JAMB UTME - Mathematics - 1984

In the figure, 0 is the centre of circle PQRS and PS//RT. If PRT = 135, then PSO is

67

\frac{1}{2}

^{\circ}

22

\frac{1}{2}

^{\circ}

33

\frac{1}{2}

^{\circ}

45

^{\circ}

90

^{\circ}

Antwortdetails

< R = 180

^{\circ}

- 45

^{\circ}

(sum of angles on a straight line)

< R = < P = 45 $^{\circ}$ (corresponding angles)

< PSO = < P = 45 $^{\circ}$ ( $△$ PSO is a right angle)

Lies die Unterrichtsnotiz zu Circles (WAEC)

Circles

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Frage 2 Bericht

Thirty boys and X girls sat for a test. The mean of the boys' scores and that of the girls were respectively 6 and 8. Find 8 if the total score was 468.

38

24

36

22

41

Antwortdetails

Le the number of girls = A; Total score of boys = 30

\times

6 = 180
Total score of girls = A

\times

8 = 8A

∴

180 + 8A = 468
8A = 288
A = 36

Lies die Unterrichtsnotiz zu Statistics (WAEC)

Lies die Unterrichtsnotiz zu Simple Operations On Algebraic Expressions (WAEC)

Statistics

Simple Operations On Algebraic Expressions

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Frage 3 Bericht

Simplify $ \frac{3^n - 3^{n-1}}{3^3 \times 3^n - 27 \times 3^{n-1}} $

1

6

1

27

4

3

Antwortdetails

\frac{3^{n} - 3^{n - 1}}{3^{3} \times 3^{n} - 27 \times 3^{n - 1}}

=

\frac{3^{n} - 3^{n - 1}}{3^{3} (3^{n} - 3^{n - 1})}

=

\frac{3^{n} - 3^{n - 1}}{27 (3^{n} - 3^{n - 1})}

=

\frac{1}{27}

Lies die Unterrichtsnotiz zu Algebraic Expressions (WAEC)

Lies die Unterrichtsnotiz zu Fractions, Decimals, Approximations And Percentage (JAMB)

Algebraic Expressions

Fractions, Decimals, Approximations And Percentage

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Frage 4 Bericht

$ \dfrac{0.0001432}{1940000} = k \times 10^n $ where $ 1 \le k < 10 $ and n is a whole number. The values K and n are

7.381 qnd -11

2.34 and 10

3.871 and 2

7.831 and -11

Antwortdetails

$\frac{0.0001432}{1940000}$ = k x 10n

where 1 $\leq$ k $\leq$ 10 and n is a whole number. Using four figure tables, the eqn. gives 7.38 x 10-11

k = 7.381, n = -11

Lies die Unterrichtsnotiz zu Number Bases (WAEC)

Number Bases

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Frage 5 Bericht

A cone is formed by bending a sector of a circle Saving an angle or 210°. Find the radius of the base of the cone. If the diameter of the circle is 12cm.

7.00cm

1.75cm

21cm

3.50cm

2.21cm

Loci

Antwort anzeigen

Frage 6 Bericht

If f(x) = 2(x - 3)2 + 3(x - 3) + 4 and g(y) = 5 + y, find g [f(3)] and f[g(4)].

3 and 4

-3 and 4

-3 and -4

3 and -4

0 and 5

Antwortdetails

f(x0 = 2(x - 3)2 + 3(x - 3) + 4
= (2 + 3) + (x - 3) + 4
5(x - 3) + 4
5x - 15 + 4
= 5x - 11
f(3) = 5 x 3 - 11
= 4

Lies die Unterrichtsnotiz zu Algebraic Expressions (WAEC)

Algebraic Expressions

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Frage 7 Bericht

A straight lie y = mx meets the curve y = x2 - 12x + 40 in two distinct points. If one of them is (5, 5) find the other

(5, 6)

(8, 8)

(8, 5)

(7,7)

(7, 5)

Antwortdetails

When y = 5, y = x2 - 12x + 40, becomes
x2 - 12x + 40 = 5
x2 - 12x + 40 - 5 = 0
x2 + 12x + 35 = 0
x2 - 7x - 5x + 35 = 0
x(x - 7) - 5(x - 7) = 0
= (x - 5)(x - 7)
x = 5 or 7

Antwort anzeigen

Frage 8 Bericht

What is the volume of this regular three dimensional figure?

