Revision Test 6 : Quadratics, logarithms and exponentials
This assignment covers the material contained in Chapters 14–16.The marks available are shown in brackets at the
end of each question.
- Solve the following equations by factorization.
(a) x^2 − 9 =0(b)x^2 + 12 x+ 36 = 0
(c) x^2 + 3 x− 4 =0(d)3z^2 −z− 4 = 0
(9) - Solvethefollowingequations,correct to3decimal
places.
(a) 5x^2 + 7 x− 3 =0(b)3a^2 + 4 a− 5 = 0
(8) - Solvetheequation3x^2 −x− 4 =0bycompleting
the square. (6) - Determine the quadratic equationinxwhose roots
are 1 and−3. (3) - The bending momentM at a point in a beam
is given byM=
3 x( 20 −x)
2
wherexmetres is
the distance from the point of support. Deter-
mine the value ofxwhen the bending moment is
50Nm. (5)
- The currentiflowing throughan electronic device
is given by i=( 0. 005 v^2 + 0. 014 v) amperes
wherevis the voltage. Calculate the values ofv
wheni= 3 × 10 −^3 .(6) - Evaluate the following, correct to 4 significant
figures.
(a) 3.2ln4. 92 −5lg17.9(b)
5 ( 1 −e−^2.^65 )
e^1.^73
(4)
- Solve the following equations.
(a) lgx=4(b)lnx= 2
(c) log 2 x=5(d)5x= 2
(e) 3^2 t−^1 = 7 t+^2 (f) 3e^2 x= 4. 2 (18)
9. Evaluate log 16
(
1
8
)
(4)
- Write the following as the logarithm of a single
number.
(a) 3log2+2log5−
1
2
log16
(b) 3log3+
1
4
log16−
1
3
log27 (8)
- Solve the equation
log(x^2 + 8 )−log( 2 x)=log3. (5) - Evaluate the following, each correct to 3 decimal
places.
(a) ln462. 9
(b) ln0. 0753
(c)
ln3. 68 −ln2. 91
4. 63
(3)
- Expandxe^3 xto six terms. (5)
- Evaluatevgiven thatv=E
(
1 −e−
t
CR
)
volts
when E=100V,C= 15 μF, R=50k and
t= 1 .5s. Also, determine the time when the
voltage is 60V. (8)
- Plot a graph of y=
1
2
e−^1.^2 x over the range
x=−2tox=+1 and hence determine, correct to
1 decimal place,
(a) the value ofywhenx=− 0 .75, and
(b) the value ofxwheny= 4 .0(8)