Basic Algebra. Mathletics Instant Workbooks. 7(4x - y) = Copyright

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1 Basic Algebra Student Book - Series I- 7(4 - y) = Mathletics Instant Workbooks Copyright

2 Student Book - Series I Contents Topics Topic - Addition and subtraction of like terms Topic 2 - Multiplication and division of pronumerals Topic 3 - Indices Topic 4 - Grouping symbols Topic 5 - Substitution Topic 6 - Common factors Topic 7 - Addition and subtraction of algebraic fractions Topic 8 - Multiplication and division of algebraic fractions Topic 9 - Problem solving and algebra Date completed Practice Tests Topic - Topic test A Topic 2 - Topic test B Author of The Topics and Topic Tests: AS Kalra ii

3 Topic : Addition and subtraction of like terms Question Simplify the following epressions by collecting like terms. a = b 5 2 = c 5a + 4a = d 9y 6y = e 3y + 7y = f 4q 3q = g 8m + 6m = h 9a a = i 2b + 5b = j 8t 2t = k 7n + 5n = l 5mn + 3mn = m 8p 5p = n 8y + 7y = o 7p 3p = p = Question 2 Simplify the following. a 5p + 6p 3p = b 8m 3m 2m + 7m = c = d 4y + 6y 3y 2y = e 2y 4y + 5y = f 8k + 4k + 2k 5k = g 8y + 2y + 5y = h 9a + 2a + 3a 7a = i 6m 3m + 0m = j p + 5p 7p = k 5a + 7a + 3a + 6a = l 6ab 3ab ab + 2ab = m = n 6a 2 + 7a 2 + 8a 2 0a 2 = o = p y 6y 3y y = Question 3 Simplify by collecting like terms. a y + 7y = b a + 7b 3a = c 3m + 7m + 8n + 9m = d 9c 6c 2c + 3d = e 8a + 7a 2m 3m = f = g 3 + 2y + 5 = h 2mn 6mn + 3mn = i 8y = j 5 + 7y 4y 2 = k 8m + 2n + 9n + 2n = l 5t + 7 2t 8 = m 7y + 6y = n 6a + 9 3a = o = p 9m + 7mn 6m 2mn = q 0m + 5n + 3n + 4m = r 5 + 3y 2 2y =

4 Topic 2: Multiplication and division of pronumerals 2

5 Topic 3: Indices 3

6 Topic 4: Grouping symbols Question Epand the following epressions. a 5(a + 3) = b 6( 7) = c 2(6 + a) = d 5( + 7) = e 9(2a + 5) = f 3(5 9) = g 2a(6 + 3a) = h (2 5) = i m(6m + 3) = j 5( 3) = k 7n(2n 3) = l 3a(a 2) = m 2(a + 5) = n 7(3p 4) = o 5a(a ) = p 3(2 2) = q ( + 9) = r (4y 7) = Question 2 Epand and simplify by collecting like terms. a 3( + 5) + 6 = b 6(a 5) 5a = c 4(m 3) + 2m = d 2( 3) = e 6y(y + 4) 2y 2 = f 6(m 2) 3m = g 5 + 3(0 ) = h 9 + 3( 2) = i 6m 2(m + ) = j 2m + 3(m 3) + 7 = Question 3 Epand and simplify. a 3( + 2) + 4( 2) = b 8(m 3) + 3(m 2) = c 5(p 7) + 3(p + 2) = d 8( + 3) + 2( ) = e 4( + 3) 2( + ) = f ( + ) ( 3) = g 5(p 6) 2(p ) = h p(5p + 6) 3(2p 3) = 4

7 Topic 5: Substitution Question If a = 2, b = 3, c = 4 and d = 5, evaluate the following. a abc = b a + b + c d = c ab + bc = d a 2 + b 2 + c 2 = e bc a = f abcd = g b 2 + c 2 ad = h b = i 3ab + 2cd = j 3a 2 c d = k 5c 2 2 = l a 3 + b 3 = Question 2 If = 5, find the value of the following epressions. a = b 65 4 = c 4( + 3) = d (2 7) 2 = e 6 2 = f 2 ( 3) = g ( + 2) 2 = h ( 3) 2 = i 3 = j (2) 2 = k 2 l 2 2 = m ( 3) 3 = n ( + 2) ( 2) = o 2 7 = Question 3 If = 6.5, y = 2.4 and z = 5.8, find correct to one decimal place the value of a + y = b + y + z = c + y z = d y = e yz = f 2 = g 2 + z 2 = h y 3 = i yz = j ( z) + 3 = k y = l ( + y) z = m ( + y) 2 3 = n + y + z = o + y + z = 5

