MATHEMATICS HOLIDAY WORK FOR S.1, S.2, S.3 AND S.4 WED, 08 TH JAN 2014.

Size: px

Start display at page:

Download "MATHEMATICS HOLIDAY WORK FOR S.1, S.2, S.3 AND S.4 WED, 08 TH JAN 2014."

Gerard Simpson
5 years ago
Views:

1 MATHEMATICS HOLIDAY WORK FOR S., S., S. AND S. WED, 08 TH JAN 0. INSTRUCTIONS:. Read the notes below on fractions carefully and answer the exercise on pages and.. Note the mistakes pointed out and avoid repeating them in the exercise.. Put your answers on separate answer sheets and come with them on the opening day of the term.. Show your working clearly and neatly.. S.M and S.T students, scan your work and send it to my before 8th Jan 0. This work on fractions is part of what I have put in my book Common mistakes in mathematics which will be out in February this year(0). This book shows most of the mistakes different students make in mathematics. HAPPY NEW YEAR TO EVERY ONE COMMON MISTAKES IN MATHEMATICS: Written by Kennedy Matumbwe GHS. Page

2 A fraction is part of a whole number. FRACTIONS There are three major types of fractions namely; () Proper fraction: This is where the numerator is smaller than the 8 99 denominator. For example,,,, etc () Improper fraction: This is where the numerator is greater than the 9 denominator. For example;,,, etc. 9 () Mixed fraction: This contains a whole number and a fraction part. For example;,, etc. 8 OPERATIONS WITH FRACTIONS (a) Addition and subtraction. Examples Work out the following; (iv) (ii) (iii) (v) 8 Answers (Since the denominator is the same, we only add the numerators) (ii) 9 8 (LCM of and is ) (Always change your final answer from improper to mixed fraction) COMMON MISTAKES IN MATHEMATICS: Written by Kennedy Matumbwe GHS. Page

3 (iii) (LCM of and is 8) (The answer is a fraction but not as some students carelessly write it) 8 (iv) (one can first handle whole numbers and fractions separately) (LCM of and is ) Method 9 (changing mixed to improper fractions) (LCM of and is ) (Final answer in mixed fraction) (v) 8 Many students make a mistake on such numbers; see how they work out this number; BODMAS (LCM of 8 and is 0) COMMON MISTAKES IN MATHEMATICS: Written by Kennedy Matumbwe GHS. Page

4 by adding it (This is a wrong answer because you have considered to be negative 0 and you take the sum to be negative) 8 See the correct working below: (b) Multiplication and Division Examples Work out the following: (iv) BODMAS (LCM of 0 and 8 is 0) (ii) (iii) 9 Answers 0 (Reduced to the simplest term) COMMON MISTAKES IN MATHEMATICS: Written by Kennedy Matumbwe GHS. Page

5 (ii) (Changed to improper fractions) (iii) (Introduce a multiplication sign and the reciprocal of the next Fraction) (iv) Some students confuse multiplying a column vector by a scalar with multiplying a fraction by a whole number. See how they carelessly answer this; 0 Wrong answer. Follow the correct working below; COMMON MISTAKES IN MATHEMATICS: Written by Kennedy Matumbwe GHS. Page

6 (c) Combined operations The order of operations used for fractions is the same as that used for whole numbers, i.e work out the brackets first, then of, divide, multiply, add and lastly subtract (BODMAS). Examples Evaluate the following: (ii) of 8 0 Answers of (BODMAS) (ii) Many students find it difficult to work out such expressions. See below the mistake they commonly make; (This is wrong unless if and are put in separate brackets) COMMON MISTAKES IN MATHEMATICS: Written by Kennedy Matumbwe GHS. Page

7 (BODMAS) (Wrong) See the different correct ways of evaluating this expression; (I) COMMON MISTAKES IN MATHEMATICS: Written by Kennedy Matumbwe GHS. Page

8 (II) (First simplify the numerator and denominator separately and later combine them again) Numerator Denominator Combining; COMMON MISTAKES IN MATHEMATICS: Written by Kennedy Matumbwe GHS. Page 8

9 RECURRING DECIMALS When fractions are changed to decimals, some of them give a definite number of decimal places. For example; terminating decimals. 0., 0., 0. 8 etc. Those are called However, there are some fractions that give decimals that never end. For example; 0..., 8... etc. When we change to a decimal, the digit in the decimal repeats itself continuously without ending. We say that is a recurring digit. Decimals with such a recurring digit are called recurring decimals. Recurring decimals can be written in the following ways; (ii) (iii) 0.. or 0.. or or 0. or or or Examples Express the following recurring decimals as fractions in their simplest terms. ().. 0. ( ) 0. Answers: ().. 0. Many students forget to put symbols to show that the decimal is a recurring decimal and this makes their working wrong since for example and COMMON MISTAKES IN MATHEMATICS: Written by Kennedy Matumbwe GHS. Page 9

10 See both workings below: Wrong Let x 0. Correct Let.. x x x x. 00x x x 00x x x 99x x 99 x This is wrong b se the recurring symbol is not seen anywhere. The recurring symbol must appear at least once in your working. x 99 x ( ) 0. Let r 0... Multiply both sides by 000 because of three recurring digits in the decimal given. 000r r r r r r r COMMON MISTAKES IN MATHEMATICS: Written by Kennedy Matumbwe GHS. Page 0

11 EXERCISE ON FRACTIONS: () Simplify the following: (a) (b) x x (c) (d) 9 (e) (f) (g) ( ) 9 (h) x x x x y x y (j) () Find the value of ( ) x. of 0 () Evaluate of fraction form.. Leaving your answer in (). Express 0. as a fraction, in the form, where q 0. (). Simplify:. () Simplify:. COMMON MISTAKES IN MATHEMATICS: Written by Kennedy Matumbwe GHS. Page

12 () Express as a common fraction. (8) Given that a ½, b ¾, and c ½, evaluate: c + a b. (9) Joseph sweeps ¼ of a compound, Milly sweeps ⅗ of the same compound and Susan sweeps the rest. (a) What fraction does Susan sweep? (b) If Susan sweeps square metres, how big is this compound? 0. Evaluate of 8. Express. as a fraction in its simplest form.. Two boys and a girl shared some money. The younger boy got of it, the elder boy got 8 of the remainder and the girl got the rest. Find the percentage share of the younger boy to the girl s share.. Evaluate / ( / ). Convert. into a fraction giving your answer as a mixed fraction. ).. Ben spends ⅔ of his income on food and ⅕ of the remainder on rent and saves the rest. If he saves shs.,800, find Ben s income. END COMMON MISTAKES IN MATHEMATICS: Written by Kennedy Matumbwe GHS. Page

Lesson 1: Arithmetic Review

Lesson 1: Arithmetic Review Topics and Objectives: Order of Operations Fractions o Improper fractions and mixed numbers o Equivalent fractions o Fractions in simplest form o One and zero Operations on