Quiz about WAEC QUIZ 4

Question 1

Simplify: $$\left(\frac{1}{\sqrt[]{3}-1}+\frac{1}{\sqrt[]{3}+1}\right)^2.$$

Accepted Answer

3

Answer

1

Answer

4

Answer

9

Question 2

Solve $$3^{2x}-4\left(3^x\right)+3=0.$$

Accepted Answer

0 or 1

Answer

0 or 3

Answer

1 or 2

Answer

1 or 3

Question 3

For what value of x will $$\log_24x+\log_2\left(x+4\right)=7\ ?$$

Accepted Answer

4

Answer

2

Answer

6

Answer

8

Question 4

Find the coefficient of $$x^4$$ in the expansion of $$\left(\frac{1}{x}-x\right)^6.$$

Accepted Answer

-6

Answer

-2

Answer

4

Answer

6

Question 5

If $$f\left(x\right)=2x^3+x^2+mx-6\ and\ f\left(-2\right)=-4,$$ find the value of m.

Accepted Answer

-7

Answer

7

Answer

6

Answer

-6

Question 6

Question 6.

Accepted Answer

10

Answer

8

Answer

12

Answer

15

Question 7

Given that $$f\left(g\left(x\right)\right)=x\ and\ f\left(x\right)=5x-2,\ find\ g\left(x\right).$$

Accepted Answer

$$g\left(x\right)=\frac{1}{5}\left(x+2\right)$$

Answer

$$g\left(x\right)=4x+2$$

Answer

$$g\left(x\right)=\frac{1}{5}\left(x-2\right)$$

Answer

$$g\left(x\right)=x+2$$

Question 8

The first and sixth terms of an exponential sequence (G.P.) are $$3\ and\frac{3}{32}$$ respectively. Find the common ratio of the sequence.

Accepted Answer

$$\frac{1}{2}$$

Answer

$$\frac{1}{6}$$

Answer

$$\frac{1}{5}$$

Answer

$$\frac{1}{3}$$

Question 9

If $$\int_1^2\left(kx^2+x+2\right)dx=0,$$ find the value of the constant k.

Accepted Answer

$$-\frac{3}{2}$$

Answer

$$\frac{3}{2}$$

Answer

$$\frac{7}{2}$$

Answer

$$-\frac{7}{2}$$

Question 10

The deviations between two ranks are -1, 1, -1, 1, 0, -3, 1, -2, 1 and 3. Calculate the Spearman's rank correlation coefficient.

Accepted Answer

0.83

Answer

0.20

Answer

0.27

Answer

0.76

Question 11

If $$f\left(x+2\right)=x^3-2x^2+x-7,\ find\ f\left(1\right).$$

Accepted Answer

-11

Answer

-9

Answer

-7

Answer

9

Question 12

If $$y=\frac{1+x}{1-x}\ ,\ find\ \frac{dy}{dx}\ .$$

Accepted Answer

$$\frac{2}{\left(1-x\right)^2}$$

Answer

$$\frac{1}{\left(1-x\right)^2}$$

Answer

$$\frac{1+x}{\left(1-x\right)^2}$$

Answer

$$\frac{x}{\left(1-x\right)^2}$$

Question 13

The sixth term of a linear sequence (A.P.) is 43 and the thirteenth term is 92.

Find the sum of the first 12 terms.

Accepted Answer

558

Answer

1116

Answer

510

Answer

360

Question 14

If $$\sqrt[]{t+3}+\sqrt[]{t+10}=7,$$ find the value of t.

Accepted Answer

6

Answer

7

Answer

8

Answer

9

Question 15

Find $$\int_{ }^{ }\left(\frac{2x^3+x^2+3}{x^2}\right)dx.$$

Accepted Answer

$$x^2+x-\frac{3}{x}+k$$

Answer

$$x+1+\frac{3}{x}+k$$

Answer

$$x^2+x+\frac{3}{x^2}+k$$

Answer

$$2x^2+1+\frac{3}{x}+k$$

Question 16

If $$\alpha\ and\ \beta$$ are the roots of the equation $$2x^2-x-2=0,$$ evaluate $$\left(\alpha^2+\beta^2\right).$$

Accepted Answer

$$2\frac{1}{4}$$

Answer

$$4\frac{1}{4}$$

Answer

$$-1\frac{3}{4}$$

Answer

$$-3\frac{3}{4}$$

Question 17

Question 17.

Accepted Answer

3

Answer

-3

Answer

7

Answer

67

Question 18

A body, M, is maintained in equilibrium by

three forces as shown in the diagram alongside.

Calculate, correct to one decimal place, the value of R.

Accepted Answer

75.8 N

Answer

115.0 N

Answer

79.4 N

Answer

34.4 N

Question 19

The table above shows the number of babies born in some villages on a certain day in a district. The mean of the distribution is 6. Find the median of the distribution.

Accepted Answer

6

Answer

1

Answer

2

Answer

3

Question 20

The table above shows the number of babies born in some villages on a certain day in a district. Find the mode of the distribution.

