Algebra Problem Sheet

8/3/2019 Algebra Problem Sheet

1/4

CH 1MCT Algebra Problem Sheet

CH 1MCT Modelling Concepts and Tools

2011/12

Algebra Problem Sheet: Revision

Section A: Croft and Davison

Initially you should attempt Croft and Davison; Chapter 5, Basic algebra, end of Chapterexercise, pp 127-128. Also attempt end of Block exercises for Chapter 7, Block 2, Solving

quadratic equations (p 220), and Block 3, Factorising polynomial expressions (p 228). You

should then make sure you can do all the problems below, because we assume that you can

transpose equations and are competent at other aspects of basic algebra, can handle indices

(powers) and surds, and can solve quadratic equations.

You should not use your calculator for any of these problems.

Section B:More problems

B.1. Evaluate: (a) |-14| (b) |11| (c) |0.080.008| (Ans: 14, 11, 0.072)

B.2. Without using a calculator, evaluate: (a) 6! (b) 5!4! (c) 11!/10! (Ans: 720, 96, 11)

3

B.4. Which of the following statements are true?

(a) -10 10(b) -10 -10(c) -10 |10|(d) |-10| < 10(e) |-10| -10(f) 11! 10!(g) 10! 12! (Ans: a, b, c, g)

B.5. Simplify: (a) (b) (Ans: 32y, 72xy)

, the latter in

fractional form. (Ans: 144, 0.81, 16,

)

(Ans: 918

, 179, b

47, 3

25, x

5, x

9y

8, 27x

12, x

6y

10, p

1/7)

B.8. Express: (a) 4-3

as a proper fraction, (b)x-6x

-5as a proper fraction, (c) 10

-6as a decimal.

(Ans:

,

, 0.000001)

3

10 2


2/4


11

212

( )

B.13. Express in floating point form: (a) 32000 (b) -184 (c) 0.49 (d) 0.0657

(Ans: 3.2x104, -1.84x10

2, 4.9x10

-1, 6.57x10

-2)

B.14. Simplify: (a) 7p3p +8q + 3q (b) 2x2

+8y27y + 5x

2

(Ans: 4p + 11q, 7x27y + 8y

2)

1

(Ans: , , , ,

, , )

1

(Ans:

,

,

,

,

,

,

, )

1

(Ans: , ,

,

,

)

1 (Ans:

,

)

B.19. Evaluate when (Ans: 97)B.20. The formula calculates the reliability of 2 components in parallel

when the individual components have reliabilitiesR1and R2. Calculate the reliability of

the system when and . (Ans: 0.8)


3/4


B.21. Transpose the following to make the identified letter (in bold) the subject: (a)

(Ans:

,

,

)

B.22. A truck of unladen massMcarrying a load m and travelling at a velocity v has a

stopping distance given by , where Fis the breaking force and tris R load can be calculated for

given values ofM, v, s, Fand tr.

B.23. The flow of water through a pipe is given by

L

HdQ

5

3

where Q is the flow of water through a pipe of lengthL and diameter d, with an

associated head loss ofH. EvansYou are designing the cooling system for a heat treatment quench furnace. Rearrange

the formula above to determine what pipe diameter, d, is necessary to achieve a flow Q

over a distanceL given an acceptable head lossH.

5

1

2

3

1:Ans.

H

LQd

B.24. Solve the following equations: (a) (b)

(Ans: -5, 1, 7/4, -7/6, , -49, 8/13, 9/200)

B.25. Solve the quadratic equation by factorising (Ans: 8, 3)B.26. Solve the quadratic equation by factorising (Ans: 4, 4)B.27. Solve the quadratic equation by factorising (Ans: 2/7, 3/2)B.28. Solve the quadratic equation by factorising (Ans: 4/3, 0)B.29. Solve the quadratic equation

using the formula, to 3 decimal places.

Hint: B.30. Solve the quadratic equation (Ans: 2, 3)B.31. Two quadratic polynomials are multiplied together. What degree (highest power) is the

resulting polynomial? (Ans: 4)

B.32. Factorise the expression into 3 linear factors if is afactor. (Ans: )

B.33. Factorise the expression into 3 linear factors if is afactor. (Ans: )

B.34. Verify that and are solutions to andhence find the remaining solutions (Ans: 3, 4, 0.6754, 13.3246)


4/4


All the problems featured on this sheet except B.12., B.22. and B.24. have either been taken

or adapted from questions generated by MathXL. If you feel you need more practice with

these topics, or any others that come up over the year, the study plan in MathXL generates

questions randomly on all the mathematical topics covered in this module. You can practise

as many questions as you require to feel confident.

(Question B.12. (a), (b), (e), (g) and B.24. were k R from the

Higher Education Academy Maths, Stats & OR network. B.12. (c), (d) and (f) were taken or

adapted fromhttp://www.mathsrevision.net/gcse/pages.php?page=6)

Date: 02/09/11
http://www.mathsrevision.net/gcse/pages.php?page=6http://www.mathsrevision.net/gcse/pages.php?page=6http://www.mathsrevision.net/gcse/pages.php?page=6http://www.mathsrevision.net/gcse/pages.php?page=6

Algebra Problem Sheet

Documents

Transcript of Algebra Problem Sheet