160cm2

48cm2

120cm2

40cm2

Antwortdetails

Volume of the three dimensional figures = v = A x h

A = $\frac{1}{2}$ x 4 x 3

= 6cm2

V = 6 x 8

= 48cm2

Lies die Unterrichtsnotiz zu Volumes (WAEC)

Volumes

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Frage 9 Bericht

If (x - 2) and (x + 1) are factors of the expression x3 + px2 + qx + 1, what is the sum of p and q

9

-3

3

17

3

2

3

Antwortdetails

x3 + px2 + qx + 1 = (x - 1) Q(x) + R
x - 2 = 0, x = 2, R = 0,
4p + 2p = -9........(i)
x3 + px2 + qx + 1 = (x - 1)Q(x) + R
-1 + p - q + 1 = 0
p - q = 0.......(ii)
Solve the equation simultaneously
p =

\frac{- 3}{2}

q =

\frac{- 3}{2}

p + q =

\frac{3}{2}

-

\frac{3}{2}

=

\frac{- 6}{2}

= -3

Lies die Unterrichtsnotiz zu Algebraic Expressions (WAEC)

Algebraic Expressions

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Frage 10 Bericht

A trader in country where their currency 'MONI'(M) is in base five bought 1035 oranges at M145 each. If he sold the oranges at M245 each, what will be his gain?

1035

10305

1025

20025

30325

Antwortdetails

Total cost of 1035 oranges at ₦145 each
= 1035 x 145
= 20025
Total selling price at ₦245 each
= (103)5 x 245
= 30325
Hence his gain = 30325 - 20025
= 10305

Lies die Unterrichtsnotiz zu Number Bases (WAEC)

Lies die Unterrichtsnotiz zu Number Bases (JAMB)

Number Bases

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Frage 11 Bericht

P varies directly as the square of Q and inversely as R. If P = 36, when Q = 3 and R = 4, find P when Q = 5 and R = 2.

72

100

90

200

125

Antwortdetails

P \propto \frac{Q^{2}}{R}

∴

P = \frac{K Q^{2}}{R}

36 = \frac{K Q^{2}}{4}

K = \frac{36 \times 4}{9}

K = 16

P = \frac{16 \times 5^{2}}{2} = 200

Antwort anzeigen

Frage 12 Bericht

Find, without using logarithm tables, the value of $ \frac{\log_{3} 27-\log_{\frac{1}{4}} 64}{\log_{3} \frac{1}{81}} $

−3

9

−3

2

6

11

43

18

Antwortdetails

log327 = 3log33
=3 log3

\frac{1}{81}

= -4 log33 = -4
let log

\frac{1}{4}

64 = (

\frac{1}{4}

)x
= 64
4-x = 43

\frac{l o g_{3} 27 - l o g_{\frac{1}{4}} 64}{l o g_{3} \frac{1}{81}}

=

\frac{3 - (- 3)}{- 4}

=

\frac{- 6}{4}

=

\frac{- 3}{2}

Lies die Unterrichtsnotiz zu Modular Arithmetic (WAEC)

Lies die Unterrichtsnotiz zu Logarithms (WAEC)

Modular Arithmetic

Logarithms

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Frage 13 Bericht

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

Antwortdetails

6 + 10 + 14 + 16 + 26 = 72

\frac{6}{72}

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

Lies die Unterrichtsnotiz zu Modular Arithmetic (WAEC)

Lies die Unterrichtsnotiz zu Sets (JAMB)

Lies die Unterrichtsnotiz zu Surds (radicals) (WAEC)

Lies die Unterrichtsnotiz zu Lengths And Perimeters (WAEC)

Modular Arithmetic

Sets

Surds (radicals)

Lengths And Perimeters

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Frage 14 Bericht

P sold his bicycle to Q at a profit of 10%. How much did the bicycle cost P?

