PLC Papers. Created For:
|
|
- Amie Woods
- 5 years ago
- Views:
Transcription
1 PLC Papers Created For:
2 Algebra and proof 2 Grade 8 Objective: Use algebra to construct proofs Question 1 a) If n is a positive integer explain why the expression 2n + 1 is always an odd number. b) Use algebra to prove that the product of two odd numbers is also odd. (1) Question 2 (4) a) If x > 3 and prove that F > 1 b) Explain what happens if x = 3 (4) (1) Total /10
3 Composite Functions 2 Grade 7 Objective: notation Interpret the succession of two functions as a composite function including the correct Question 1. The functions f and g are such that ( ) = 4 ( ) = Write in its simplest form the function (a) ( ). (2) (b) ( ). (2) (Total 4 marks)
4 Question 2. The functions p and r are such that ( ) = 2 2 ( ) = 4-3 (a) Write in its simplest form, the function ( ) (b) Calculate the value of. (2) (1) (c) Calculate the value of. (2) ( 1). (2) (Total 6 marks) Total /10
5 Expand the product of two or more binomials 2 Grade 7 Objective: Expand the product of two or more binomials Question 1. (a) Show that ( 2)( + 1)(2 3)= (3) (b) Show that (3 1)( + 5)(3 1) = (3) (Total 6 marks)
6 Question 2. Work out (2 1) 2 (3 4 ) (Total 4 marks) Total /10
7 Exponential Graphs 2 Grade 8 Objective: Recognise, sketch, and interpret graphs of exponential functions Question 1 For each of the 3 statements, indicate whether it is TRUE or FALSE. You explain your answers. (a) The graph =2 passes through the point (2, 2). (b) The graph =5 passes through the point (-1, 0.2). (c) The graph =10 passes through the point (3, 100).
8 Question 2 Here are the equations of six different graphs: =0 =5 = 5 =( +5) 2 1 = =5 Match one of the equations to each of the following graphs: (3)
9 Question 3 (a) Complete the table of values for y = 2 x x y (2) (b) On the grid, draw the graph of y = 2 x (2) (Total 4 marks) TOTAL /10
10 Factorising difficult quadratic expressions 2 Grade 7 Objective: Factorise a quadratic expression of the form ax 2 + bx + c Question 1 Factorise x 2-17x+30 (2 Marks) Question 2 Factorise 5x 2 +14x+8 (3 Marks) Question 3 Factorise 9x 2-25 (2 Marks) Question 4 Factorise 5x 2-8x-4 (3 Marks) Total marks / 10
11 Geometric Sequences 2 Grade 7 Objective: Recognise and use geometric sequences (r n, where n is an integer and r can be a surd) Question 1. Find the 5 th and 6 th terms of the sequences below. (a) 0.3, 0.9, 2.7, 8.1,,, (1) (b) -5, 1, -0.2, 0.04,,, (1) Question 2. (Total 2 marks) (a) Write down the first four terms of the geometric sequence with nth term 3 n.... (2) (b) State the term-to-term rule of the sequence.... (1) Question 3. In this geometric sequence, the first term is 3 and the term-to-term rule is multiply by 3. Continue the sequence for three more terms. 5, 5, 5 5,,,,
12 Question 4. Work out the missing terms in this geometric sequence., 3 8, 1 1 8, 3 3 8, (Total 2 marks) Total /10
13 Gradients and area under a graph 2 Grade 8 Objective: Calculate or estimate the gradient of a graph and the area under a graph Question 1 A straight line has been drawn on a grid. Calculate the gradient of the line. (2) (Total 2 marks) Question 2 Work out the gradient of the line 5 3 =20 (2) (Total 2 marks)
14 Question 3 The graph of = is drawn on the grid below. Calculate an estimate to the gradient of the curve at the point Q(-1, 3). (3)
