JAMB/UTME PREP

A group of market women sell at least one of yam, plantain and maize. 12 of them sell maize, 10 sell yam and 14 sell plantain. 5 sell plantain and maize, 4 sell yam and maize, 2 sell yam and plantain only while 3 sell all the three items. How many women are in the group?

• 25

• 19

• 18

• 17

Answer explanation

Let the three items be M, Y and P. n{M ∩ Y} only = 4-3 = 1 n{M ∩ P) only = 5-3 = 2 n{ Y ∩ P} only = 2 n{M} only = 12-(1+3+2) = 6 n{Y} only = 10-(1+2+3) = 4 n{P} only = 14-(2+3+2) = 7 n{M∩P∩Y} = 3 Number of women in the group = 6+4+7+(1+2+2+3) as above =25 women.

Tags

Algebra

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)

Answer explanation

81a⁴ - 16b⁴ = (9a²)² - (4b²)²= (9a² + 4b²)(9a² - 4b²)

N:B 9a² - 4b² = (3a - 2b)(3a + 2b)

Tags

Algebra

In the figure above , TS//XY and XY = TY, ∠STZ = 34°, ∠TXY = 47°, find the angle marked n?

• 47

• 52

• 56

• 99

Answer explanation

In Δ TYXXY = TY ∴y =47° base ∠s of ISCΔBut y+x+34+47 = 180 interior opposite ∠s are supplementary47 + x + 34 + 47 = 180x + 128= 180x = 180- 128x = 52°

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Trigonomentry

Geometry

A chord drawn 5 cm away from the center of a circle of radius 13 cm. Calculate the length of the chord?

• 7cm

• 9cm

• 12cm

• 24cm

Answer explanation

x² + 5² = 13²

x² + 2⁵ = 169

x² = 144

x = √ 144 = 12

Length of the chord AB = 2x

2×12= 24cm

Tags

Trigonomentry

Geometry

Find r, if 6r7₈ = 511₉

• 3

• 2

• 6

• 5

Answer explanation

6r7₈ = 511₉

6 x 8² + r x 8¹ + 7 x 8⁰ = 5 x 9² + 1 x 9¹ + 1 x 9⁰

6 x 64 + 8r + 7 x 1 = 5 x 81 + 9 + 1 x 1384 + 8r + 7 = 405 + 9 + 1

r = 415 - 391

 8r = 24

r = 3

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Number Bases

Subtract 16418₉ from 18630₉.

• 1121₉

• 2112₉

• 2113₉

• 2211₉

Tags

Number Bases

 $Simplify\ \left(\frac{3}{4}of\ \frac{4}{9}\div9\ \frac{1}{2}\right)\ \div1\ \frac{5}{19}$

•  $\frac{1}{5}$ 

•  $\frac{1}{4}$ 

•  $\frac{1}{36}$ 

•  $\frac{1}{25}$ 

Tags

Indices

BODMAS

• 1 - 4 log3

• -1 + 2 log 3

• -1 + 5 log2

• 1 - 2log 2

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Logarithms

Simplify  $\sqrt[]{27}$ +  $\frac{3}{\sqrt[]{3}}$ 

• 4 $\sqrt[]{3}$ 

•  $\frac{4}{\sqrt[]{3}}$ 

• 3 $\sqrt[]{3}$ 

• 3 $\sqrt[]{4}$ 

Answer explanation

 $\sqrt[]{27}$ +  $\frac{3}{\sqrt[]{3}}$ 

= 9×3−−−−√9×3 + 3×3√3√×3√3×33×3

= 33–√3 + 3–√3

= 4 $\sqrt[]{3}$ 

The angle of elevation of the top of a tree from a point on the ground 60m away from the foot of the tree is 78°. Find the height of the tree correct to the nearest whole number.

• 148m

• 382m

• 282m

• 248m

Answer explanation

tan78=h60tan⁡78=h60

h=60tan78h=60tan⁡78

h=60×4.705=282.27mh=60×4.705=282.27m

≊≊ 282m to the nearest whole number.

Tags

Angle of Elevation