₦200

₦196

₦180

₦205

₦150

Antwortdetails

Let the selling price(SP from P to Q be represented by x
i.e. SP = x
When SP = x at 10% profit
CP =

\frac{100}{100}

+ 10 of x =

\frac{100}{110}

of x
when Q sells to R, SP = ₦209 at loss of 5%
Q's cost price = Q's selling price
CP =

\frac{100}{95}

x 209
= 220.00
x = 220
=

\frac{2200}{11}

= 200
= ₦200.00

Lies die Unterrichtsnotiz zu Sine, Cosine And Tangent Of An Angle (WAEC)

Lies die Unterrichtsnotiz zu Percentages (WAEC)

Lies die Unterrichtsnotiz zu Modular Arithmetic (WAEC)

Sine, Cosine And Tangent Of An Angle

Percentages

Modular Arithmetic

Antwort anzeigen

Frage 15 Bericht

Find the area of the shaded portion of the semicircular figure.

\frac{r^{2}}{4} (4 π - 3 \sqrt{3})

\frac{r^{2}}{4} (2 π - 3 \sqrt{3})

\frac{1}{2} r^{2} π

\frac{1}{8} r^{2} \sqrt{3}

\frac{r^{2}}{4} (4 π - 3 \sqrt{3})

Antwortdetails

Asector =

\frac{60}{360} \times π r^{2}

= $\frac{1}{6} π r^{2}$

A $△$ = $\frac{1}{2} r^{2} \sin 60^{o}$

$\frac{1}{2} r^{2} \times \frac{\sqrt{3}}{2} = \frac{r^{2} \sqrt{3}}{4}$

A $shaded portion$ = Asector -
A $△$

= ( $\frac{1}{6} π r^{2} - \frac{r^{2} \sqrt{3}}{4})^{3}$

= $\frac{π r^{2}}{2} - \frac{3 r^{2} \sqrt{3}}{4}$

= $\frac{r^{2}}{4} (2 π - 3 \sqrt{3})$

Lies die Unterrichtsnotiz zu Number Bases (JAMB)

Lies die Unterrichtsnotiz zu Areas (WAEC)

Number Bases

Areas

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Frage 16 Bericht

The sides of a triangle are $ (x + 4)\text{cm} $, $ x\text{cm} $ and $ (x - 4)\text{cm} $, respectively If the cosine of the largest angle is $ \frac{1}{5} $, find the value of $ x $

24cm

20cm

28cm

7cm

88

7

Antwortdetails

< B is the largest since the side facing it is the largest, i.e. (x + 4)cm

Cosine B = $\frac{1}{5}$
= 0.2 given
b2 - a2 + c2 - 2a Cos B
Cos B = $\frac{a^{2} + c^{2} - b^{2}}{2 a c}$
$\frac{1}{5}$ = $\frac{x^{2} + ? (x - 4)^{2} - (x + 4)^{2}}{2 x (x - 4)}$
$\frac{1}{5}$ = $\frac{x (x - 16)}{2 x (x - 4)}$
$\frac{1}{5}$ = $\frac{x - 16}{2 x - 8}$
= 5(x - 16)
= 2x - 8
3x = 72
x = $\frac{72}{3}$
= 24

Lies die Unterrichtsnotiz zu Algebraic Expressions (WAEC)

Algebraic Expressions

Antwort anzeigen

Frage 17 Bericht

Rationalize $ \frac{5\sqrt{7}-7\sqrt{5}}{\sqrt{7}-\sqrt{5}} $

-2 \sqrt{35}\)

