S3 Credit Homework 1 - Integers

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1 S Credit Homework 1 - Integers 1. Evaluate the following without a calculator: ( ) (b) 16 + ( 8) (c) 4 ( 7) + ( 1) (d) 7 5 ( 5). If x = and y = find: x - y - - = -5 xy (b) x (c) ( x ) (d) x y. Solve the following equations: x - 1 = 6x 9 x 6x = x = -8 x = x + = x 9 (b) x 1= x + 11 (c) x + 7 = 4x + 1 (d) x 7 = 6x + 5 n 4. Write these numbers in standard form ( a 10 ) 56 = = (b) (c) (d) (e) (f) (g) (h)

2 S Credit Homework - Pythagoras 1 A bypass is being built to reduce the traffic passing through Veesty as shown on the diagram. 5km km Veesty 7km Calculate the total length of the bypass. The diagram shows the front view of a garage..9m m.8m Calculate the length of the sloping edge of the roof. The point P has coordinates (- 8. 7) and the point Q has coordinates (5, - 9). Calculate the length of the line PQ to to decimal places. 4 Show that triangle ACD is right angled. A 40 m 780 m B x m D 180 m 70 m C

3 S Credit Homework Brackets Calculate: + ( 5) (b) 5 d ( d ) (c) q ( 6) (d) 15 f ( ) ( x 7) = x 7 = x 1 Remove the brackets: ( 5x ) (b) x( x+ 4 y) (c) ( x + ) (d) 4 y(y 5) Simplify: y( y ) + ( y+ 4) (b) 5( x ) (4x+ ) ( x+ 4)( x+ 7) = x + 7x+ 4x+ 8 = x + x Calculate: ( x+ 5 )( x+ 6) (b) ( y )( y 7) (c) ( x+ 5)( x 4) (d) ( y 6 )( y+ 8) 5 A rectangular field that has length 5x metres and breadth x + 5 metres. Farmer MacDonald wants to erect a fence around the field. Find the total length of fencing required. Farmer MacDonald has calculated that it would cost 1 per squares metre to sow grass in the field. Find the cost of sowing the area of the field. 5x x + 5

4 S Credit Homework 4 Brackets 1 Solve: 7 4 = + 1 (b) x x ( x+ 5) = 5 ( x 7) Solve: + 4( ) = 1 x x (b) 6( x 1) 5= 4 ( x + 1) ( x+ 4)( x+ 7) = x + 7x+ 4x+ 8 = x + x Multiply: + + ( x )( x ) (b) ( x 1)( x + 1) ( ) ( ) a+ b = a + ab+ b a b = a ab+ b 4 Calculate: ( x + 1) (b) ( 5x ) (c) ( ) ( x+ x ) Greenfield Cars display their cars on a square patch of ground. The length of the patch of ground is 4x metres long The owner wants to tarmac the display area. Laying tarmac costs 15 per square metre. How much will it cost the owner to tarmac the display area? 4x

5 S Credit Homework 5 Trigonometry 1 ( ) ( ) a+ b = a + ab+ b a b = a ab+ b ( ) ( )( ) (4x+ 7) = 4x + 4x = x 56x 49 1 Solve: ( x + 4) (b) ( 5x + 1) (d) ( x 5) (e) ( 4x 1) n Write these numbers in standard form ( a 10 ) 759 (b) (c) 0.48 (d) = = Calculate the size of the marked angle: SOH CAH TOA (b) (c) 9 cm 15 cm x o 5 m m 1 cm x o 45 cm x o 4 Mary has ladder 6 metres long. Mary places the ladder against a wall. The top of the ladder is 5. metres from the ground. For safety reasons, the angle the ladder makes with the ground must be between 55 and 65. Is it safe for Mary to use the ladder? (Justify your answer)

