Year 8. Semester 2 Revisions

Transcription

1 Semester Revisions Year 8 Semester Two Revisions 01 Students are advised to review previously completed tests, assignments and homework followed by this semester one revision booklet. Be sure to seek extra help early to clarify any difficulties with content before the exam. Page 1 of 19

2 Semester Revisions Unit 7: Index Laws Review of Index Form o If a number or a variable is multiplied by itself several times, it can be written using short- cut notation referred to as index form. o When written in index form, the number or variable that is being multiplied is called the base, while the number showing how many times it is being multiplied is called the power, index or exponent. For example, in the number 4, is the base and 4 is the power, index or exponent. o When the base is multiplied by itself the number of times indicated by the power, index or exponent, the answer is called a basic numeral. For example, 4 = x x x = 16 Index Form Factor Form Basic Numeral First Index Law (Multiplying Indices with the same base) o The numbers in index form with the same base can be multiplied together by being written in factor form first. For example, 5 x 5 = (5 x 5 x 5) x (5 x 5) = 5 5. o The simpler and faster way to multiply numbers in index form with the same base is to use the first index law. The First Index Law states: a m x a n = a m+n. This means that when numbers or variables are written in index form with the same base are multiplied by each other, the powers (indices) are added together. For example, 5 x 5 = 5 + = 5 5. o If the variables in index form that are being multiplied have numerical coefficients, the coefficients are multiplied together and the variables in index form by each other. For example, a 4 x a 5 = ( x ) x (a 4 x a 5 ) = 6a 9 o When there is more than one variable involved in the multiplication question, the First Index Law is applied to each variable separately. For example, 7m x n 5 x m 8 x n 4 = (7 x x ) x (m x m 8 ) x (n 5 x n 4 ) = 4m 11 n 9 Second Index Law (Dividing Indices with the same base) o The numbers in index form with the same base can be divided by first being written in factor form. For example, 6 4 = 6 = = = 4 o The simpler and faster way to divide the numbers in index form is to apply the Second Index Law. The Second Index Law states: a m a n = a m n. This means that when the numbers in index form with the same base are divided, the powers are subtracted. For example, 6 4 = 6 4 = o When the numerical coefficients are present, we divide them as we would divide any other numbers and then apply the Second Index Law to the variables. o If the numerical coefficients do not divide nicely, we simplify the fraction that is formed. o When there is more than one variable involved in the division question, the Second Index Law is applied to each variable separately. Third Index Law (the power of zero) o Any base that has an index of 0 is equal to 1. o The Third Index Law states: a 0 = 1 o If it is in brackets, any numeric or algebraic expression that is raised to the power of zero is equal to 1. For example ( x ) 0 = 1 and (abc ) 0 = 1 Fourth Index Law (raising a power to another power) o The Fourth Index Law states that when raising a power to another power, the indices are multiplied; that is, (a m ) n = a mxn. For example, (5 ) 4 = 5 x4 = 5 1. Page of 19

3 Semester Revisions o Every number and variable inside the brackets should have its index multiplied by the power outside the brackets. That is, ( a b) m = a m b m ( ) 4 = 4 4 " a % $ ' # b & and m = am " % $ ' b m # & o Any number or variable that does not appear to have an index really has an index of one. That is, = 1 and a bc = a b 1 c 4 and = 4 4 Practice 1. State the base and power for each of the following. a) 8 4 b) 7 10 c) 0 11 d) m 5 e) c 4 f) n 6. Write each of the following in index form. a) b) c) m m m m m d) d d d. Write the following indices in factor form. a) 4 b) 5 4 c) 7 5 d) n 7 e) a 4 f) k 6 4. Write each of the following as a basic numeral. a) 5 b) 4 4 c) 8 d) 7 4 e) 6 f) Write each of the following in index form. a) 1 n n i i i 6 r r r b) 11 x j x j x j x j x j x 9 x p x p x k 6. Write each of the following in factor form. a) 4b c 5 b) 19a 4 n m 7. Simplify each of the following, giving your answer in index form. a) 7 x b) 6 14 x 6 c) e x e d) 6 8 x 6 x 6 e) 10 x 10 x 10 4 f) g 15 x g x g 1 8. Simplify each of the following. a) a x a 4 x e x e 4 b) 4p x h 7 x h 5 x p c) m x 5m x 8m 4 Page of 19 d) 5p 4 q x 6p q 7 e) 8u w x uw x u 5 w 4 f) 7b c x b 6 c 4 x b 5 c 9. Simplify each of the following, giving your answer in index form. a) b) b 17 c) b d) f 1 9 f Simplify each of the following. a) 8w 1 w 5 b) 1q 4 4q 0 45p 14 c) d) 81m6 9 p 4 18m 11. Simplify each of the following. a) 8p6 p 4 16 p 5 b) 7x9 y c) 16h7 k 4 1xy 1h 6 k d) 5m 1 4n 7 15m 8n

