1. Set 1
REVISION TEST 1 – HUM 1012 ENGINEERING MATHEMATICS 1
1. a. Simplify ( ) ( )nmnm 3433 +−−−
b. Simplify )n2m3()n4m8( 2
−−+
2. Simplify ( ) ( )2222
261520
5
3
baba −−+
3. Simplify ( ) ( )ghgghg 233 −+−−
4. Simplify ( )
−−+
2
2432
x
x and then state the coefficient and unknown.
5. Simplify the following.
(a) 3y + 4 ( ) ( )xyyx +−−− (b)
ba
ba 22
+
− . (c) pqr5rqp25 32
÷
6. Expand the following.
(a) ( ) )y2x(y42x +− (b) )pq(p5 −−
7. Factorize
(a) 814 2
−y
(b) 369 2
−x
(c) bb 364 3
−
(d) 22
44 qpqp +−
(e) xx 43
− .
8. Change the subject to b for
2
102
bca
a
+
=
9. Change the subject to a for
2
2
1
atuts +=
10. Change the subject to s for 222
2asuv −= .
11.Express t as a subject of the formula
2
2
atu
s
+
= .
12. Given that
1n
23nH
−
+= ,
(a) write n as the subject of the formula.
(b) calculate the value of n if H = 8.
13. Given that the volume of a cylinder hrV 2
π= . Make r as the subject, then find the value
of r if V = 42cm3
, h = 3cm and π= 3.142 .
14. (a) Solve 6
7
5
2 =−
j
j (b) Solve 94
6
−= k
k
15. Solve 98 =−x
16. Solve the following equations.
2. (a) 58y −=+ .
(b) 3x2
+ 7x – 5 = 0.
(c) m - 6 = 10 – 3m
17. A customer pays 50 dollars for a coffee maker after a discount of 20 dollars. What is the
original price of the coffee maker?
18. Half a number plus 5 is 11.What is the number?
17. By using formulae, solve
(a) 10204 2
−=− xx
(b) 02x5x3 2
=−+
18. By using formulae, solve mm
3
10
12
−=+
19.Solve the quadratic equation 0943 2
=++− yy using the formula.
Given that the formula is
a
acbb
y
2
42
−±−
= .
20. Solve the following inequalities :
(a) 91x4 <+<
(b) 37x −<−
(c) 7
2
x
>−
(d) 62x410 ≤+≤
(e) 14x6216 <−≤−
(f) 015x2x2
<−+
(g) 2
x65x17 −≥+
(h) 0x2x5 2
≤+
21.Solve the following simultaneous equations:
(a) 20y4x3 =+ and 5yx3 =+
(b) 2xy =− and 4yx4x2
−=++
22. Solve the following system:
23. Solve
x + y− z= 4
x − 2y+ 3z= −6
2x + 3y+ z= 7
24. Solve the following system:
x −y + 2z = 9
2x + y −z = 1
