I.G.C.S.E. Algebra 02. You can access the solutions from the end of each question

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1 I.G.C.S.E. Algebra 0 Index: Please click on the question number you want Question 1 Question Question 3 Question 4 Question 5 Question 6 Question 7 Question 8 Question 9 Question 10 You can access the solutions from the end of each question

2 Question 1 The distance travelled by an accelerating missile is given by Find s when u = m/s, t = 60s and a = 10m/s. 1 s ut at = +. Click here to read the solution to this question

3 Solution to question 1 1 s ut at = + when u m/s, t 60s = = and a = 10m/s. 1 s = ut + at 1 = = = 1810m Click here to read the question again ( ) ( )( )

4 Question Find a formula for the area of the following shape in terms of a, b and c. c a c Click here to read the solution to this question b

5 Solution to question c a c b b c Area = + ( ) ac b c c = ac + bc c Click here to read the question again

6 Question 3 Evaluate the following if x = 5, y = 4 and z =. a. xy z y b. x y z x+ y + z c. z + y + x Click here to read the solution to this question

7 Solution to question 3 x = 5, y = 4 and z =. a. b. ( ) ( ) xy z 5 4 = = = y ( ) ( ) ( ) ( ) ( ) ( ) x y z = = = = x + y + z c. z y x ( ) ( ) ( ) + + = = = 5 = 5 Click here to read the question again

8 Question 4 Simplify as far as possible a. 4x 3y + x b. + c. m 3m x x x x x y + d. ( 3 ) x x + x Click here to read the solution to this question

9 Solution to question 4 a. 4x 3y + x = 6x 3y b. x x+ x y = 3x x y c. m 3m 5m x + x = x d. ( ) x x + 3x = x x + 9x = x + 8x Click here to read the question again

10 Question 5 Remove the brackets and collect the like terms in the following a. 4x+ ( x ) b. a ( 3 a) c. ( 3x+ 4)( x+ ) d. ( x )( x+ 1) e. ( 5x )( 3 x) f. 3x( x+ )( x ) g. ( 7x ) h. ( x + 3) ( x ) Click here to read the solution to this question

11 Solution to question 5 a. 4x+ ( x ) = 4x+ x 4 = 6x 4 b. a ( 3 a) = a 3+ a = 3a 3 c. ( 3x+ 4)( x+ ) = 3x( x+ ) + 4( x+ ) = x + x+ x = x + x + x x+ 1 = x x+ 1 x+ 1 d. ( )( ) ( ) ( ) = + 4 x x x = x 3x 5x 3 x = 5x 3 x 3 x e. ( )( ) ( ) ( ) = x x + x = x x 3x x + x = 3x x x + x f. ( )( ) ( ) ( ) = 3x ( ) ( ) = 3x x x + x 4 = 3x x 4 3 1x g. ( 7x ) = ( 7x )( 7x ) = 7x( 7x ) ( 7x ) = 49x 14x 14x x 8x = + 4 h. ( x + 3) ( x ) = ( x + 3)( x+ 3) ( x )( x ) = x( x + 3) + 3( x + 3) x( x ) ( x ) ( x x + 4) = x 3x 3x 9 x = + + x 6x 9 x x = 10x Click here to read the question again

12 Question 6 Solve the following equations a. 3x = 7 b. 3 x = 5 c. 9x 7 = 3 x 7 3 x x 3 5x x+ 1 x = x 3 x 4 d. ( ) + ( ) = + e. ( )( ) ( )( ) Click here to read the solution to this question

13 Solution to question 6 a. 3x = 7 3x = 9 x = 3 b. 3 x = 5 7 3x = x = 3 = 11 3 c. 9x 7 = 3 x 10x = 10 x = 1 3 x x = 3+ 5x 3x x = 3+ 5x 9 3x = 3+ 5x 1 = 8x 3 x = 1 = 1 d. ( ) ( ) e. ( x+ 1)( x ) = ( x 3)( x 4) x( x ) + ( x ) = x( x 4) 3( x 4) x x x = x x x x = 7x+ 1 6x = 1 x = 1 3 Click here to read the question again

14 Question 7 Solve the following equations a. 5 3 x = b. 4 6 = x 3 x c. x + 5 x 1 = Click here to read the solution to this question

15 Solution to question 7 a. 5 = 3 x 5 = 3x 5 x = 3 = 1 3 b. 4 6 = x 3 x 3 6 ( x) = ( x ) (cross multiplying) 6 x = 6x 1 4 = 10x 1 x = 5 = 5 c. ( 1 ) x+ 5 x 1 = ( x + 5) 1x 1 = x = ( x ) 3x+ 15 4x = x = 13 x = 13 Click here to read the question again

16 Question 8 The sum of three consecutive even numbers is 144. Form an equation and find the numbers Click here to read the solution to this question

17 Solution to question 8 As the numbers are consecutive even numbers the difference between the numbers is. Hence let the fist number be x the second number is x + and the third number is x + 4. The sum of these numbers is 144. ( ) ( ) x+ x+ + x+ 4 = 144 3x + 6 = 144 3x = 138 x = 46 The first number is x = 46 x + = 46 + = 48 The second number is ( ) The third number is x + 4 = ( 46) + 4 = 50 The numbers are 46, 48 and 50. Click here to read the question again

18 Question 9 The length of a rectangle is 5 more than its width. If the perimeter is 90 cm find the width. Click here to read the solution to this question

19 Solution to question 9 Consider the following diagram x + 5 Length x x width x + 5 Let the width be x. the length is 5 more than the width which is written x + 5, The perimeter is the distance around the rectangle. Therefore the width is 0 cm. ( ) ( ) x+ x+ 5 + x+ x+ 5 = 90 4x + 10 = 90 4x = 80 x = 0 Click here to read the question again

20 Question 10 The product of two consecutive odd numbers is 1 more than the square of the smaller number. Find the smaller number. Click here to read the solution to this question

21 Solution to question 10 Let the smaller odd number be x. The second consecutive odd number is x +. Now the difference between the product of these two consecutive odd numbers and the smaller one squared is 1. Product of two consecutive odd numbers Hence the smaller number is 6. ( ) x x x + = 1 x + x x = 1 x = 1 x = 6 The square of the smaller number The difference is 1 Click here to read the question again

Basic Fraction and Integer Operations (No calculators please!)

Basic Fraction and Integer Operations (No calculators please!) P1 Summer Math Review Packet For Students entering Geometry The problems in this packet are designed to help you review topics from previous mathematics courses that are important to your success in Geometry.