4 Semester Revisions 1. Find the value of each of the following. a) 16 0 b) 44 0 c) f 0 d) h 0 e) (1w 7 ) 0 f) ( x 8) 0 1. Find the value of each of the following. a) 1m k 0 b) 7c m 0 c) 16t 0 8y d) 4d 0 9 p 0 1q Simplify each of the following. a 6a a) b) 5b7 10b 5 8 f f 7 c) 1a 5 5b 1 4 f 5 f d) 8u 9 v 5 u 5 4u Simplify each of the following leaving your answer in index form. a) ( ) 4 b) (6 8 ) 5 c) (11 5 ) 4 d) ( w 9 q ) 4 10! $ 7e 5! $ e) # & f) # & " % " r q 4 % 16. Simplify each of the following. ( ) ( g 4 ) b) ( h ) 8 ( j ) 8 c) ( e 7 ) 8 ( e 5 ) d) ( g 7 ) ( g 9 ) a) j Simplify each of the following. ( ) 4 ( a 6 ) b) ( d 7 ) ( d ) c) ( 10r 1 ) 4 ( r ) a) a 18. Simplify each of the following. a) ( a ) 4 ( a ) b) ( n 5 ) ( n 6 ) c) 19. Simplify each of the following. b 4! $! 5h 10 $ a) # & b) # & " d % " j % c)! # " k 5 t 8 $ & % ( c 6 ) 5 ( c 5 ) d) d)! 5y 7 $ # & " z 1 % Unit 8: Measurement (Video s posted on Mr. McEwen s Website) ( k ) 10 ( k ) 8 Conversions in the Metric System o Metric units of length include millimetres (mm), centimetres (cm), metres (m) and kilometres (km). o To convert between the units of length, we use the following conversion chart: o When converting from a large unit to a smaller unit, multiply by the conversion factor (resulting in the decimal place moving to the right). When converting from a smaller unit to a larger unit, divide by the conversion factor (resulting in the decimal place moving to the left). Page 4 of 19

5 Semester Revisions Perimeter of - Dimmensional Figures (including irregular and composite shapes) o The perimeter of a shape is the total distance around the shape. o To find the perimeter of any shape, identify the length of all sides, ensure that all measurements are in the same units, add all side lengths together and include units with your answer. (See attached formula sheet for the six - dimensional figures with their formulas) Area of - Dimmensional Figures (including Irregular and Composite Shapes) o The area of a shape is the amount of flat surface enclosed by the shape. o Area is measured in square units, such as square millimetres (mm ), square centimetres (cm ), square metres (m ) and square kilometres (km ). o Area units can be converted using a similar chart to the one from earlier in this note but each conversion factor must be squared. (See p. 51 of the textbook for the conversion chart and see attached formula sheet for the six - dimensional figures with their formulas) Circles (Circumference and Area) o The circumference (C) is another term for the perimeter of a circle. The diameter (d) of a circle is the name given to the straight- line distance across a circle through its centre. The straight- line distance from the centre of the circle to the outside is called the radius (r). The ratio of the circumference over the diameter is called pi (π) and is approximately equal to.14 The circumference of a circle is found using the formula C = πd or C = πr. The area of a circle can be found using the formula A = πr where r is the radius of the circle. Volume of Prisms o Volume is the amount of space inside a three- dimensional object. o Volume is measured in cubic units such as mm, cm or m. o Volume units can be converted using a similar chart to the earlier one yet the conversion factors are cubed. (see p. 65 of the textbook) o The volume of any prism is the cross- sectional area multiplied by the height, depth or length of the prism. If the shape comes to a common point (vertex) than the volume is one- third the cross- sectional area multiplied by the height. (see the attached formula sheet) Practice 0. Convert the following measurements; a) 0 mm = cm b) 1.5 cm = mm c) 0.0 cm = mm d).8 km = m e) 0.04 m = cm f) 400 mm = m g).7 m = mm h) 6071 m = km i) km = cm Page 5 of 19

