Review Guide for Term Paper (Teza)

Transcription

1 Review Guide for Term Paper (Teza) We will soon have a term paper over the material covered in Chapters 1, 2, 8, 9, 15, 22, 23, 16 and 3. In Chapter 1 we covered: Place value, multiplying and dividing by 10 n nearest whole and 10 n, ordering rational numbers, rounding to the number, to the th n place or to the In Chapter 2 we covered: th n decimal place and the order of operations. Expressions, especially finding expressions from geometrical figures (often involving areas and perimeters) or otherwise, equations and formulas (for these last two we only covered their definition). In Chapter 8 we covered: The set of integers Z, operations on Z:,,,: and the corresponding sign rules. Powers and Roots: calculation of squares, cubes and square roots and cube roots, factors, primes, prime factors, highest common factor (HCF) and lowest common multiples (LCM). In Chapter 9 we covered: Equations, including methods to solve linear equations and equations which come from word problems; Functions, including calculating the output of particular functions; Graphs of line, which included how to find the equation of a simple linear graphs and how to check if given points are or not on a given linear graph of a given equation; In Chapter 15 we covered: Definition of a fraction and of equivalent fractions and how to check that two fractions are equivalent; How to convert a fraction to its decimal form and a decimal form to a fraction. Form of the decimal form depending on the prime factors decomposition of the denominator of the fraction in fully simplified form. What are and how to convert between mixed numbers and improper fractions; How to compare and order fractions; How to add, subtract, multiply and divide fractions and decimals or combinations of these; What are percentages, how to convert between percentages and fractions or decimals, and how to solve problems with percentage increase or decrease; How to solve practical problems which involve fractions. 1

2 In Chapter 22 we covered: Definitions and example of ratio; What does it mean that two fractions are in proportion and how to find the element of a fraction in proportion with another; What does it mean that two pairs of numbers (or two quantities) are in direct proportion, and how to solve practical (or other types of) problems which involve direct proportion; How to divide a quantity in a given ratio and solve related problems. In Chapter 23 we covered: Deriving formulas from information given (in words or mathematical, say as a set of points) ; Using formulas in problems: substituting in formulas, or solving from one variables in a formula when all the other variables are given. In Chapter 16 we covered: Definition and notation of a sequence; How to list (find) the terms of a sequence when the n th term formula is given; How to find the term the term rule for a given sequence (given as a list of numbers or by a diagram); How to find the n th term rule of a given (given as a list of numbers or by a diagram); How to find the equation of a line given by its graph; How to graph a linear equation. In Chapter 3 we covered: Classification of quadrilaterals (the definitions of parallelogram, rectangle,square, rhombus, trapezium and kite); Triangles and classifications of triangles (by sides and by angles); Congruent triangles and cases of congruence. As practice problems: Do the following review problems without a calculator : 2

3 Practice problems: Chapter 1:

4 3. 4

5 Write these numbers in the order of their size, starting with the smallest: a) b) c) Round the following numbers to the degree of accuracy shown: a) 6.37 to i) nearest whole number ii) one decimal place b) to i) nearest whole number ii) one decimal place iii) two decimal places c) 7346 to i) nearest whole number ii) nearest (multiple of) 10 iii) nearest (multiple of a) hundred iv) nearest multiple of a thousand d) to i) nearest (multiple of) a hundred thousands 5

6 8. a) A bridge can safely carry tonnes. Round this weight sensibly to a whole number of tonnes. b) A submarine will work safely to a depth of 67.3 metres. What rounded figure would you use as the safe working depth? c) Houses are built with wooden panels. Each house needs 15 panels. How many houses can be built from 1000 panels? Chapter 2: Expand and simplify the expressions below: a 3(f + 2) + 5(f 3)... b 6u(4 u) + 3u(u + 2)... c 6r(4r + 4) 5r(3r + 4)... d 5t(2t + 3) t(3t 1)... e 2y( 5x 3y) 8x(3x 2y)... 6

7 3. One of the expressions below gives the area for this shape. A 4(x + 6) 1(x 2) B 2(x ) + 2(1 + x 2) C 2(4 + x + 6) 2(1 + x 2) a) Which expression is the correct one?... b) Expand it and simplify it to find the area.... c) What do the other expressions represent (with respect to this shape)? d) Write the area of the figures below, as expressions using brackets. Then expand the expressions and simplify them. 4. Write the area and the perimeters of the figures below, as expressions using brackets as needed. Then expand the expressions and simplify them. a) Area =... Perimeter = b) Area = Perimeter =.. 7