15 Question 4 The scatter graph shows the cost of cars in a used car showroom. (a) Draw a line of best fit and calculate the gradient of this line. (2) (b) Give an interpretation of this gradient. (1) TOTAL /10
16 Quadratic equations (completing the square) 2 Grade 8 Objective: Solve quadratic equations by completing the square. Question 1. Rewrite in the form ( + ) 2 (Total 1 mark) Question 2. Solve = 0 by completing the square. (Total 2 marks)
17 Question 3. Solve = 0 by completing the square. Leave your answers in surd form. Question 4. Solve = 0 by completing the square. Give your answers to 3 significant figures. (Total 4 marks) TOTAL /10
18 Quadratic equations (needing re-arrangements) 2 Grade 7 Objective: Solve quadratic equations that need rearrangement Question 1. Solve 6(18+4 ) +2 = 12 (Total 2 marks) Question 2. Show that 10 6 = can be written as = 0 and hence calculate the two solutions. (Total 2 marks)
19 Question 3. Solve 21 5 = Question 4. Solve 42 8 = TOTAL /10
20 Quadratic equations (quadratic formula) 2 Grade 7 Objective: Solve quadratic equations by using the quadratic equation formula. Question 1. Solve = 0. Give your answer to 3 significant figures. = or = Question 2. Solve = 0. Give your answer to 2 decimal places. = or =
21 Question 3. a) Solve = 0 Give your answer to 2 decimal places. = or = (3) b) Write down the solutions, correct to 2 decimal places, of = 0 = or = (1) (Total 4 marks) TOTAL /10
22 Represent quadratic inequalities 2 Grade 7 Objective: Represent the solution to a quadratic inequality on a number line, using set notation and on a graph Question 1. a) Solve x + 24 > 0 Represent your solution on a number line. b) Write the integer answers for part a) in set notation. (Total 2 marks) Question 2. Solve Display your answer on a sketch of the graph of the solution (Total 2 marks)
23 Question 3. For which values of x is the expression less than or equal to the expression ? Represent the possible values of on a number line. Question 4. Find the set(s) of all values for which > 7 Display your answer on a sketch of the graph of the solution TOTAL /10
24 Simultaneous equations (non-linear) 2 Grade 7 Objective: Question 1. Solve two simultaneous equations (one linear, one quadratic) algebraically and approximately graphically Solve this pair of simultaneous equations. = =2 8 (Total 2 marks) Question 2. Solve these simultaneous equations. = 6 2 =8 (Total 2 marks)
25 Question 3. Calculate the solutions to these simultaneous equations =29 = 7 Question 4. Use graphical methods to find the approximate solutions to this pair of simultaneous equations 2 5. = = 4 TOTAL /10
26 Solve quadratic inequalities 2 Grade 7 Objective: Solve quadratic inequalities in one variable Question 1. Solve a) 2 81 > 0 b) < 0 c) Question 2. Solve the inequality (Total 2 marks)
27 Question 3. Solve the inequality 2 < (Total 2 marks) Question 4. Solve > 2 TOTAL /10
28 Translations and reflections of a function 2 Grade 7 Objective: Sketch translations and reflections of a function Question 1 The graph of = ( ) is shown below. Below each sketch below, write down the equation of the transformed graph y = y = (4) (Total 4 marks)
29 Question 2 The graph of = ( ) is shown on the grid below. (a) On the same grid draw the graph of = ( ) (2) (b) On grid above draw the graph of =3 ( ) (2)
30 (c) On grid above draw the graph of = ( ) + 2 (2) (Total 6 marks) TOTAL /10