6 Semester Revisions 1. Find the perimeter of the following shapes. Remember to state a formula, show your workings and include units with your final answer. It may be necessary for you to determine any missing sides before you can proceed.. Find the circumference of each of these circles. Remember to state a formula, show your workings and include units with your final answer. Round your final answer to two decimal places. Page 6 of 19

7 Semester Revisions. Find the circumference of each of these circles. Remember to state a formula, show your workings and include units with your final answer. Round your final answer to two decimal places. 4. Find the perimeter of each of these shapes. Remember to state a formula, show your workings and include units with your final answer. Round your final answer to two decimal places. a) b) c) d) 5. Find the area of each of these shapes. Remember to state a formula, show your workings and include units with your final answer. a) b) c) d) 6. Find the area of each of the following circles. Remember to state a formula, show your workings and include units with your final answer. Round your final answer to two decimal places. Page 7 of 19

8 Semester Revisions 7. Find the area of each of these shapes. Remember to state a formula, show your workings and include units with your final answer. Round your final answer to two decimal places. a) b) c) d) 8. Find the area of each of the following trapeziums. Remember to state a formula, show your workings and include units with your final answer. a) b) c) d) 9. Find the volume of each of the following shapes. Remember to state a formula, show your workings and include units with your final answer. If necessary, round your final answer to two decimal places. a) b) c) d) e) f) Unit 9: Algebra Using Variables o A variable (or pronumeral) is a letter or symbol that represents a value in an algebraic expression. o In algebraic expressions such as a + b, the variables represent some unknown values. Substitution o If the value of a variable (or variables) is known, it is possible to evaluate (work out the value of) an algebraic expression by using substitution. Replace the variable with the number and solve. Page 8 of 19

9 Semester Revisions Simplifying Expressions o Expressions can often be written in a more simple form by collecting (adding or subtracting) the numerical coefficients of like terms. Ie: a + 7a = 10a & a 7a = - 4a o Like terms are ones that contain exactly the same variables, raised to the same powers. Ie: ab and 7ab are like terms but a b and 7ab are not like terms. Multiplying and Dividing Expressions with Variables o When multiplying or dividing expressions with variables, we multiply or divide the signs (positive & negatives) and the numbers first then simplify the variables using your first and second law of indices. Expanding Brackets (Distributive Property) o The distributive property is the name given to the process of expanding brackets. The number, variable or combination of number and variable outside a bracket must be multiplied by all terms inside the bracket. Ie: (x+) = x + 6 & x(x- 1) = x - x & x(4x+5y) = 1x +15xy Once the distributive property has been applied, you don t need the brackets anymore and the like terms can be collected. Ie: (x+4) - 5(x- ) = x + 8 5x + 10 = - x + 18 Factorising (Highest Common Factors) o Factorising is the opposite process to expanding. o Factorising involves identifying the highest common factor of both the number parts and the variable parts. Ie: a + ab = a(a + b) Practice: 0. Using x and y to represent numbers, write algebraic expressions for the following; a. The sum of x and y b. The difference between y and x c. Five times y subtracted from three times x d. The product of 5 and x e. Twice the product of x and y f. The sum of 6x and 7y g. y multiplied by itself 1. Jake is now m years old. Write algebraic expressions for the following; a. Jake s age 5 years from now. b. Jake s age years ago. c. His sister s age if she is p years younger than Jake. d. Jake s mother is 5 times his age.. Find the value of the following algebraic expressions if a = and b = 6; a a) a b) 6a c) 5b d) e) a + 8 f) b g) a + b h) b a i) 5+ b j) a + 7 k) a + b l) 0 b m) b a n) b a o) a b p) - ab q) 5a b r) b 9a Page 9 of 19

