MCQ Questions

Question No. 1

Make the variable given in brackets the subject of the equation.

Answer :

a) a + 2 = (b + 3)/5 (b)

b) x = 6(y − z) (z)

c) a² = 16 b² c² (c)

d) a = [n/(n − 2)]·180 (n)

e) d = √(b² − 4 a c) (a)

f) a = b² + 2 c (b)

g) V = π r² h (r)

h) A = 2 π r² + 2 π r h (h)

i) a = (b + 3)/(b − 3) (b)

j) x² = y² + w² (w)

k) 1/m = 1/n − 1/p (p)

l) C = (5/9)(F − 32) (F)

m) T = 2 π √(k/(M H)) (H)

n) 1/x = 1 − 1/(y + 1) (y)

o) S = n/2 [2 a + (n − 1) d] (d)

Question No. 2

Solve the following equations.

Question No. 3

Describe how the area of a square varies with its length. Write down the relationship in mathematical terms.

Answer :

Question No. 4

Given that y varies as the square of x, and that y = 9 when x = 4, find:

Answer :

a) the formula relating y and x

b) the value of y when x = 12

Question No. 5

If y varies directly as x varies, and y = 7 when x = 4:

Answer :

a) establish a relationship between x and y

b) find the value of x when y = 1/2

Question No. 6

Given that p varies as the square of q varies, and that p = 90 when q = 15,

Answer :

a) find the value of p when q = 5

b) find the value(s) of q when p = 160

Question No. 7

Given that the surface area of a sphere, A, varies directly with the square of its radius, r, and that A = 4πr²:

Answer :

a) establish a relationship between A and r

b) find the value of A when r = 1/2

c) find the value of r when A = 16πr²

Question No. 8

If m is directly proportional to n and m = 3 when n = 18, find the value of m when n = 42.

Answer :

Question No. 9

Given that r varies directly as t varies, and r = 175 when t = 35,

Answer :

a) establish a relationship between r and t

b) find the value of r when t = 3

c) find the value of t when r = 200

Question No. 10

The height, h, of water in a can varies directly as the time taken, t, to fill the can varies. Given that h = 4.2 cm when t = 10 seconds, find the time taken for the can to be filled to a height of 6.3 cm.

Answer :

Question No. 11

The volume of air in a sphere varies directly with the cube of its radius. The volume is 64 cm³ when the radius is 8 cm. Find the volume when the radius is 10 cm.

Answer :

Question No. 12

Given that y is directly proportional to the square of x and y = 40 when x = 2,

Answer :

a) establish a relationship between y and x

b) find the value of y when x = 5

Question No. 13

Given that m is inversely proportional to n and that m = 2 when n = 5, find:

Answer :

a) the relationship between m and n

b) the value of m when n = 10

c) the value of n when m = 6

Question No. 14

The table represents the relationship ‘y varies inversely as x varies’. Find the values of a and b.

Answer :

Question No. 15

If y varies inversely as the square of x − 4 varies, write the equation relating y and x − 4, including the constant of proportionality.

Answer :

Question No. 16

If in question 1, y = 5 when x = 2, find:

Answer :

a) a relationship between y and x − 4

b) the value of y when x = 5

c) the values of x when y = 1/5

Question No. 17

Given that v varies inversely as the square of u varies, and v = 10 when u = 5, find:

Answer :

a) the equation relating v and u²

b) the value of v when u = 10

c) the values of u when v = 10

Question No. 18

Given: r varies inversely as the square root of t varies. Write the relationship between r and t, including the constant of proportionality.

Answer :

Question No. 19

If r is 4 when t = 9:

Answer :

a) establish a relationship between r and t

b) find the value of r when t = 25

c) find the value of t when r = 8

Question No. 20

If x varies inversely as the square root of y varies, and x = 1 when y = 4:

Answer :

a) establish a relationship between x and y

b) find the value of x when y = 9

c) find the value of y when x = 12

Question No. 21

Given that a is inversely proportional to b, find the values of x and y in the table (b: 7, x, 11; a: 99, 77, y).

Answer :

a) find x

b) find y

Question No. 22

Quantity y is inversely related to x. Given that y = 20 when x = 2, find:

Answer :

a) the relationship between y and x

b) the value of y when x = 10

c) the value of x when y = 2

Question No. 23

Given that y varies inversely as the square root of x varies, and y = 40 when x = ½, find:

Answer :

a) the relationship between y and x

b) the value of y when x = ⅓

c) the value of x when y = 1.6

Question No. 24

If x varies inversely as the square root of y varies, and x = 2 when y = 9, find:

Answer :

a) the value of x when y = 16

b) the value of y when x = ½

Question No. 25

Given that y is inversely proportional to x + 8, find:

Answer :

a) the relationship between y and x + 8 if y = 1 when x = 1

b) the value of y when x = 10

Question No. 26

Given that z is inversely proportional to the square of (p − 12), find:

Answer :

a) the relationship between z and (p − 12) if z = 13 when p = 13

b) the value of z when p = 9

c) the value of p when z = 1/13

Question No. 27

If p ∝ 1/√q and q = 25 when p = 2, find the value of q when p = 100.

Answer :

Question No. 28

If y varies inversely as the cube of x varies, and y = 2 when x = 2, find the value of y when x = 4.

Answer :

Question No. 29

Given that y varies inversely as the cube of (a + 3) varies, and y = 2 when a = 1, find the value of y when a = 4.

Answer :

Question No. 30

P ∝ QR when Q = 4, R = 9 and P = 6.

Answer :

a) Find the relationship between P, Q and R.

b) Find Q when P = 8 and R = 12.

Question No. 31

If A, B and C are related so that A ∝ B²/C, and A = 36 when B = 3 and C = 4, calculate B when A = 200 and C = 2.

Answer :

Question No. 32

M varies directly with N and inversely with P. M = 3 when N = 240 and P = 40.

Answer :

a) Write the equation relating M, N and P.

b) Calculate M when N = 120 and P = 30.

Question No. 33

A varies jointly with B and √C. When A = −18, B = 2 and C = 9, find B when A = 10 and C = 4.

Answer :

Question No. 34

The volume of wood in a tree V varies directly with height h and inversely with the square of circumference c. If V = 144 m³ when h = 20 m and c = 1.5 m, find the height h when V = 1 000 m³ and c = 2 m. Write the answer to the nearest metre.

Answer :

Question No. 35

M varies directly with N and inversely with P². If M = 8 when N = 6 and P = 3, express M in terms of N and P.

Answer :

Question No. 36

The quantity n is partly constant and partly varies with m². Given that n = 11 when m = 1 and n = 5m when m = 2, find n when m = 4.

Answer :

Question No. 37

The resistance r to the movement of a vehicle is partly constant and partly proportional to v². If r = 350 N when v = 50 km/h and r = 190 N when v = 30 km/h, find the speed v that gives r = 302.5 N.

Answer :

Question No. 38

The Afolabi family receives a monthly electricity bill C. When E = 500 kW, C = ₦7 420; when E = 600 kW, C = ₦7 604.

Answer :

a) Write a formula relating C, A and E.

b) Calculate C when E = 550 kW.

Question No. 39

The cost of running a business is partly constant and partly varies with the number of employees. If the cost is ₦28 295 for 60 employees and ₦32 495 for 75 employees, find the cost for 80 employees.

Answer :

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