8 Topic 6: Common factors Question Factorise the following by taking the highest common factor out. a 5a + 5 = b 8 8 = c 3y 3 = d = e 6m + 6 = f 7m + 7 = g 3p + 6 = h 4q + 8 = i 6 9y = j 4 6 = k 9b 8 = l 5a + 20 = m 2a + 6 = n 3m + 2 = o 6n 24 = p 8 32 = q 3a + 5 = r 2a + 4 = Question 2 Factorise by taking the common factor out. a 3a + 3b = b 5m + 5n = c 6p 6q = d 7a + 4b = e 3l 9m = f m 2 + 7m = g y 2 + 6y = h 9 8y = i 3a 24b = j 4 + 4y = k mp 3p = l 8 32y = m 6 36 = n 3m + 2m 2 = o 5y y 2 = p 9 6 = q 8m 8n = r = s = t 6pq 2p 2 = u 0 0y = Question 3 Factorise the following. a = b = c = d = e = f 6a + 24 = g 3a + 2 = h 4a + 6 = i 6a 2 = j 4y 8 = k 2 0 = l 8y 4 = m 3p 9q = n 5 25 = o 5 = Question 4 Factorise. a 7a + 7b = b 4a 20 = c 9 9y = d 3m + 5 = e 6 6t = f m 2 4m = g 5ab a 2 = h 7m 4n = i 8ab 6a 2 b = j 4 2a = k 3 5p = l 3m 6n = m 9m 36 = n 4a 20a 2 = o 7 = 6

9 Topic 7: Addition and subtraction of algebraic fractions Question Find the sum of these algebraic fractions. a = b = c a 7 + a 7 = d = e m 4 + m 4 = f = g 5a 8 + a 8 = h y 3 + y 4 = i 2a 3 + a 5 = j = k 5m 6 + m 3 = l 7a 6 + a 8 = Question 2 Subtract the following algebraic fractions. a = b 5p 9 4p 9 = c 2b 3 b 3 = d 3m 4 m 4 = e 2 5 = f 5p 7 2p 7 = g a 6 a 2 = h p 8 2p 2 = i = j a + 2 2a 3 = k = 4 l y 2 3y + = 3 Question 3 Find the answers to the following. a = b = c = d 5p 7 3p 7 = e 2m 5 m 5 = f p 6 + 2p 3 = g = h 2a 5 + a 5 = i = j 2a 5 a 5 = k 5a 3 + a 5 = l a a 2 3 = 7

10 Topic 8: Multiplication and division of algebraic fractions 8

11 Topic 9: Problem solving and algebra Write the sum of 2 and 3y. 2 Write the product of m and n. 3 Write the average of 2, y and 3z. 4 Find the epression 3 more than 2. 5 If the first number is, write the net consecutive integer. 6 Find the area of a square with side length metres. 7 Write the perimeter of a rectangle of length 5 cm and width 7 cm. 8 Find the perimeter of a square with side length 8 cm. 9 Find the volume of a cube with side length 5 cm. 0 Find the number less than 3 + 4y. Increase 5 by 2. 2 Write the perimeter of the following shapes. a b c Find the area of the following shapes. a b c Your pocket money is $ per week. How much do you earn in 7 weeks? 5 If I bought p pens and 3q pencils and my sister bought 5p pens and 2q pencils, how many pens and pencils do we have altogether? 6 Three different types of sweets cost 5y, 3y and 2y cents each. If I buy 4 of each type, what would be the total cost? 9

12 Topic Test PART A Instructions This part consists of 2 multiple-choice questions Each question is worth mark Fill in only ONE CIRCLE for each question Calculators are NOT allowed Time allowed: 5 minutes Total marks = 2 Marks Total marks achieved for PART A 2 0

13 Topic Test PART B Instructions This part consists of 5 questions Each question is worth mark Write answers in the answers-only column Time allowed: 20 minutes Total marks = 5 Questions Answers only Marks Total marks achieved for PART B 5