statistics (WAEC)

Statistics

Tazama Jibu

Swali 48 Ripoti

The scores of 16 students in a mathematics test are 65, 65, 55, 60, 60, 65, 60, 70, 75, 70, 65, 70, 60, 65, 65,
70. What is the sum of the median and modal scores?

125

130

140

150

Measures Of Dispersion

Statistics

Tazama Jibu

\(x\)	\(-2\)	\(-1\)	\(0\)	\(1\)	\(2\)	\(3\)
\(y=x^3-x+3\)		\(3\)	\(3\)	\(3\)	\(9\)	\(27\)






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