31 Trigonometric Graphs 2 Grade 8 Objective: Recognise, sketch, and interpret graphs of trigonometric functions Question 1 Sketch the graph of y = tan x for (3) Question 2 Here is the graph of y = cos x for On the axes above, sketch the graph =cos(2 ) 2 for (3)
32 Question 3 The graph of y = sin x for is shown below. What are the coordinates of the 4 points labelled on the graph? (, ) (, ) (, ) (, ) (4) (Total 4 marks) TOTAL /10
33 Turning points and completing the square 2 Grade 7 Objective: Deduce turning points by completing the square Question 1 The graph of y = f(x) is shown below. Write down the turning point of the graph. (, ) (2) (Total 2 marks)
34 Question 2 The expression can be written in the form ( ) 2 (a) Find the values of p and q. p = q = (3) The equation of a curve is = ( ) where ( )= The diagram shows a sketch of the graph = ( ). B B is the minimum point of the curve. (b) Write down the coordinates of B. (, ) (1)
35 Question 3 Use completing the square to find the minimum point of the curve = (4) (Total 4 marks) TOTAL /10
36 General iterative processes 2 Grade 7 Objective: Work with general iterative processes Question 1. The cubic equation x 3 + 2x 5 = 0 has a solution which lies between 1 and 2. Use the decimal search method and the table below to find the solution correct to 1dp. x Value of x 3 + 2x 5 Positive or Negative? Question 2. Xn+1 = with X1 = 1.4 (a) Work out the values of X2 and X3... (b) Work out the solution correct to 2 decimal places.... (2)... (1)
37 Question 3. This iterative process can be used to find approximate solutions to the equation x 3 3x 1 = 0 to 2dp. Start with a value of x 3 Work out the value of Is your answer to 2 decimal places the same as your value of x to 2 decimal places? Yes No This is an approximate solution to x 3 3x 1 = 0 Use your answer as the next value of x and start again Use this iterative process to find a solution to 2 decimal places to x 3 3x 1 = 0. Start with x = 2 Total /10... (Total 4 marks)
38
39 PLC Papers Created For:
40 Algebra and proof 2 Grade 8 Solutions Objective: Use algebra to construct proofs Question 1 a) If n is a positive integer explain why the expression 2n + 1 is always an odd number. 2n is a multiple of 2 so it must be even so 2n + 1 is the number after an even number so it must be odd. b) Use algebra to prove that the product of two odd numbers is also odd. Question 2 (2n + 1) (2m + 1) = 4mn + 2n + 2m + 1 = 2 ( 2mn + n + m) ( 2mn + n + m) must be even so 2 ( 2mn + n + m) + 1 must be odd a) If x > 3 and prove that F > 1 Expand and simplify brackets Factorise Explain why factorised part is even State result must be odd Factorise numerator Factorise denominator Simplify fraction Explain why F > 1 (1) (4) x + 2 > x so numerator is bigger than denominator hence F > 1 b) Explain what happens if x = 3 If x = 3 then x 3 = 0 If you divide by x 3 you are dividing by 0 so F is undefined (May write you can t divide by 0) (4) (1) Total /10
41 Composite Functions 2 Grade 7 Solutions Objective: notation Interpret the succession of two functions as a composite function including the correct Question 1. The functions f and g are such that ( ) = 4 ( ) = Write in its simplest form the function (a) ( ) ( ) = ( + ) (M1) ( ) = + (A1). (2) (b) ( ) ( ) = ( ) + (M1) ( ) = + (A1). (2) (Total 4 marks)
