Basic Engineering Mathematics, Fifth Edition

Revision Test 4: Algebra and simple equations

This assignment covers the material contained in Chapters 9–11.The marks available are shown in brackets at the
end of each question.

1. Evaluate 3pqr^3 − 2 p^2 qr+pqr when p=

1

2

,

q=−2andr=1. (3)

In problems 2 to 7, simplify the expressions.

2.

9 p^2 qr^3

3 pq^2 r

(3)

3. 2( 3 x− 2 y)−( 4 y− 3 x) (3)


4. (x− 2 y)( 2 x+y) (3)


5. p^2 q−^3 r^4 ×pq^2 r−^3 (3)


6. ( 3 a− 2 b)^2 (3)

7.

a^4 b^2 c

ab^3 c^2

(3)

8. Factorize
   (a) 2x^2 y^3 − 10 xy^2
   (b) 21ab^2 c^3 − 7 a^2 bc^2 + 28 a^3 bc^4 (5)


9. Factorize and simplify
   2 x^2 y+ 6 xy^2
   x+ 3 y

−

x^3 y^2

x^2 y

(5)

10. Remove the brackets and simplify
    10 a−3( 2 a−b)− 4 (b−a)+ 5 b


11. Simplifyx÷ 5 x−x+( 2 x− 3 x)x (4)


12. Simplify 3a+ 2 a× 5 a+ 4 a÷ 2 a− 6 a (4)


13. Solve the equations

(a) 3a= 39

(b) 2x− 4 =9(3)

14. Solve the equations

(a)

4

9

y= 8

(b) 6x− 1 = 4 x+5(4)

15. Solve the equation
    5 (t− 2 )− 3 ( 4 −t)= 2 (t+ 3 )− 40 (4)


16. Solve the equations:

(a)

3

2 x+ 1

=

1

4 x− 3

(b) 2x^2 = 162 (7)

17. Kinetic energy is given by the formula,
    Ek=

1

2

mv^2 joules, wheremis the mass in kilo-

grams andvis the velocity in metres per second.

Evaluate the velocity when Ek= 576 × 10 −^3 J

and the mass is 5kg. (4)

18. An approximate relationship between the num-
    ber of teethTon a milling cutter, the diameter
    of the cutterDand the depth of cutdis given
    byT=

12. 5 D

D+ 4 d

.EvaluatedwhenT=10 and

D=32. (5)

19. The modulus of elasticityEisgivenbythefor-
    mulaE=

FL

xA

whereFis force in newtons,L

is the length in metres,x is the extension in

metres andAthe cross-sectional area in square

metres. EvaluateA, in square centimetres, when

E= 80 × 109 N/m^2 ,x=2mm,F= 100 × 103 N

andL= 2 .0m. (5)