10 Semester Revisions. Substitute r = and s = 5 into the following algebraic expressions and evaluate; a) (r + s) b) (s r) c) 5(r + s) d) 8(s r) e) s(r + 4) f) s(r ) g) r(r + 1) h) rs(7 + s) i) r (5 r) j) s (s + 15) k) 4r(s + r) l) 1r(r s) 4. Find the value of the following algebraic expressions if a = and b = - 5; a) a + b b) b + a c) ab d) ab 5 e) ab f) 5 a g) 1 ab h) a i) (a + ) j) b(a 4) k) 1 a(b ) l) 5a + 6b 5. Simplify each of the following expressions; a) 4c + c b) c 5c c) a + 5a 4a d) 6q 5q e) - h h f) 7x 5x g) a 7a a h) - f + 7f i) 4p 7p j) - h + 4h k) 11b + b + 5b l) 7t 8t + 4t 6. Simplify each of the following expressions; a) x + 7x y b) x + 4x - 1 c) f 7f d) u 4u + 6 e) m + p + 5m f) - h + 4r h g) 11a 5b + 6a h) 9t i) 1 g + 5 j) 6m + 4m - n + n k) 5k 5 + k - 7 l) n 4 + n 5 7. Simplify each of the following expressions; a) x + x b) y + y c) a + a d) d + 6d e) 7g 8g f) y + 7y g) b + 5b h) 4a a i) g g j) a a + 5 k) 11x 6 + 1x + 6 l) 1s + 7 s 8. Simplify the following expressions; a) 4 g b) 6 5r c) 7gy d) 9m 4d e) 1m 1n f) 8w x g) 11q 4s h) 11ab d 7 i) 4a b c Page 10 of 19

11 Semester Revisions 9. Simplify the following algebraic expressions; 8 f a) b) 10r 5 c) 14q 1q d) 8 f 4 f e) 7h h f) 0d 48d g) 16m 8m h) 64q 44p i) 5x 70x 40. Simplify the following algebraic expressions; 15 fg 8xy a) b) 1 c) 11xy 11x d) 1ab 8b e) 5 jk kj f) 10mxy 5mx g) 1xy x h) 14abc 7bc i) 18adg 45ag 41. Simplify the following algebraic expressions; 5p 1 4q 7 a) 15p 8q b) 8x 7y z 6x 14y c) a ab b 5a b d) rk s 6st 5rt e) 15gt 10ag g 5t f) 4ht dk 1hk 9dt 4. Use the Distributive Property to expand the following expressions; a) (d + 4) b) 6(g + 6) c) 1(4 + c) d) 11(t ) e) g(g + 7) f) (a + 5) g) 7(6 + x) h) (t 6) i) g(g + 5) 4. Use the Distributive Property to expand the following expressions; a) x(x 6y) b) 5y(x 9y) c) - 5x(x + 6) d) - y(6 + y) e) - 4f(5 f) f) - h(b 6h) g) 4a(5b + c) h) - a(g 7a) i) - w(9w 5z) 44. Expand the brackets using the distributive property and then simplify by collecting any like terms. a) 7(5x + 4) + 1 b) 6(v + 4) + 6 c) 4r + r( + r) d) (x 4) + 1 e) 1 + 5(r 5) + r f) 4 + r( r) r + 5r g) 5 g + 6(g 7) h) 4(f g) + f 7 i) x( + 4r) + 9x 6xr Page 11 of 19