42 Question 2. The functions p and r are such that ( ) = 2 2 ( ) = 4-3 (a) Write in its simplest form, the function ( ) ( ) = ( ) (M1) = (A1) (b) Calculate the value of. (2) (1) ( ) = 2 (A1) ( ) = = 8-3 = 5 (A1) (c) Calculate the value of. (2) ( 1) ( ) = = = (A1) ( ) = ( ) = = (A1). (2) (Total 6 marks)
43 Total /10
44 Expand the product of two or more binomials 2 Grade 7 Solutions Objective: Expand the product of two or more binomials Question 1. (a) Show that ( 2)( + 1)(2 3)= + ( )( + ) = + = ( ) ( ) = + + = +. (3) (b) Show that (3 1)( + 5)(3 1) = ( )( + ) = + = + ( + )( ) = + + = + +. (3) (Total 6 marks)
45 Question 2. Work out (2 1) 2 (3 4 ) ( )( ) = + = + ( + ) ( ) = + + = = + +. (Total 4 marks) Total /10
46 Exponential Graphs 2 Grade 8 Solutions Objective: Recognise, sketch, and interpret graphs of exponential functions Question 1 For each of the 3 statements, indicate whether it is TRUE or FALSE. You explain your answers. (a) The graph =2 passes through the point (2, 2). 2 2 = 4 not 2 (or explanation that leads to this) FALSE (C1) (b) The graph =5 passes through the point (-1, 0.2). 5-1 = 1/5 = 0.2 (or explanation that leads to this) TRUE (C1) (c) The graph =10 passes through the point (3, 100) = 1000 not 100 (or explanation that leads to this) FALSE (C1)
47 Question 2 Here are the equations of six different graphs: =0 =5 = 5 =( +5) 2 1 = =5 Match one of the equations to each of the following graphs: = 5 (A1) =( +5) 2 1 (A1) =5 (A1) (3)
48 Question 3 (a) Complete the table of values for y = 2 x x y ¼ o.e. ½ o.e (b) On the grid, draw the graph of y = 2 x Any 3 correct All correct (M1) (A1) (2) Points plotted correctly from their table Fully correct graph (smooth) (M1) (G1) (2) (Total 4 marks) TOTAL /10
49 Factorising difficult quadratic expressions 2 Grade 7 Solutions Objective: Factorise a quadratic expression of the form ax 2 + bx + c Question 1 Factorise x 2-17x+30 (x-15)(x-2) A2 (2 Marks) Question 2 Factorise 5x 2 +14x+8 5x 2 +10x +4x+8 5x(x+2) +2(x+2) M1 (5x+2)(x+2) A2 (3 Marks) Question 3 Factorise 9x 2-25 (3x+5)(3x-5) A2 (2 Marks) Question 4 Factorise 5x 2-8x-4 5x 2-10x +2x-4 5x(x-2) +2(x-2) M1 (5x+2)(x-2) A2 (3 Marks) Total marks / 10
50 Geometric Sequences 2 Grade 7 Solutions Objective: Recognise and use geometric sequences (r n, where n is an integer and r can be a surd) Question 1. Find the 5 th and 6 th terms of the sequences below. (a) 0.3, 0.9, 2.7, 8.1,,, 24.3, 72.9 (A1) (1) Common ratio is = 24.3 and = 72.9 (b) -5, 1, -0.2, 0.04,,, , (A1) (1) Common ratio is = and = Question 2. (Total 2 marks) (a) Write down the first four terms of the geometric sequence with nth term 3 n. 3 1, 3 2, 3 3, 3 4, (M1) 3, 9, 27, 81, (A1)... (2) (b) State the term-to-term rule of the sequence. The term-to-term rule is multiply the previous term by (1)
51 Question 3. In this geometric sequence, the first term is 3 and the term-to-term rule is multiply by 3. Continue the sequence for three more terms. 5, 5, 5 5,,,, 25, 25 5, = = 5 5 =25 (M1) 25 5 = 25 5 (A1) = = 25 5 = 125 (A1) Question 4. Work out the missing terms in this geometric sequence. 1 8, 3 8, 1 1 8, 3 3 8, Common ratio is 3. (M1) = 1 2 and 3 3 8, 3 = and (A1) (Total 2 marks) Total /10
52 Gradients and area under a graph 2 Grade 8 Solutions Objective: Calculate or estimate the gradient of a graph and the area under a graph Question 1 A straight line has been drawn on a grid. Calculate the gradient of the line. = 4 2 (M1) m = -2 (A1) (2) (Total 2 marks) Question 2 Work out the gradient of the line 5 3 = 20 Correct attempt to make y the subject: = (M1) = 3 5 (A1) (2) (Total 2 marks)