4\sqrt{7}\) - 6

\sqrt{5}

-√35

4\sqrt{7}\) - 8

\sqrt{5}

√35

Antwortdetails

\frac{5 \sqrt{7} - 7 \sqrt{5}}{\sqrt{7} - \sqrt{5}}

=

\frac{5 \sqrt{7} - 7 \sqrt{5}}{\sqrt{7} - \sqrt{5}}

x

\frac{\sqrt{7} + \sqrt{5}}{\sqrt{7} + \sqrt{5}}

=

\frac{(5 \times 7) + (5 \sqrt{7} \times 5) - (7 \times \sqrt{5} \times 7) (- 7 \times 5)}{(\sqrt{7})^{2}}

=

\frac{5 \sqrt{35} - 7 \sqrt{35}}{2}

=

\frac{- 2 \sqrt{35}}{2}

= -

\sqrt{35}

Lies die Unterrichtsnotiz zu Positive And Negative Integers, Rational Numbers (WAEC)

Lies die Unterrichtsnotiz zu Surds (radicals) (WAEC)

Positive And Negative Integers, Rational Numbers

Surds (radicals)

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Frage 18 Bericht

A variable point p(x, y) traces a graph in a two-dimensional plane. (0, 3) is one position of P. If x increases by 1 unit, y increases by 4 units. The equation of the graph is

-3 =

\frac{y + 4}{x + 1}

4y = -3 + x

\frac{y}{x}

=

\frac{- 3}{4}

4x = y + 3

Antwortdetails

P(x, y), P(0, 3) If x increases by 1 unit and y by 4 units, then ratio of x : y = 1 : 4

\frac{x}{1}

=

\frac{y}{4}

y = 4x
Hence the sign of the graph is y + 3 = 4x

Lies die Unterrichtsnotiz zu Algebraic Expressions (WAEC)

Lies die Unterrichtsnotiz zu Coordinate Geometry (WAEC)

Algebraic Expressions

Coordinate Geometry

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Frage 19 Bericht

If the price of oranges was raised by $ \frac{1}{2} $k per orange. The number of oranges a customer can buy for ?2.40 will be less by 16. What is the present price of an orange?

2

\frac{1}{2}

\frac{2}{15}

5

\frac{1}{3}

20

Antwortdetails

Let x represent the price of an orange and
y represent the number of oranges that can be bought
xy = 240k, y =

\frac{240}{x}

.....(i)
If the price of an oranges is raised by

\frac{1}{2}

k per orange, number that can be bought for ?240 is reduced by 16
Hence, y - 16 =

\frac{240}{x + \frac{1}{2}}

=

\frac{480}{2 x + 1}

=

\frac{480}{2 x + 1}

.....(ii)
subt. for y in eqn (ii)

\frac{240}{x}

- 16
=

\frac{480}{2 x + 1}

=

\frac{240 - 16 x}{x}

=

\frac{480}{2 x + 1}

= (240 - 16x)(2x + 1)
= 480x
= 480x + 240 - 32x2 - 16
480x = 224 - 32x2
x2 = 7
x =

\sqrt{7}

= 2.5
= 2

\frac{1}{2}

k

Lies die Unterrichtsnotiz zu Variation (WAEC)

Lies die Unterrichtsnotiz zu Solution Of Linear Equations (WAEC)

Variation

Solution Of Linear Equations

Antwort anzeigen

Frage 20 Bericht

If $ \sin \theta = \frac{x}{y} $ and $0^o < 90^o$, then find $ \frac{1}{\tan \theta} $.

x

√y²−x²

y

x

√y²+ x²

y²−x²

x

Antwortdetails

\frac{1}{t a n θ}

=

\frac{c o s θ}{s i n θ}

sin

θ

=

\frac{x}{y}

cos

θ

=

\frac{\sqrt{y^{2} - x^{2}}}{y}

Lies die Unterrichtsnotiz zu Sine, Cosine And Tangent Of An Angle (WAEC)

Sine, Cosine And Tangent Of An Angle

Antwort anzeigen

Frage 21 Bericht

If $a = \frac{2x}{1-x}$ and $b = \frac{1+x}{1-x}$, then $a^2 - b^2$ in the simplest form is $\frac{3x+1}{1-x}$

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

3x²−1

(x−1)²

3x−2

x−1

3x−2

1−X

3x²−1

(x−1)

Antwortdetails

a2 - b2 = (

\frac{2 x}{1 - x}

)2 - (

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

)2
= (

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

)(

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

)
= (

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

)(

\frac{x - 1}{1 - x}

)
=

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

Lies die Unterrichtsnotiz zu Linear Inequalities (WAEC)

Linear Inequalities

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Frage 22 Bericht

In the figure, PQRSTW is a regular hexagon. QS intersects RT at V. Calculate TVS.

