1. Calculate the gradients of the lines AB and CD shown below. (2) (a) Find the gradient of the line AB. (2)

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1 DETERMINING the EQUATION of a STRAIGHT LINE 1. alculate the gradients of the lines AB and D shown below. (2) A B 0 x D 2. A line passes through the points A( 2, 4) and B(8, 1). (a) Find the gradient of the line AB. (2) (b) Find the equation of the line AB. (2) 3. Find the equation of the line passing through P(4, 6) which is parallel to the line with equation 4x = 0. (4) 4. A straight line has equation 3 2x = 6. Find the gradient and -intercept of the line. (3) 5. Find the equation of the straight line joining the points P( 4, 1) and Q(2, 3). (3) 16 marks Pegass 2013

2 FUNTIONAL NOTATION 1. A function is defined as f (x) = x 2 4. Evaluate (a) f ( 1) (b) f (0) (c) f (9) (4) 2. A function is defined b the formula g(x) = 12 5x (a) alculate the value of g(5) + g( 2) (3) (b) If g(k) = 14, find k. (3) 3. A function is defined as f (x) = x Find a simplified expression for f (a + 2) f (a 5) (6) 16 marks Pegass 2013

3 EQUATIONS and INEQUATIONS 1. Solve these equations (a) 2x 12 = 3 (b) 5z + 9 = 4 (c) 6 9 = (6) 2. Solve these equations b first multipling out the brackets (a) 3(2x 4) = 6 (b) 6(a 1) = 4(a + 2) (5) 3. Solve these inequalities (a) 7x > 42 (b) 3x 2 > 11 (3) 4. Solve these inequalities (a) 9x + 2 6x + 11 (b) 5( 2) > 2( + 4) (5) 5. Solve these inequalities, giving our answer from the set { 3, 2, 1, 0, 1, 2, 3, 4, 5, 6} (a) 7x 3 > 2x 23 (b) 9( + 2) 7( + 4) (5) 24 marks Pegass 2013

4 WORKING with SIMULTANEOUS EQUATIONS 1. Two lines have equations 2x + 3 = 12 and x + = 5. B drawing graphs of the two lines, find the point of intersection of the 2 lines. (3) 2. Solve, b substitution, the equations 3a + 1 2b = 14 4 a = 0 5b + 3 (4) 3. Solve, b elimination, the equations 3p 2q = 4 p 3q = 13 (3) 4. Mr. Martini is ordering tea and coffee for his cafe. He spends exactl 108 on these each month. In March he orders 4kg of tea and 6kg of coffee. In April he changes his order to 8kg of tea and 3 kg of coffee. How much do the tea and coffee cost each per kilogram? (6) 5. An electrical goods warehouse charges a fixed price per item for goods delivered plus a fixed rate per mile. The total cost to a customer 40 miles from the warehouse for the deliver of 5 items was 30. A customer who lived 100 miles awa paid 54 for the deliver of 2 items. Find the cost to a customer who bought 3 items and lives 70 miles awa. (5) 6. A straight line with equation = ax + b passes through the points (2, 4) and ( 2, 2). Find the equation of the line. (4) 25 marks Pegass 2013

5 HANGING the SUBJET of a FORMULA 1. The formula for changing from o to o 5 F is = F 32 9 hange the subject of the formula to F. (3) H w hange the subject of the formula to m. (4) 2 m 3. hange the subject of the formula to x: A = x (3) 4. Given that A = b c, express b in terms of A and c. (4) b 14 marks Pegass 2013

6 QUADRATI GRAPHS 1. (a) This graph has equation in the form = kx². Find the value of k. (2, 8) O x (2) (b) This graph has equation of the form = (x + p)² + q. Write down its equation. O (3, 2) x (2) 2. Sketch the graphs of the following showing clearl an intercepts with the axes and the turning point. (a) = (x 4)(x + 2) (b) = (x 5)² + 3 (7) 3. For the quadratic function = 3 (x + ½) 2, write down (a) its turning point and the nature of it. (3) (b) the equation of the axis of smmetr of the parabola. (1) 15 marks Pegass 2013

7 WORKING with QUADRATI EQUATIONS 1. Draw a suitable sketch to solve these quadratic equations. (a) x(x 4) = 0 (b) x 2 + 8x + 12 = 0 (5) 2. Solve these quadratic equations algebraicall. (a) 5x 2 15x = 0 (b) 6x 2 7x 3 (5) 3. Solve the equation 3x 2 3x 5 = 0, giving our answer correct to 2 decimal places. (4) 4. Solve the equation 4x(x 2) = 7, giving our answer correct to 1 decimal place. (5) 5. D The graph shows the parabola = x x 2. Find the coordinates of A, B, and D. (6) A 0 B x 6. Use the discriminant to determine the nature of the roots of these quadratic equations. (a) x² 6x + 8 = 0 (b) 4x² + x + 3 = 0 (5) Pegass marks

Find the length of side of one of the (4) 2.

O Height of the tunnel with a horizontal floor AB which is 2 4 metres wide.

alum is making a picture frame, ABD. A B It is 25 cm high and 21 5 cm wide.