53 Question 3 The graph of = is drawn on the grid below. Calculate an estimate to the gradient of the curve at the point Q(-1, 3). Consider points just above and just below, i.e. x = -1.1 and x = -0.9 (M1) (-1.1, 3.499) and (-0.9, 2.501) = (M1) = 4.99 m = (or -5) (A1) (3)
54 Question 4 The scatter graph shows the cost of cars in a used car showroom. (a) Draw a line of best fit and calculate the gradient of this line. Using their line, = or use of any other points (M1) m = (A1) (2) (b) Give an interpretation of this gradient. The value of a car goes down by 1000 every year it gets older (or similar explanation) (C1) (1) TOTAL /10
55 Quadratic equations (completing the square) 2 Grade 8 SOLUTIONS Objective: Solve quadratic equations by completing the square. Question 1. Rewrite in the form ( + ) ( + 3) 2 2 (A1) (Total 1 mark) Question 2. Solve = 0 by completing the square = 0 ( 5) 2 16 = 0 (M1) ( 5) 2 = 16 5 = ±4 = 5 ± 4 = 9 = 1 (A1) (Total 2 marks)
56 Question 3. Solve = 0 by completing the square. Leave your answers in surd form = 0 ( 4) 2 28 = 0 (M1) ( 4) 2 = 28 4 = ± 28 = 4 ± 28 = 4 ± 2 7 (M1) (A1) Question 4. Solve = 0 by completing the square. Give your answers to 3 significant figures = 0 (M1) = 0 ( + 3.5) = 0 (M1) ( + 3.5) 2 = = ± = 3.5 ± = = 7.77 (M1) (A1) (Total 4 marks) TOTAL /10
57 Quadratic equations (needing re-arrangement) 2 Grade 7 Solutions Objective: Solve quadratic equations that need rearrangement Question 1. Solve 6(18+4 ) +2 = = 12 ( + 2) = = 12 2 (M1) 9 = 2 = ±3 (A1) (Total 2 marks) Question 2. Show that 10 4 = can be written as = 0 and hence calculate the two solutions. 10( 2) 4( 1) = 1( 1)( 2) = = = (M1) 0 = ( 3)( 6) = 3 = 6 (A1) (Total 2 marks)
58 Question 3. Solve 21 5 = ( + 1) 5( + 2) = 4( + 2)( + 1) (M1) = 4( ) = = (M1) 0 = (2 + 1)(2 3) = 1 2 = 3 2 (A1) Question 4. Solve = 5 42( + 1) 8( + 3) = 5( + 3)( + 1) (M1) = 5( ) = = (M1) 0 = (5 + 1)( 3) = 1 5 = 3 (A1) TOTAL /10
59 Quadratic equations (quadratic formula) 2 Grade 7 SOLUTION Objective: Solve quadratic equations by using the quadratic equation formula. Question 1. Solve = 0. Give your answer to 3 significant figures. = 5± ( 5) (M1) = or = = or = 1.43 (A2) = or = Question 2. Solve = 0. Give your answer to 2 decimal places. = 3± (M1) = or = = 3.86 or = 9.86 (A2) = or =
60 Question 3. a) Solve = 0 Give your answer to 2 decimal places. = 3± ( 3) (M1) = or = = 3.56 or = 0.56 (A2) = or = (3) b) Write down the solutions, correct to 2 decimal places, of = 0 4( 2 3 2) = 0 = 3.56 or = 0.56 (A1) = or = (1) (Total 4 marks) TOTAL /10
61 Represent quadratic inequalities 2 Grade 7 Solutions Objective: Represent the solution to a quadratic inequality on a number line, using set notation and on a graph Question 1. a) Solve x + 24 < 0 Represent your solution on a number line. ( + 8)( + 3) < 0 8 < < 3 b) Write the integer answers for part a) in set notation. { -7, -6, -5, -4 } (A1) (A1) (Total 2 marks) Question 2. Solve Display your answer on a sketch of the graph of the solution ( 7)( + 3) (Total 2 marks)
62 Question 3. For which values of x is the expression less than or equal to the expression ? Represent the possible values of on a number line (M1) (3 + 5)( 2) 0 (M1) (A1) Question 4. Find the set(s) of all values for which > 7 Display your answer on a sketch of the graph of the solution > (7 )( + 3) > (M1) > 0 ( + 9)( + 2) > 0 (M1) ( 7)( + 3) 0-3 7