Accepted Answer

5

Answer

6

Answer

4

Answer

3

Question 21

What is the probability of picking a letter T from the word INSTITUTION?

Accepted Answer

0.27

Answer

0.02

Answer

0.09

Answer

0.33

Question 22

For what range of values of x is $$3x^2-4x-4$$ negative?

Accepted Answer

$$-\frac{2}{3}

Answer

$$-2<x<\frac{2}{3}$$

Answer

$$x<-\frac{2}{3}\ ,\ x>2$$

Answer

$$x<-2\ ,\ x>\frac{2}{3}$$

Question 23

If $$\sin y=\frac{1}{2}\ and\ \cos x=\frac{1}{3},\ evaluate\ \sin\left(y-x\right).$$

Accepted Answer

$$\frac{1-2\sqrt[]{6}}{6}$$

Answer

$$\frac{1-\sqrt[]{2}}{6}$$

Answer

$$-\frac{2}{3}$$

Answer

$$-\frac{1}{2}$$

Question 24

Question 24.

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 25

A bag contains 5 red balls and 3 black balls. Two balls are drawn in succession without replacement. What is the probability of drawing one of each colour?

Accepted Answer

$$\frac{15}{28}$$

Answer

$$\frac{15}{32}$$

Answer

$$\frac{15}{56}$$

Answer

$$\frac{15}{64}$$

Question 26

Differentiate $$\left(\frac{1}{5}x^2-1\right)^5$$ with respect to x.

Accepted Answer

$$2x\left(\frac{1}{5}x^2-1\right)^4$$

Answer

$$10x\left(\frac{1}{5}x^2-1\right)^4$$

Answer

$$\frac{1}{5}\left(x^2-1\right)^4$$

Answer

$$\frac{1}{6}\left(x-1\right)^6$$

Question 27

A boy kicks a football of mass 3Kg, initially at rest, with a force of 12N.

If the ball moves in a straight line for 2 seconds, calculate the distance covered.

Accepted Answer

8 m

Answer

18 m

Answer

16 m

Answer

12 m

Question 28

Find the domain of the function $$f:x\rightarrow\sqrt[]{4-x^2}.$$

Accepted Answer

$$\left\{x:-2\le x\le2\right\}$$

Answer

$$\left\{x:x\ge-2\right\}$$

Answer

$$\left\{x:x\le2\right\}$$

Answer

$$\left\{x:x=-2,\ x=2\right\}$$

Question 29

The curves of $$y=2x^2+5x+3\ and\ y=3x^2-6x+4$$ intersects at two points. Which of these equations gives the values of x at these points?

Accepted Answer

$$x^2-11x+1=0$$

Answer

$$x^2-11x-1=0$$

Answer

$$x^2+11x+1=0$$

Answer

$$x^2+11x-1=0$$

Question 30

An arc of a circle with radius 14cm subtends an angle of $$\frac{2\pi}{5}$$ radians at the centre. Calculate its length. $$\left[Take\ \pi=\frac{22}{7}\right]$$

Accepted Answer

17.6 cm

Answer

10.4 cm

Answer

12.8 cm

Answer

13.9 cm

Question 31

In how many ways can a committee of 5 men and 3 women be

chosen from 8 men and 5 women?

Accepted Answer

560

Answer

100

Answer

370

Answer

480

Question 32

If $$\left(x-2\right)$$ is a factor of $$2x^3-x^2-8x+4\ ,$$ find the other two factors.

Accepted Answer

$$\left(x+2\right)\ and\ \left(2x-1\right)$$

Answer

$$\left(x+2\right)\ and\ \left(x-1\right)$$

Answer

$$\left(x-2\right)\ and\ \left(2x+1\right)$$

Answer

$$\left(x-2\right)\ and\ \left(x+1\right)$$

Question 33

A ball is thrown vertically upwards and its height $$h\ m$$ after

t seconds is $$h=12t-4.5t^2\ .$$ Find the greatest height reached.

Accepted Answer

8.00 m

Answer

7.96 m

Answer

13.43 m

Answer

14.18 m

Question 34

Question 34.

Accepted Answer

(-8, -2)

Answer

(3, 11)

Answer

(8, 2)

Answer

(11, 3)

Question 35

A uniform beam, PQ of length 100cm weighs 35N. It is placed on a support

at a point 40cm from P. Weights of 54N and W are attached to P and Q respectively to keep the beam in equilibrium. Find, correct to the nearest

whole number the value of W.

Accepted Answer

30 N

Answer

69 N

Answer

60 N

Answer

35 N

Question 36

Given that p * q = $$p^2+q^2+pq$$ and p * (p+1) = 61, find the value of p.

Accepted Answer

-5 or 4

Answer

3 or 7

Answer

-3 or 4

Answer

-4 or 5

Question 37

An object of mass 5Kg is suspended from the ceiling of a lift by a string.

Find the tension in the string when the lift is descending with an acceleration

of $$1.5\ ms^{-2}.$$ $$\left[Take\ g=10\ ms^{-2}\right]$$

Accepted Answer

42.5 N

Answer

50.0 N

Answer

60.0 N

Answer

72.5 N

WAEC QUIZ 4

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