Engineering Mathematics

Stroud, K. A. Booth, Dexter J.

Chapter 2

Programme F.2 Introduction to algebra - all with Video Answers

Educators

Section 1

Test exercise F.2

Problem 1

Simplify each of the following:
(a) $2 a b-4 a c+b a-2 c b+3 b a$
(b) $3 x^{2} y z-z x^{2} y+4 y x z^{2}-2 x^{2} z y+3 z^{2} y x-3 z y^{2}$
(c) $c^{p} \times c^{-q} \div c^{-2}$
(d) $\frac{\left(x^{\frac{1}{2}}\right)^{-\frac{2}{3}} \div\left(y^{3}\right)^{2} \times\left(x^{\frac{3}{5}}\right)^{-\frac{5}{3}}}{\left(x^{\frac{1}{4}}\right)^{-1} \times\left(y^{\frac{1}{3}}\right)^{6}}$

M Hassan Anwar

M Hassan Anwar

Numerade Educator

Problem 2

Remove the brackets in each of the following:
(a) $2 f(3 g-4 h)(g+2 h)$
(b) $(5 x-6 y)(2 x+6 y)(5 x-y)$
(c) $4\{3[p-2(q-3)]-3(r-2)\}$

M Hassan Anwar

Numerade Educator

Problem 3

Evaluate by calculator or by change of base where necessary:
(a) $\log 0.0270$
(b) $\ln 47.89$
(c) $\log _{7} 126 \cdot 4$

M Hassan Anwar

Numerade Educator

Problem 4

Rewrite the following in log form:
(a) $V=\frac{\pi h}{4}(D-h)(D+h)$
(b) $P=\frac{1}{16}(2 d-1)^{2} N \sqrt{S}$

M Hassan Anwar

Numerade Educator

Problem 5

Express the following without logarithms:
(a) $\log x=\log P+2 \log Q-\log K-3$
(b) $\log R=1+\frac{1}{3} \log M+3 \log S$
(c) $\ln P=\frac{1}{2} \ln (Q+1)-3 \ln R+2$

M Hassan Anwar

Numerade Educator

Problem 6

Perform the following multiplications and simplify your results:
(a) $(3 x-1)\left(x^{2}-x-1\right)$
(b) $\left(a^{2}+2 a+2\right)\left(3 a^{2}+4 a+4\right)$

M Hassan Anwar

Numerade Educator

Problem 7

Simplify each of the following:
(a) $\frac{x^{3}}{y^{2}} \div \frac{x}{y^{3}}$
(b) $\frac{a b}{c} \div \frac{a c}{b} \times \frac{b c}{a}$

M Hassan Anwar

Numerade Educator

Problem 8

Perform the following divisions:
(a) $\left(x^{2}+2 x-3\right) \div(x-1)$
(b) $\frac{n^{3}+27}{n+3}$
(c) $\frac{3 a^{3}+2 a^{2}+1}{a+1}$

M Hassan Anwar

Numerade Educator

Problem 9

Factorize the following:
(a) $36 x^{3} y^{2}-8 x^{2} y$
(e) $x^{2}+10 x+24$
(b) $x^{3}+3 x^{2} y+2 x y^{2}+6 y^{3}$
(f) $x^{2}-10 x+16$
(c) $4 x^{2}+12 x+9$
(g) $x^{2}-5 x-36$
(d) $(3 x+4 y)^{2}-(2 x-y)^{2}$
(h) $6 x^{2}+5 x-6$

M Hassan Anwar

Numerade Educator