60

^{\circ}

90

^{\circ}

120

^{\circ}

30

^{\circ}

80

^{\circ}

Antwortdetails

From the diagram, PQRSTW is a regular hexagon.

Hexagon is a six sided polygon.

Sum of interior angles of polygon = (2n - 4)90 $^{\circ}$ = [2 x 6 - 4] x 90 = 8 x 90 = 720 $^{\circ}$

each angle = $\frac{720^{o}}{6} = 120^{o}$ and TVS = $\frac{120}{2} = 60^{o}$

Lies die Unterrichtsnotiz zu Triangles And Polygons (WAEC)

Triangles And Polygons

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Frage 23 Bericht

A man invested a total of ₦50000 in two companies. If these companies pay dividends of 6% and 8% respectively, how much did he invest at 8% if the total yield is ₦3700?

₦15000

₦29600

₦27800

₦21400

₦35000

Antwortdetails

Total yield = ₦3,700
Total amount invested = ₦50,000
Let x be the amount invested at 6% interest and let y be the amount invested at 8% interest
then yield on x =

\frac{6}{100}

x and yield on y =

\frac{8}{100}

y
Hence,

\frac{6}{100}

x +

\frac{8}{100}

y
= 3,700.........(i)
x + y = 50,000........(ii)
6x + 8y = 370,000 x 1
x + y = 50,000 x 6
6x + 8y = 370,000.........(iii)
6x + 6y = 3000,000........(iv)
Eqn (iii) - Eqn (ii)
2y = 70,000
y =

\frac{70, 000}{2}

= 35,000
Money invested at 8% is ₦35,000

Lies die Unterrichtsnotiz zu Modular Arithmetic (WAEC)

Lies die Unterrichtsnotiz zu Ratio, Proportions And Rates (WAEC)

Modular Arithmetic

Ratio, Proportions And Rates

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Frage 24 Bericht

Using $ \triangle $ XYZ in the figure, find XYZ.

29

^{\circ}

31

^{\circ}

31

^{\circ}

20'

31

^{\circ}

18'

Antwortdetails

\frac{\sin y}{3} = \frac{\sin 120^{o}}{5}

sin 120 $^{\circ}$ = sin 60 $^{\circ}$

5 sin y = 3 sin 60 $^{\circ}$

sin y = $\frac{3 \sin 60^{o}}{5}$

$\frac{3 \times 0.866}{5}$

= $\frac{2.598}{5}$

y = sin-1 0.5196 = 30 $^{\circ}$ 18'

Lies die Unterrichtsnotiz zu Triangles And Polygons (WAEC)

Triangles And Polygons

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Frage 25 Bericht

XYZ is a triangle and XW is perpendicular to YZ at = W. If XZ = 5cm and WZ = 4cm, Calculate XY.

5

\sqrt{3}

cm

3

\sqrt{5}

cm

3

\sqrt{3}

cm

5cm

6cm

Antwortdetails

by Pythagoras theorem, XW = 3cm

Also by Pythagoras theorem, XY2 = 62 + 32

XY2 = 36 + 9 = 45

XY = $\sqrt{45} = 3 \sqrt{3}$

Lies die Unterrichtsnotiz zu Triangles And Polygons (WAEC)

Triangles And Polygons

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Frage 26 Bericht

The table below is drawn for a graph $y = x^3 - 3x + 1$.