63 TOTAL /10
64 Simultaneous equations (non-linear) 2 Grade 7 Solutions Objective: Solve two simultaneous equations (one linear, one quadratic) algebraically and approximately graphically Question 1. Solve this pair of simultaneous equations. = = = = 0 (M1) ( + 4)( + 3) = 0 = 4 = 16 = 3 = 14 (A1) (Total 2 marks) Question 2. Solve these simultaneous equations. = 6 2 = 8 (2 8) = = = 0 (M1) ( 3)( 1) = 0 = 3 = 2 = 1 = 6 (A1) (Total 2 marks)
65 Question 3. Calculate the solutions to these simultaneous equations = 29 = ( 7) 2 = 29 (M1) = = = 0 (M1) ( 5)( 2) = 0 = 5 = 2 = 2 = 5 (A1) Question 4. Use graphical methods to find the approximate solutions to this pair of simultaneous equations 2 5. = = 4 TOTAL /10
66 Solve quadratic inequalities 2 Grade 7 SOLUTIONS Objective: Solve quadratic inequalities in one variable Question 1. Solve a) 2 81 > 0 ( + 9)( 9) > 0 < 9, > 9 (A1) b) < 0 (2 + 7)(2 7) < < < 7 2 (A1) c) (2 11) (A1) Question 2. Solve the inequality ( 6)( 3) 0 (M1) 3, 6 (A1) (Total 2 marks)
67 Question 3. Solve the inequality 2 < < 0 ( 6)( + 4) < 0 (M1) 4 < < 6 (A1) (Total 2 marks) Question 4. Solve > > 0 (M1) (3 + 4)( 2) > 0 (M1) < 4 3, > 2 (A1) TOTAL /10
68 Translations and reflections of a function 2 Grade 7 Solutions Objective: Sketch translations and reflections of a function Question 1 The graph of = ( ) is shown below. Below each sketch below, write down the equation of the transformed graph y = -f(x) y = f(x+1) - 3 (4) (Total 4 marks)
69 Question 2 The graph of = ( ) is shown on the grid below y = f(x) y = f(-x) (a) On the same grid draw the graph of = ( ) (2) y = f(x) y = 3f(x) (b) On grid above draw the graph of =3 ( ) (2)
70 y = f(x) y = -f(x)+2 (c) On grid above draw the graph of = ( ) + 2 (2) (Total 6 marks) TOTAL /10
71 Trigonometric Graphs 2 Grade 8 Solutions Objective: Recognise, sketch, and interpret graphs of trigonometric functions Question 1 Sketch the graph of y = tan x for (3) Question 2 Here is the graph of y = cos x for y = cos x y = cos(2x) -2 On the axes above, sketch the graph =cos(2 ) 2 for (3)
72 Question 3 The graph of y = sin x for is shown below. What are the coordinates of the 4 points labelled on the graph? ( 0, 0 ) ( 90, 1 ) ( 270, -1 ) ( 360, 0 ) (4) (Total 4 marks) TOTAL /10
73 Turning points and completing the square 2 Grade 7 Solutions Objective: Deduce turning points by completing the square Question 1 The graph of y = f(x) is shown below. Write down the turning point of the graph. ( 2.5, 1.25 ) B1 B1 (2) (Total 2 marks)
74 Question 2 The expression can be written in the form ( ) 2 (a) Find the values of p and q. (x 4) M1 (x 4) 2-9 p = 4 B1 q = -9 B1 SC B1 for -4, 9 (3) The equation of a curve is = ( ) where ( )= The diagram shows a sketch of the graph = ( ). B B is the minimum point of the curve. (b) Write down the coordinates of B. ( 4, -9 ) (1) (Total 4 marks)
75 Question 3 Use completing the square to find the minimum point of the curve = (x + 4) M1 (x + 4) 2 15 M1 Min point at ( -4, -15) B1 B1 (4) (Total 4 marks) TOTAL /10