12 Semester Revisions 45. Simplify the following expressions by expanding the brackets and then collecting like terms. a) h(k + 7) + 4k(h + 5) b) 6n(y + 7) n(8y + 9) c) 4g(5m + 6) 6(gm + ) d) 11b(a + 5) + b(4 5a) e) 5a(a 7) 5(a + 7) f) 7c(f ) + c(8 f) 46. Factorise the following expressions; a) x + 6 b) 8x + 1 c) d + 8 d) 11h + 11 e) 1g 4 f) 48 1q g) 14g 7gh h) 5a 15abc i) 1ac 4c + dc j) 1abc + 9acd 65acf k) x y 18x 4 y + 0x y Unit 10: Linear Equations Solving One- Step Linear Equations o For an equation, the expression on the left- hand side of the equals sign has the same value as the expression on the right- hand side. o If the same arithmetic operation is performed to both sides of an equation, the equation remains valid. That is, the equation remains a true statement. o To solve an equation means to find the value of the variable or pronumeral that, when substituted, will make the equation a true statement. o To solve a linear equation, perform the same arithmetic operations to both sides of the equation until the variable is left by itself. To undo the operation of addition we subtract on both sides, to undo the operation of subtraction we add on both sides, to undo the operation of multiplication we divide on both sides and to undo the operation of division we multiply on both sides. Solving Two- Step Linear Equations o To solve two- step equations, undo the operations in reverse order. BIDMAS backwards. Therefore SAMDIB (undo subtraction/addition first, then undo multiplication/division, the undo any indices and finally undo the brackets). Solving Linear Equations with Variables on Both Sides o Equations can have variables on both sides. Move all variables to the same side of the equals sign and all numbers to the other side. When moving a number or a variable remember to use the opposite operation when moving it to the other side of the equals sign. Solving Linear Equations with Multiple Brackets o If there are brackets present in an equation, remove the brackets by expanding the expression using the distributive property. Collect all like terms and then solve for the unknown variable. Solving Linear Equations with Decimals & Fractions o If solving an equation that contains fractions, multiply each term by the lowest common denominator to clear all fractions. If solving an equation that contains decimals, multiply each term by 10 if they have 1 or less decimal places, multiply each term by 100 if they have or less decimal places, etc Page 1 of 19

13 Semester Revisions Practice 47. Solve the following equations for the unknown variable. a) x + = 19 b) k 4 = 1 c) a. = 1.5 d) 1.8 = - w e) n = 8 f) - m = 15 g) g 5 =1 h) y = 4 i) 4.5 =.4 + c 48. Solve the following equations for the unknown variable. a) 4t 6 = - 10 b) - = - x c) - 5 y = 6 d) 5 + n = - 15 e) p 7 = 14 f) t 4 =1 g) 5+ k = h) x + 1. =.9 i) 4k.5 = 1.5 j) 4.d = 1.6 k) 0.6g 1.6 = 0.8 l) 6. = 0.1 n 49. Solve the following equations for the unknown variable. a) 6w + = 4w 8 b) 7m 1 = 4m + m c) 8m = 5m + 18 d) 16h = 7 + 7h e) p + 9 = - 15p f) - 4r + 15 = r g) 14f + 4 = 9f 11 h) 108 7x = - 4x i) 9m + 7 = 6m 50. Solve the following equations for the unknown variable. a) ( z) = 1 z b) 7 + (b ) = b + 4 c) (x + ) = 9 + (x + 4) d) (4k 1) + (5 k) = 7k e) 4(x + ) (x + 1) = ( x + ) f) (n 5) (n + ) = (n 1) g) (a 4) (a ) = 4(a + 1) + 4 h) 5(c + 4) = 4(c ) 7 i) - (1 + 7x) 6(- 7 x) = 6 j) - (4x + ) + 4(6x + 1) = Solve the following equations for the unknown variable. a a) 4 a = a b) ( b +1) ( = b ) 5 c) k 4 = k + d) ( x +1) x 6 = e) 4 = c + 4 c +1 f) 1 z 5 = z +1 1 Page 1 of 19