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

From x = -2 to x = 1, the graph crosses the x-axis in the range(s)

-1 < x < 0 and 0 < x < 1

-2 < x < -1 and 0 < x < 1

-2 < x < -1 and -1 < x < 0

0 < x < 1

Antwortdetails

If the graph of y = x3 - 3x + 1 is plotted,the graph crosses the x-axis in the ranges -2 < x < -1 and 0 < x < 1

Antwort anzeigen

Frage 27 Bericht

In the figure, TSP = PRQ, QR = 8cm, PR = 6cm and ST = 12cm. Find the length SP.

4cm

16cm

9cm

14cm

Impossible, insufficient data

Antwortdetails

\frac{P Q}{6 + R T} = \frac{6}{12} = \frac{6}{P S}

(Similar triangles)

$\frac{6}{12} = \frac{8}{P S}$

PS = $\frac{12 \times 8}{6}$

= 16cm

Antwort anzeigen

Frage 28 Bericht

If $pq + 1 = q^2$ and $t = \frac{1}{p} - \frac{1}{pq}$ express $t$ in terms of $q$

1

P-Q

1

q-1

1

q+1

1 + q

1

1-q

Antwortdetails

Pq + 1 = q2......(i)
t =

\frac{1}{p}

-

\frac{1}{p q}

.........(ii)
p =

\frac{q^{2} - 1}{q}

Sub for p in equation (ii)
t =

\frac{1}{q^{2} - \frac{1}{q}}

-

\frac{1}{\frac{q^{2} - 1}{q} \times q}

t =

\frac{q}{q^{2} - 1}

-

\frac{1}{q^{2} - 1}

t =

\frac{q - 1}{q^{2} - 1}

=

\frac{q - 1}{(q + 1) (q - 1)}

=

\frac{1}{q + 1}

Lies die Unterrichtsnotiz zu Solution Of Linear Equations (WAEC)

Lies die Unterrichtsnotiz zu Algebraic Fractions (WAEC)

Solution Of Linear Equations

Algebraic Fractions

Antwort anzeigen

Frage 29 Bericht

Simplify $ \frac{\left(\frac{2}{3}-\frac{1}{5}\right)-\frac{1}{3}\text{ of }\frac{2}{5}}{3-\frac{1}{1\frac{1}{2}}} $

1

7

1

3

Antwortdetails

$\frac{2}{3} - \frac{1}{5}$ = $\frac{10 - 3}{15}$
= $\frac{7}{15}$
$\frac{1}{3}$ Of $\frac{2}{5}$ = $\frac{1}{3}$ x $\frac{2}{5}$
= $\frac{2}{5}$
( $\frac{2}{3} - \frac{1}{5}$ ) - $\frac{1}{3}$ of $\frac{2}{5}$
= $\frac{7}{15} - \frac{2}{15}$ = $\frac{1}{3}$
3 - $\frac{1}{1 \frac{1}{2}}$ = 3 - $\frac{2}{3}$
= $\frac{7}{3}$
$\frac{\frac{2}{3} - \frac{1}{5} of \frac{2}{15}}{3 - \frac{1}{1 \frac{1}{2}}}$
= $\frac{\frac{1}{3}}{\frac{7}{3}}$
= $\frac{1}{3}$ x $\frac{3}{7}$
= $\frac{1}{7}$

Lies die Unterrichtsnotiz zu Fractions, Decimals And Approximations (WAEC)

Lies die Unterrichtsnotiz zu Number Bases (WAEC)

Lies die Unterrichtsnotiz zu Logarithms (WAEC)

Lies die Unterrichtsnotiz zu Quadratic Equations (WAEC)

Fractions, Decimals And Approximations

Number Bases

Logarithms

Quadratic Equations

Antwort anzeigen

Frage 30 Bericht

Bola choose at random a number between 1 and 300. What is the probability that the number is divisible by 4?