8 c) Area =.... Perimeter =.... d) Area =.... Perimeter =.. e) For the shape in part d, what does the expression for the area become if y = 2? f ) For the shape in part d, what happens if y = 1? Chapters 8 and 23: 1. 8

9

10

11 Here is a five digit number with a missing digit: 35?84. Find the missing digit is the number is divisible by 3 but not by 9. Show your working. 11. Find a test for divisibility by 15. Give examples to show how your test works. 12. Find a test for divisibility by 18. Give some examples to show that your test works. 13. a) Find the smallest number that is divisible by 2, 3, 4, 5 and 6 : b) What can you say about any number that is divisible by 2, 3, 4, 5 and 6? 14. How many prime numbers are less than 100? Circle the correct answer: 15. Calculate: a) 900,1260 HCF(900,1260) b) 864,1440 HCF(864,1440) c) 900,1260 LCM 900,1260 d) 864,1440 LCM 864,1440 e) 616,952 HCF(616,952) f) 616,952 LCM 616,952 g) 840, 480,600 HCF(840, 480,600) h) 840, 480,600 LCM 840, 480, a) The product of two numbers is 24. The difference between the numbers is 11. Find the two numbers. b*) The product of three numbers is 24. The sum of these three numbers is 4. Find the numbers. 11

12 Chapter 9: 1. b) Graph this line on a set of axis xoy. 2. On a coordinate grid, draw the straight line represented by each of these equations: a) y x 2 b) 1 y x 1 2 c) y 3 d) x = -1 e) y 2x 3 f) y x 3 g) y x 1 3. For each of the straight lines shown in the following questions, write in a table of coordinates (a T chart) of five of the points of the line, and from these, deduce the equation of the line: 12

13 13

14 Chapter 15:

15

16 6. Place < or > between these pairs of numbers to show which number is larger: a) b) c) d) Put these fractions and decimals in order from lowest to highest: a) b) Calculate: 2 1 a) 3 b) 1 6 c) d) e) f) g) : 1 : h) i) 1.25 : j) Chapter 22: 1. 15% of the students in a school of 720 students are left handed. What number of students in that school are right handed? 2. Write the first quantity as a percentage of the second: a) 10 out of 60 b) 21 out of A school has 40 teachers and 480 students. What is the teacher : student ratio in the form of 1 : n? 4. The teacher : student ratio in a school is 1:20. There are 24 teachers. How many students are there? 5. A heater uses 4 units of electricity in 40 minutes. How many units does it use in 3 hours? 6. The ratio of girls to boys in a class if 6:5. There are 18 girls. How many boys are there? 16

17 7. A paint mix uses red and white paint in the ratio 3: litres of red paint are used. How much white paint is used? 8. A combine harvester produces 8 tones of grain in 3 hours. How many tones does is produce in 96 hours? 9. Divide 150 in the ratio 3: Divide 1 hour in the ratio 5: Divide 2 Kg in the ratio 2: Divide 2 Km in the ratio 3:8:4. 13*. Salim draws a quadrilateral. The angles are in the ratio 1:4:5:2. Calculate the largest angle of the quadrilateral. 14. There are 24 coins in Angela s purse. The ratio of 50 cent to 25 cent to 10 cent coins is 2:3:7. a) How many 10 cent coins does she have? b) How much money does she have in coins in total? Chapter 16: 1. 17

18 2. 3. Write the first 4 terms of the sequence given: a) b) c) an an an n n n 10 d) a 7 n 5 n e) n an 2 f) 2 n an n 1 2 e* ) Write the term to term rule for the sequences a)-f) above 4. The 6 th term of a sequence is 5. The 10 th term is 7. Which of these position to term rule is the correct one for this 5. sequence (circle your choice) : n n a) an n 1 b) an 2 n 7 c) an 2 d) an

19 c) Work out the position to term rule for: i) The grey squares:. ii) The white squares: iii) All squares :. 6) 7) For each of the following sequences : a) b) c) d) i) determine the term to term rule ii) using this term to term rule, write the next two terms of the sequence. 19

20 8. For each of the following sequences : a) b) c) d) i) write down the next two terms ii) write down the n th term (the position to term rule) for the sequence. Chapter 3: 1. 20

21 2. 21

22 3. 4. i) Look at the shapes below and name each shape according to the definitions of the main quadrilaterals (square, rectangle, parallelogram, rhombus, trapezium, isosceles trapezium and kite): 22

23 ii*) Give the definition of each of these quadrilaterals, after the model below: square, rectangle, parallelogram, rhombus, trapezium, isosceles trapezium and kite. A sqare is : A rectangle is : 23