14 Semester Revisions Answers: 1.a) Base = 8 & Power = 4 b) Base = 7 & Power = 10 c) Base = 0 & Power = 11 d) Base = m & Power = 5 e) Base = c & Power = 4 f) Base = n & Power = 6.a) 6 b) 9 4 c) m 5 d) d.a) 4 x 4 b) 5 x 5 x 5 x 5 c) 7 x 7 x 7 x 7 x 7 d) n x n x n x n x n x n x n e) a x a x a x a f) k x k x k x k x k x k 4.a) 4 b) 56 c) 56 d) 451 e) 16 f) a) 1 x x 6 x n x i x r 6.a) 4 x b x b x b x c x c x c x c x c b) 11 x 9 x j 5 x p x k b) 19 x a x a x a x a x n x n x n x m 7.a) 9 b) 6 17 c) e 4 d) 6 11 e) 10 6 f) g 8 8.a) 6a 6 e 7 b) 8h 1 p 6 c) 80m 9 d) 0p 6 q 9 e) 48u 9 w 7 f) 4b 14 c 9 9.a) 11 7 b) 1 c) b 8 d) f 6 10.a) 4w 7 b) q 4 c) 5p 10 d) 9 m4 11.a) 18p10 16p 5 = 9 8 p5 b) 9 4 x8 y c) 4 hk d) 100m1 n 7 10m n = 5 6 m10 n 6 1.a) 1 b) 1 c) 1 d) 1 e) 1 f) 1 1.a) 1m b) 1 c) d) 6p 1 = p 14.a) 1a5 1a 5 =1 0b1 b) 5b = c) 4 f 10 1 f 10 = d) 8u9 v 8u 9 = v 15.a) 8 b) 6 40 c) d) 4 w 6 q 8 e) 0 0 f) 7 e 10 r 4 q 8 16.a) g 1 j 18 b) h 4 j 16 c) e 56 x e 10 = e 66 d) g 1 x g 18 = g 9 17.a) 9a 8 x 4a 1 = 6a 0 b) 8d 1 x 7d 6 = 16d 7 c) 10000r 48 x 4r 6 = 40000r a) a 1 a 6 = a 6 b) n 15 n 1 = n c) c0 c 10 = c0 d) k 0 = k14 16 k 19.a) 9b8 d 6 b) 5h0 4 j 4 c) 8k 15 7t 4 d) 15g1 7z 9 Page 14 of 19

15 Semester Revisions 0.a) cm b) 15 mm c) 0.00 mm d) 800 m e).4 cm f).4 m g) 700 mm h) km i) a) b) c) d) P = l + w P = l + w P = a + b + c P = ( 4) + ( ) P = ( 5) + ( 1) P = P = 8+ 6 P =10 + P =106mm P =14cm P =1cm P = add all sides P = P =18cm e) f) g) h) P = a + b P = l + w P = 4l P = 8x P = ( 11) + ( 5) P = ( 6.5) + ( 5) P = 4( 60) P = 8( 9) P = +10 P =1+10 P = 40mm P = 7mm P = mm P = cm i) 1.5 cm = 15 mm j) 4 m = 400 cm k) 0.6 m = 60 cm l).4 m = 40 cm P = l + w P = a + b + c P = a + b + c P = a + b + c + d P = ( 60) + ( 6) P = P = P = P = P =160cm or P = 86cm or P = 7mm P =19cm or P =1.6m P = 8.6m P =1.9m.a) b) c) C = πd C =.14 C = 6.8cm C = πd C = C = 1.4cm.a) b) c) C = πr C = πr C =.14 4 C = C = 5.1m C =106.76mm C = πd C =.14 7 C = 1.98mm C = πr C =.14 8 C = 50.4cm 4.a) b) P = πd + d.14 P = + P = 8.4mm P = πr 4 + r.14 0 P = 4 P = 71.4cm + ( 0) Page 15 of 19

16 Semester Revisions 4.c) d) P = πd + l + w P = P = 5.75cm ( 0) P = πd + l ( ) P = P = 50.7m 5.a) b) c) 1.9 m = 190 cm d) A = bh A = l A = lw ( A =16 A = ( ) ( 1.5) A = )( 190) A = 56cm A = 4.5m A =1757cm or A =1.757m A = bh ( )(.4) A = 4.6 A =11.04mm 6.a) b) A = πr A =.14 ( 1) A = 45.16cm A = πr A =.14 ( 1.5) A = 4.91km 7.a) b) A = πr ( ) A = A = 0.9cm A = πr 4 ( ) A = A =1.85m c) d) A = πr + πr ( ).14 1 A = A = A =108.56cm +.14 ( 10.5) A = πr + πr + bh ( ) A = + A = A = 9.7cm.14 ( 1.5) +.5 Page 16 of 19