6 S Credit Homework 6 Trigonometry 1 The diagram shows a square OABC with length equal to 1 unit. y A B (1, 1) O C x Copy the diagram and put in the lengths of the side OC and BC. Using triangle OBC, calculate length of OB. (Leave your answer as a square root.) Add this value to the diagram. What is the size of angle BOC? Using triangle OBC, find, expressed as a fraction, the values of: sin 45 = cos 45 = tan 45 = The Diagram shows an equilateral triangle ORT of side units. y R O S T x Copy the diagram and put in the length of the side OS. Using triangle ORS, calculate length of RS. (Leave your answer as a square root.) What is the size of angle ROS? What is the size of angle ORS? Using triangle ORS, find, expressed as a fraction, the values of: sin 60 = cos 60 = tan 60 = sin 0 = cos0 = tan 0 =

7 S Credit Homework 7 - DST 1 Expand the brackets ( x+ ) ( x+ ) (b) ( y + )( y 7) (c) ( x + 5) (d) ( y 6) Change the following to hours: hours 15 minutes (b) hours 45 minutes (c) 4 hours 1 minutes (d) 7 hours 48 minutes 6 hours 6 minutes = hours 60 = hours or.6 hours 5 A car travels at an average speed of 87 kilometres per hour. How far will it have travelled in 4hour and 0 minutes? 4 A coach set off at 8.15am. The coach arrived at its destination 74 kilometres away at.0pm. Calculate the average speed of the coach? 5 Mary s flight left at 7.45am. If the plane journey was1800 kilometres and the average speed of the plane was 540 kilometres per hour, at what time did the flight arrive?

8 S Credit Homework 8 Factors 1 ( x ) 8x 1= 4 1 Factorise: 6 x + 9 (b) 1 8x (c) m 4m (d) 6d 8 d ( )( ) a b = a b a+ b Factorise: x y (b) (c) (d) x 16 4a 5b x x x x a b c 4 = 1; = ; = 4. x x x x( x 4) + 1( 4 x) ( x 4)( x+ 1) ac = 4; b = factors 4 and 1 Factorise: x + 8x+ 15 (b) y 10y+ 1 (c) x + x 10 (d) x 5x 6 4 A ladder 5metres long is placed against the wall of a house, with its foot metres from the wall. h m Calculate, correct to 1 decimal place, the height the ladder reaches up the wall. m

9 S Credit Homework 9 Factors a = ; b= 4 ( ) ( 4) = 9 16 = 7 a b = 1 If a = ; b= 4; c= 5. Calculate: a b (b) ab + c (c) 5 a (d) 10 cb Factorise: ( )( ) a b = a b a+ b p q (b) y 5 (c) 9x 16y (d) 18x 4 = 1; = ; = 4. x x a b c x x x x( x 4) + 1( x 4) ( x 4)( x+ 1) ac = 4; b = factors 4 and 1 Factorise: x + x 18 (b) x 1x + 0 (c) 5x + x 7 (n) x 6x 6 4 Plot the points A(,1), B(4,), C(4,4), D(,) What shape is ABCD? (b) P,Q,R,S are the images of A,B,C,D under reflection in the y-axis. Plot the points P,Q,R and S, and write down their coordinates.

S Credit Homework 10 Scale Factor 1 Factorise: ( )( ) p q = p q p+ q m 4n (b) 16 x (c) 4a 9b (d) c 1 Factorise: x + x a = b = c = 8 ; ; 8.

10 S Credit Homework 10 Scale Factor 1 Factorise: ( )( ) p q = p q p+ q m 4n (b) 16 x (c) 4a 9b (d) c 1 Factorise: x + x a = b = c = 8 ; ; factors 4 and 6 x( x 4) + ( x 4) ( x+ )( x 4) ac = 4; b = x x+ x m + m 0 (b) t + 11t 1 (c) 8b b (n) 4 7 y y+ A ceramic company makes two similar ornaments for Scottie Dogs, the Eiffel Tower and the Parthenon. For each two similar ornaments, calculate the scale factor and the value of x. 18 cm 0 cm x cm 40 cm (b) 4 m 15 m (c) x cm 10 cm 18 cm x cm 4 cm 6 cm

11 S Credit Homework 11 Similar Shapes 1 Remove the brackets: ( x+ ) ( x 5) (b) ( x 1) ( x ) (c) ( m 4) (d) ( d f ) Factorize: x y (b) x (c) 4 (d) 16 a 5b x x The two rectangles are similar, find the value of x. 5 cm.8 cm 4 Calculate the value of x. 1.5 cm x cm 6cm 10cm xcm 8cm 5 Calculate the length of the line BC. A 5cm B 7cm C D 1cm E