8 APPLYING the THEOREM of PYTHAGORAS 1. A square snakes & ladders board has 100 squares and a diagonal of length 35 cm. Find the length of side of one of the (4) 2. The figure shows the cross section of a tunnel 2 5m. O Height of the tunnel with a horizontal floor AB which is 2 4 metres wide. The radius OA of the cross section is 2 5 A B metres. Find the height of the tunnel. (4) 3. alum is making a picture frame, ABD. A B It is 25 cm high and 21 5 cm wide. 25cm d To check whether the frame is rectangular, he measures the diagonal, d. It is 31 5 cm long. D 21 5cm (4) Is the frame rectangular? 4. alculate the perimeter of this field, which is made up of a rectangle and a right angled triangle. 80 m (4) Pegass m 16 marks 70 m

9 APPLYING PROPERTIES of SHAPES (1) 1. Find the missing angles in each of these diagrams. Each circle has centre. (7) (a) (b) (c) 30 o a o d o g o b o e o c o 25 o f o h o i o l o m o j o k o 2. Use smmetr in the circle to find the missing angles in the circles (centre ) below. (4½) (a) (b) (c) e o g o h o 40 o a o b o c o f o d o 61 o i o 25 o 3. alculate the sizes of the missing angles in each diagram. (4½) (a) 40 o 20 o (b) i o h o c o 55 o g o a o b o d o e o f o 4. PR is a tangent to the circle, centre O, at T. (4) O alculate the length of the line marked x. 13cm 5cm Pegass 2013 P x T R 20 marks

A window is in the shape of a rectangle 4m b 2m with a semicircle of diameter 4m on top.

10 APPLYING PROPERTIES of SHAPES (2) 1. Find the area of each shape below. (a) (b) (4) 7 cm 9 cm 18 cm 9 cm 2. Find each shaded area below. 8 5 m (a) (b) (6) 7 m 7 m 3 5 m 15 m 7 m 3. A window is in the shape of a rectangle 4m b 2m with a semicircle of diameter 4m on top. Find the area of glass in the window. (3) 2m 4. B dividing the pentagon into triangles or otherwise, find the size of angle AB. 4m (2) A Pegass 2013 B 15 marks

11 SIMILARITY (1) 1. alculate the value of x and in the diagrams below. (7) (a) J 720cm K (b) A 640cm 600cm cm L B 15cm x cm 5 5cm N 270cm M D 20cm E km 2 km P The diagram shows a sstem of roads which are represented below as similar triangles. M 3 km R A man driving from P to S, reaches R before discovering that the road between R and S is blocked. T 3 6 km S He takes the detour P R M T S. P PM = 2 5 km, MR = 3 km, PR = 2 km and ST = 3 6 km. M 3 R How much greater was his journe than going directl from P to S? T 3 6 S (5) 12 marks Pegass 2013

12 SIMILARITY (2) 1. These two rugs are mathematicall similar. 3m 2m The area of the larger one is 4 5m². What is the area of the smaller one? (3) 2. I have two triangular plots in m garden which I have had turfed. The diagrams below show plans of both areas. Equal angles are marked with the same shape. 5 1m 1 1m 1 7m 3 1m The cost depends on the area being tiled. It cost to bu turf for the smaller area. How much did it cost for the larger one if the triangles are mathematicall similar? (3) 3. These two parcels are mathematicall similar. The smaller one has dimensions which are half those of the larger. If the smaller one has volume 150cm 3, calculate the volume of the larger. (3) 4. These two perfume bottles are mathematicall similar. 4cm 2 5cm The cost depends on the volume of perfume in them. The larger bottle costs 62. Find the cost of the smaller bottle correct to the nearest penn. (3) Pegass marks

13 TRIGONOMETRY (1) 1. Write down the equations of the following graphs. (6) (a) 4 (b) o 360 o x o 360 o x Write down the equation of each graph shown below: (5) (a) x o 8 (b) x o 3. Make a neat sketch of the function = 3 sin 2x o, 0 x 360, showing the important values. (3) 4. Make a neat sketch of each of the following for 0 x 360, showing all important points. (a) = 4sin(x 45) o (b) = 2cos xº + 1 (6) Pegass marks

14 TRIGONOMETRY (2) 1. Write down the exact values of : (a) sin 60 o (b) tan 225 o (c) cos 300 o (d) sin 315 o (4) 2. Write down the period of the following (a) = 3 cos 2x o (b) = 2 sin 5x o (c) = 4 cos ½ x o (3) 3. Solve for 0 x 360, giving our answer correct to 3 significant figures. (a) sin xº = (b) 4cos xº + 7 = 6 (c) tan 2 xº = 25 (11) 4. Prove the following identities: 1 (a) (sin xº + cos xº) 2 = sin xºcos xº (b) tanxº sinxº = cos x cos x o (6) 24 marks Pegass 2013

S4 - N5 HOMEWORK EXERCISE No Solve the simultaneous equations x + 3y = 9 and 2x y = 4 graphically.

S4 - N5 HOMEWORK EXERCISE No Solve the simultaneous equations x + 3y = 9 and 2x y = 4 graphically. S4 - N5 HOMEWORK EXERCISE No. 1 1. (a) Make r the subject of the formula : A = πr2 (b) Make b the subject of the formula: L = 3a b 2. Solve the simultaneous equations x + 3y = 9 and 2x y = 4 graphically.