17 Semester Revisions 8.a) b) A = 1 h [ a + b ] A = 1 ( ) [ + 6] A = 9cm A = 1 h [ a + b ] A = 1 ( 4.5 ) [ 9 + 6] A =.75m c) d) A = 1 h [ a + b ] A = 1 ( 18 ) [ ] A = 51mm A = 1 h [ a + b ] A = 1 ( 48 ) [ ] A = 10m 9.a) b) c) V = A Base Height V =.8 V = 8.4cm V = A Base Height V = ( πr ) h V =.14 ( ) 5 V =1157.6cm V = A Base Height V = bh h 6 V = 8 V = 8008cm d) e) f) V = A Base Height V = ( πr ) h V =.14 ( 15) 0 V =1410cm V = A Base Height V = bh h V = V =16cm V = A Base Height V = lwh ( )( 1.5) ( 1.5) V = 1.0 V =1.88m 0.a) x + y b) y x c) x 5y d) 5x e) (xy) f) 6x + 7y g) (y)(y) or y 1.a) m + 5 b) m c) m p d) 5m Page 17 of 19

18 Semester Revisions.a) 4 b) 1 c) 0 d) 1 e) 10 f) 4 g) 8 10 h) 4 i) 8 j) 1 k) l) m) 14 n) 1 5 o) p) - 6 q) r).a) 16 b) 4 c) 40 d) 16 e) 5 f) 15 g) 4 h) 150 i) 18 j) 500 k) 96 l) a) - b) - c) - 10 d) - e) - 0 f) g) h) i) 1 j) 10 k) 8 l) a) 6c b) - c c) 4a d) q e) - h f) x g) - 6a h) 4f i) - p j) h k) 18b l) t 6.a) 10x y b) 7x 1 c) - f + 11 d) - u + 6 e) 7m + p f) - 5h + 4r g) 17a 5b h) 9t i) 17 g j) 10m n k) 7k 1 l) 4n 9 7.a) x b) 5y c) 4a d) 7d e) - g f) 10y g) 7b h) a i) - g j) 4a + 9 k) x l) 11s a) 1g b) 0r c) 1gy d) 6dm e) 156mn f) 48wx g) 1qs h) 1abd i) 4abc 1 9.a) 4f b) r c) d) q 11p 1 e) 9 f) g) h) i) 40.a) 5fg b) e) 5 f) xy 4 a c) y d) 7 y g) 1y h) a i) 5 d Page 18 of 19

19 Semester Revisions 41.a) b) c) d) e) f) 5 6 p10 q 5 4 x yz 5 b 9 5 k g 5a 16h 9d 4.a) d + 1 b) 6g + 6 c) c d) 11t e) g + 7g f) a + 10 g) 4 + 1x h) 6t 18 i) g + 10g 4.a) x 18xy b) 15xy 45y c) - 5x 0x d) - 1y y e) - 0f + 8f f) - 6bh + 18h g) 0ab + 1ac h) - 6ag + 1a i) - 18w + 10wz 44.a) 5x + 49 b) 6v + 0 c) 6r + r d) 9x e) 8r 1 f) - 0r + 11r + 4 g) 9g 7 h) 11f 1g 7 i) 18x + 6xr 45.a) 10hk + 1h + 0k b) - 6ny + 15n c) 8gm + 4g 18 d) 18ab + 67b e) 5a 5a 5 f) 11cf + c 46.a) (x + ) b) 4(x + ) c) (d + 4) d) 11(h + 11) e) 1(g ) f) 1(4 q) g) 7g( h) h) 5a(1 bc) i) c(1a 4 + d) j) 1ac(b + d 5f) k) x y(1 6x y + 10xy ) 47.a) x = 16 b) k = 16 c) a =.8 d) w = e) n = 4 f) m = - 5 g) g = 60 h) y = 1 i) c = a) t = - 1 b) x = 1 c) y = - 11 d) n = - 10 e) p = 7 f) t = 16 g) k = - 1 h) x = 0.9 i) k = 1 j) d = - k) g = 4 l) n = a) w = - 5 b) m = 1 c) m = 6 d) h = 8 e) p = f) r = g) f = - h) x = 6 i) m = a) z = 1 b) b = c) x = 11 d) k = 7 e) 1 = x f) - 15 = n g) a = - h) c = 1 i) 5 = x j) x = 4 51.a) a = - 10/11 b) b = - c) k = - 1 d) - 5 = x e) c = 17 f) z = 1 Page 19 of 19