1

4

6

4

7

4

Antwortdetails

Numbers divisible by 4 between 1 and 300 include 4, 8, 12, 16, 20 e.t.c. To get the number of figures divisible by 4, We solve by method of A.P
Let x represent numbers divisible by 4, nth term = a + (n - 1)d
a = 4, d = 4
Last term = 4 + (n - 1)4
288 = 4 + 4n - n
=

\frac{288}{4}

= 72
rn(Note: 288 is the last Number divisible by 4 between 1 and 300)
Prob. of x =

\frac{72}{288}

=

\frac{1}{4}

Lies die Unterrichtsnotiz zu Probability (WAEC)

Probability

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Frage 31 Bericht

The larger value of y for which (y - 1)2 = 4y - 7 is

2

4

6

7

8

Antwortdetails

(y - 1)2 = 4y - 7
y2 - 2xy + 1 = 4y - 7
y2 - 6y + 8 = 0
(y - 4)(y - 2)
y = 4 or 2 = 4

Lies die Unterrichtsnotiz zu Bearings (WAEC)

Lies die Unterrichtsnotiz zu Circles (WAEC)

Lies die Unterrichtsnotiz zu Surds (radicals) (WAEC)

Lies die Unterrichtsnotiz zu Quadratic Equations (WAEC)

Bearings

Circles

Surds (radicals)

Quadratic Equations

Antwort anzeigen

Frage 32 Bericht

In the diagram, find the size of the angle marked ao

60o

80o

120o

160o

Antwortdetails

2 x s = 280o(Angle at centre = 2 x < at circum)

S = $\frac{280^{o}}{2}$

= 140

< O = 360 - 280 = 80o

60 + 80 + 140 + a = 360o

(< in a quad); 280 = a = 360

a = 360 - 280

a = 80o

Lies die Unterrichtsnotiz zu Angles (WAEC)

Angles

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Frage 33 Bericht

A right circular cone has a base radius r cm and a vertical angle 2yo. The height of the cone is

r tan yo cm

r sin yo cm

r cot yo cm

r cos yo cm

r cosec yo cm

Antwortdetails

\frac{r}{h}

= tan yo
h =

\frac{r}{t a n y^{o}}

= r cot yo

Lies die Unterrichtsnotiz zu Introductory Calculus (WAEC)

Lies die Unterrichtsnotiz zu Circles (WAEC)

Introductory Calculus

Circles

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Frage 34 Bericht

Measurements of the diameters, in centimeters, in centimeters, of 20 copper spheres are distributed as shown below:

Class boundary in cm	frequency
3.35 − 3.45	3
3.45 − 3.55	6
3.55 − 3.65	7
3.65 − 3.75	4

What is the mean diameter of the copper spheres?

3.40cm

3.58cm

3.56cm

3.62cm

Antwortdetails

\begin{array}{cc} x(mid point) & f & f x \\ 3.4 & 3 & 10.2 \\ 3.5 & 6 & 21.0 \\ 3.6 & 7 & 25.2 \\ 3.7 & 4 & 14.8 \end{array}

\sum f

= 20

\sum f x

= 71.2
mean =

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

=

\frac{71.2}{20}

= 3.56

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Frage 35 Bericht

The cumulative frequency function of the data below is given below by the equation $y = cf(x)$. What is $cf(5)$?

Score($n$)	Frequency($f$)
3	30
4	32
5	30
6	35
8	20

30

32

55

62

92

Antwortdetails

If y = cf(x)
cf(5) = 30 + 32 + 30
= 92

Lies die Unterrichtsnotiz zu Probability (WAEC)

Lies die Unterrichtsnotiz zu Linear Inequalities (WAEC)

Lies die Unterrichtsnotiz zu Statistics (WAEC)

Probability

Linear Inequalities

Statistics

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Frage 36 Bericht

Find the x co-ordinates of the points of intersection of the two equations in the graph.

1, 1

0, 4

0, 0

4, 0

4, 9

Antwortdetails

If y = 2x + 1 and y = x2 - 2x + 1

then x2 - 2x + 1 = 2x + 1

x2 - 4x = 0

x(x - 4) = 0

x = 0 or 4

Lies die Unterrichtsnotiz zu Modular Arithmetic (WAEC)

Lies die Unterrichtsnotiz zu Coordinate Geometry (WAEC)

Modular Arithmetic

Coordinate Geometry

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Frage 37 Bericht

Find a factor which is common to all 3 binomial expressions $4a^2 - 9b^2,\; 8a^3 + 27b^3,\; (4a + 6b)^2$.