12 S Credit Homework 1 Change of Formula 1 1 Multiply: ( 4x+ ) ( x 4) (b) ( 5x + ) (b) ( x ) Factorize: x 4x +1 (b) 5 x + x (c) 5x + x 7 Make r the subject of the formula. b = c+ 4r 4 Change the subject of the formula to g. T = π l g 5 In the formula h = A π r, What is the effect on h if: A is increased (c) A is halved (b) r is increased (d) r is doubled? 6 Use the formula 5 C = F 9 to calculate which place is warmer. ( ) Kusedasi Turkey Palma Spain 104 F 5 C

13 S Credit Homework 1 Change of Formula 1 Calculate the value of the angle marked xº, correct to 1 decimal place. cm (b) 4.7 cm xº 6 cm xº.4 cm Calculate the value of the side marked x, correct to 1 decimal place. 4 m 68º x m (b) x m 4º 8.9 m Make r the subject of the formula. V = 4 π r 4 Change the subject of the formula to h : A = π r( r+ h ) 5 Change the subject of the formula to d. M 4d What is the effect on M if: d is increased (c) d is halved (b) d is decreased (d) d is doubled?

14 S Credit Homework 14 Simultaneous Equations 1 1 Solve the following pairs of simultaneous equations algebraically. a) x y = 1 x+ y = 1 b) x y = x+ y = 16 c) x 5y = 4x y = 5 d) x+ y = 11 x+ y = 4

15 S Credit Homework 15 Simultaneous Equations 1 Two groups are going to the pictures. The first group had four adults and one child and their cost was 41 The second group had two adults and one child and their cost was Let x = the cost of an adult ticket y = the cosy of a child ticket Make a pair of simultaneous equations using the information above. Hence calculate the cost for a group containing three adults and four children An adult train fare costs 10 more than a child fare. Also the adult fare is three times the cost of a child fare. Make a pair of simultaneous equations using the information above. How much would it cost for two adults and three children GELO produce sizes of toy bricks for children. A young girl is playing with some bricks and makes the following pattern consisting of three rows. 0.4 cm 7. cm Let x centimetres represent the length of the larger brick and y centimetres the length of the smaller brick. By considering the bottom row, write down an equation connecting x and y. By considering the top row, write down another equation connecting x and y. Hence find the length of the middle row

16 S Credit Homework 16 Area 1 Factorize: 4 9 x y (b) x 1x + 0 Calculate the length of the line AB if A is the point ( 4, ) and B is the point (, 8). Calculate the areas of the following geometrical shapes correct to 1 decimal place. 17 cm (b) cm 7cm (c) 19 cm 54cm 4cm 7cm 4 Calculate the following shaded areas correct to 1 decimal place. (b) cm 1cm cm 1cm

17 S Credit Homework 17 Statistics 1 For each equation make g the subject of the equation D = 5 f + g (b) Q = 9y g Factorise 5x + x 7 (b) x 11x + 15 The table show the results of a survey of customer spending in a Bar Diner. (b) (c) Write down the modal class In which class interval is the median? Calculate the mean amount spent to the nearest pound. Amount ( ) Frequency The barchart show the amount of time pupils spend travelling to school. How many pupils took part in the survey? Number 8 (b) Write down the modal time. 6 7 (c) (d) In which class interval is the median? Calculate the mean time to the nearest minute Time

18 S Credit Homework 18 Volume 1 If x = 5 and y = 7 find: x + y (b) x + y (c) y x Remove the brackets: ( x 7) ( x+ 5) (b) ( 5 x ) Calculate the volumes of the following prisms correct to 1 decimal place. 7cm (b) 1 cm 1 cm 6 cm (c) 7cm 6cm 18cm 4 Calculate the area of the label around the can, correct to 1 decimal place. 6 cm 9 cm

Wednesday 15 January 2014 Morning Time: 2 hours

Write your name here Surname Other names Pearson Edexcel Certificate Pearson Edexcel International GCSE Mathematics A Paper 4H Centre Number Wednesday 15 January 2014 Morning Time: 2 hours Candidate Number