1

Simplify 0.000215 x 0.000028 and express your answer in standard form

A

6.03 x 10^{9}

B

6.02 x 10^{9}

C

6.03 x 10^{-9}

D

6.02 x 10^{-9}

CORRECT OPTION:
d

0.000215215 x 0.000028

= 215 x 10^{-4} x 28 x 10^{-4}

= 215 x 28 x 10^{-6-6}

= 6020 x 10^{-12}

= 6.020 x 10^{3} x 10^{-12}

= 6.02 x 10^{3 - 12}

= 6.02 x 10^{-9}

= 215 x 10

= 215 x 28 x 10

= 6020 x 10

= 6.020 x 10

= 6.02 x 10

= 6.02 x 10

2

Factorize: x + y - ax = ay

A

(x - y)(1 - a)

B

(x + y)(1 + a)

C

(x + y)(1 - a)

D

(x - y)(1 + a)

CORRECT OPTION:
c

x + y - ax = ay

= (x + y) -a(x + y) = (x + y)(1 - a)

= (x + y) -a(x + y) = (x + y)(1 - a)

3

A car uses one litre of petrol for every 14km. If one of petrol cost N63.00, how far can the car go with N900.00 worth of petrol?

A

420km

B

405km

C

210km

D

200km

CORRECT OPTION:
d

1 litre = N63.00

xlitres = N900.00

x x N63 = N900 x 1 litre

x = \(\frac{900}{63} \times litre\)

x = \(\frac{100}{7}\) litres

Also, 1 litre = 14km

\(\frac{100}{7}\) = y

y x 1 litre = \(\frac{100litre}{7}\) x 14km

y = 20km

xlitres = N900.00

x x N63 = N900 x 1 litre

x = \(\frac{900}{63} \times litre\)

x = \(\frac{100}{7}\) litres

Also, 1 litre = 14km

\(\frac{100}{7}\) = y

y x 1 litre = \(\frac{100litre}{7}\) x 14km

y = 20km

4

Correct 0.002473 to 3 significant figure

A

0.002

B

0.0024

C

0.00247

D

0.0025

CORRECT OPTION:
c

5

Simplify 1\(\frac{1}{2} + 2\frac{1}{3} \times \frac{3}{4} - \frac{1}{2}\)

A

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

B

-2\(\frac{1}{4}\)

C

2\(\frac{1}{8}\)

D

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

CORRECT OPTION:
d

1\(\frac{1}{2} + 2\frac{1}{3} \times \frac{3}{4} - \frac{1}{2}\)

\(\frac{3}{2} + \frac{7}{3} \times \frac{3}{4} - \frac{1}{2} = \frac{3}{2} + \frac{7}{4} - \frac{1}{2}\)

= \(\frac{6 + 7 - 2}{4} = \frac{11}{4}\)

= 2\(\frac{3}{4}\)

\(\frac{3}{2} + \frac{7}{3} \times \frac{3}{4} - \frac{1}{2} = \frac{3}{2} + \frac{7}{4} - \frac{1}{2}\)

= \(\frac{6 + 7 - 2}{4} = \frac{11}{4}\)

= 2\(\frac{3}{4}\)

6

The sum of 2 consecutive whole numbers is \(\frac{5}{6}\) of their product, find the numbers

A

3, 4

B

1, 2

C

2, 3

D

0, 1

CORRECT OPTION:
c

Let the no. be x and x + 1

x + (x + 1) = \(\frac{5}{6}\) of x(x + 1)

2x + 1 = \(\frac{5}{6}\) x(x + 1)

6(2x + 1) = 5x^{2} + 5x

12x + 6 = 5x^{2} + 5x

5x^{2} + 5x - 12x - 6 = 0

5x^{2} - 7x - 6 = 0

5x^{2} - 10x + 3x - 6 = 0

5x(x - 2) + 3(x - 2) = 0

(5x + 3)(x - 2) = 0

(5x + 3)(x - 2) = 0

(5x + 3) = 0

x - 2 = 0

for (5x + 3) = 0

5x = -3

x = \(\frac{-3}{5}\) (Imposible since x is a whole number)

x - 2 = 0

x = 2

x = \(\frac{-3}{5}\)(Impossible since x is a whole number)

x - 2 = 0

x = 2

The numbers are x = 2

x + 1 = 2 + 1

= 3

x + (x + 1) = \(\frac{5}{6}\) of x(x + 1)

2x + 1 = \(\frac{5}{6}\) x(x + 1)

6(2x + 1) = 5x

12x + 6 = 5x

5x

5x

5x

5x(x - 2) + 3(x - 2) = 0

(5x + 3)(x - 2) = 0

(5x + 3)(x - 2) = 0

(5x + 3) = 0

x - 2 = 0

for (5x + 3) = 0

5x = -3

x = \(\frac{-3}{5}\) (Imposible since x is a whole number)

x - 2 = 0

x = 2

x = \(\frac{-3}{5}\)(Impossible since x is a whole number)

x - 2 = 0

x = 2

The numbers are x = 2

x + 1 = 2 + 1

= 3

7

A casting is made up of Copper and Zinc. If 65% of the casting is Zinc and there are 147g of Copper. What is the mass of the casting?

A

320g

B

420g

C

520g

D

620g

CORRECT OPTION:
b

%Zinc + %Copper = 100%

65% + %Copper = 100%

%Copper = 100% - 65% = 35%

%Copper = \(\frac{\text{Mass of % Copper}}{\text{Mass of Casting}}\) x 100%

Mass of Casting = \(\frac{147}{35}\) x 100%

= 420g

65% + %Copper = 100%

%Copper = 100% - 65% = 35%

%Copper = \(\frac{\text{Mass of % Copper}}{\text{Mass of Casting}}\) x 100%

Mass of Casting = \(\frac{147}{35}\) x 100%

= 420g

8

Given that P = {x : 1 \(\leq x \leq 6\)}, and Q = {x : 2 \(\leq x \leq 10\)} where x is an integer. Find n(P \(\cap\))

A

4

B

6

C

8

D

10

CORRECT OPTION:
a

P = {1, 2, 3, 4, 5, 6}; Q = {3, 4, 5, 6, 7, 8, 9}

P \(\cap\) Q) = {2, 4, 5, 6}

n(P \(\cap\) Q) = 4

P \(\cap\) Q) = {2, 4, 5, 6}

n(P \(\cap\) Q) = 4

9

The sum of 6 and one-third of x is one more than twice x, find x

A

x = 7

B

x = 5

C

x = 3

D

x = 2

CORRECT OPTION:
c

6 = \(\frac{1}{3}x\) = 1 + 2x

6 = 1 = \(\frac{2x}{1} - \frac{x}{3}\)

5 = \(\frac{6x - x}{3} = \frac{5x}{3}\)

5 = \(\frac{5x}{3}\)

3 x 5 = 5x

15 = 5x

x = \(\frac{15}{5}\)

= 3

6 = 1 = \(\frac{2x}{1} - \frac{x}{3}\)

5 = \(\frac{6x - x}{3} = \frac{5x}{3}\)

5 = \(\frac{5x}{3}\)

3 x 5 = 5x

15 = 5x

x = \(\frac{15}{5}\)

= 3

10

Given that = {x: -2 < x \(\leq\) 9}, where x is an integer what is n(T)?

A

9

B

10

C

11

D

12

CORRECT OPTION:
c

T = {-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

n(T) = 11

n(T) = 11

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