4a + 6b

4a - 6b

2a + 3b

2a - 3b

None

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Frage 38 Bericht

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

(x2 - 1)(x + 2)

x2(x + 2)

x2 + 34

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

Change Of Subject Of A Formula/Relation

Solution Of Linear Equations

Algebraic Expressions

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Frage 39 Bericht

The cost of production of an article is made up as follows: Labour ₦70, Power ₦15, Materials ₦30, Miscellaneous ₦5. Find the angle of the sector representing Labour in a pie chart

210o

105o

106o

175o

90o

Antwortdetails

Total cost of production = ₦120.00
Labour Cost =

\frac{70}{120}

x

\frac{360^{o}}{1}

= 120o

Lies die Unterrichtsnotiz zu Algebraic Expressions (WAEC)

Algebraic Expressions

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Frage 40 Bericht

If 2x + 3y = 1 and x - y = 11, find (x + y).

5

3

8

2

11

Solution Of Linear Equations

Algebraic Expressions

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Frage 41 Bericht

The quadratic equation whose roots are $1 - \sqrt{13}$ and $1 + \sqrt{13}$ is

x2 + (1 -

\sqrt{13}

)x + 1 +

\sqrt{13}

= 0

x2 - 2x - 12 = 0

x2 - 2x + 12 = 0

x2 + 12 + 2x2 = 0

Antwortdetails

1 -

\sqrt{13}

and 1 +

\sqrt{13}

Product of roots = (1 -

\sqrt{13}

) (1 +

\sqrt{13}

) = -12
x2 - (sum of roots) x + (product of roots) = 0
x2 - 2x + 12 = 0

Lies die Unterrichtsnotiz zu Quadratic Equations (WAEC)

Quadratic Equations

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Frage 42 Bericht

Tunde and Shola can do a piece of work in 18 days. Tunde can do it alone in x days, whilst Shola takes 15 days longer to do it alone. Which of the following equations is satisfied by x?

x2 - 5x - 10 = 0

x2 - 20x + 360 = 0

x2 - 21x - 270 = 0

3x2 - 65x + 362 = 0

Solution Of Linear Equations

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Frage 43 Bericht

Two fair dice are rolled. What is the probability that both show up the same number of points.

1

36

7

36

1

2

1

3

1

6

Antwortdetails

A dice has 6 faces, 2 dice has 6 x 6 = 36 combined face
Prob. of both showing the same number of points
=

\frac{6}{36}

=

\frac{1}{6}

Lies die Unterrichtsnotiz zu Probability (WAEC)

Probability

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Frage 44 Bericht

In a racing competition, Musa covered a distance 5x km in the first hour and (x + 10)km in the next hour. He was second to Nzozi who covered a total distance of 118km in the two hours. Which of the following inequalities is correct?

-1 < x < x < 0

-3 < x < 3

0

\leq

x < 18

15 < x < 18

Antwortdetails

Total distance covered by Musa in 2 hrs
= x + 10 + 5x
= 6x + 10
Ngozi = 118 km
If they are equal, 6x + 10 = 188
but 6x + 10 < 118

6x < 108

= x < 18

0 < x < 18 = 0 $\leq$ x < 18

Lies die Unterrichtsnotiz zu Linear Inequalities (WAEC)

Linear Inequalities

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Frage 45 Bericht

Factorize $6x^2 - 14x - 12$

2(x + 3)(3x - 2)

6(x - 2)(x + 1)

2(x - 3)(3x + 2)

6(x + 2)(x - 1)

(3x - 4)(2x + 3)

Antwort anzeigen

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






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Score(\(n\))	Frequency(\(f\))
3	30
4	32
5	30
6	35
8	20