76 General iterative processes 2 Grade 7 Solutions Objective: Work with general iterative processes Question 1. The cubic equation x 3 + 2x 5 = 0 has a solution which lies between 1 and 2. Use the decimal search method and the table below to find the solution correct to 1dp. x Value of x 3 + 2x 5 Positive or Negative? (1.1) 5 = Negative (1.2) 5 = Negative (1.3) 5 = Negative (1.4) 5 = Positive (1.31) 5 = Negative (1.32) 5 = Negative (1.33) 5 = Positive Question 2. Correct iterations that identify change of sign (solution) is between 1.3 and 1.4 (M1) Correct iterations that identify change of sign (solution) is between 1.32 and 1.33 (M1) Xn+1 = with X1 = 1.4 (a) Work out the values of X2 and X3 (b) Work out the solution correct to 2 decimal places. So x = 1.3 to 1dp (A1)... X2 = (B1) X3 = (B1 ft from X2)... Using the ANS key to continue to generate terms X9 = and X10 = (2) Both round to 1.47 (B1)... (1)
77 Question 3. This iterative process can be used to find approximate solutions to the equation x 3 3x 1 = 0 to 2dp. Start with a value of x 3 Work out the value of Is your answer to 2 decimal places the same as your value of x to 2 decimal places? Yes No This is an approximate solution to x 3 3x 1 = 0 Use your answer as the next value of x and start again Use this iterative process to find a solution to 2 decimal places to x 3 3x 1 = 0. Start with x = 2 Substitutes in x = 2 to get x = (M1) Second pass through the flow diagram to give x = (M1) Third pass through the flow diagram to give x = (M1) Fourth pass through the flow diagram to give x = so x = 1.88 to 2dp (A1)... (Total 4 marks) Total /10
78
PLC Papers. Created For:
PLC Papers Created For: Algebra and proof 2 Grade 8 Objective: Use algebra to construct proofs Question 1 a) If n is a positive integer explain why the expression 2n + 1 is always an odd number. b) Use
More informationPLC Papers Created For:
PLC Papers Created For: Quadratics intervention Deduce quadratic roots algebraically 1 Grade 6 Objective: Deduce roots algebraically. Question 1. Factorise and solve the equation x 2 8x + 15 = 0 Question
More informationPLC Papers. Created For:
PLC Papers Created For: Algebraic argument 2 Grade 5 Objective: Argue mathematically that two algebraic expressions are equivalent, and use algebra to support and construct arguments Question 1. Show that
More informationPLC Papers Created For:
PLC Papers Created For: Josh Angles and linear graphs Graphs of Linear Functions 1 Grade 4 Objective: Recognise, sketch and interpret graphs of linear functions. Question 1 Sketch the graph of each function,
More informationPLC Papers Created For:
PLC Papers Created For: Daniel Inequalities Inequalities on number lines 1 Grade 4 Objective: Represent the solution of a linear inequality on a number line. Question 1 Draw diagrams to represent these
More informationYEAR 9 SCHEME OF WORK - EXTENSION
YEAR 9 SCHEME OF WORK - EXTENSION Autumn Term 1 Powers and roots Spring Term 1 Multiplicative reasoning Summer Term 1 Graphical solutions Quadratics Non-linear graphs Trigonometry Half Term: Assessment
More informationSection A Plotting Straight Line Graphs Grade D / C
Name: Teacher Assessment Section A Plotting Straight Line Graphs Grade D / C 1. (a) Complete the table of values for = 3x + x 0 1 3 5 10 16 19 (b) On the grid draw the graph of = 3x + for values of x from
More informationChapter 1- Polynomial Functions
Chapter 1- Polynomial Functions Lesson Package MHF4U Chapter 1 Outline Unit Goal: By the end of this unit, you will be able to identify and describe some key features of polynomial functions, and make
More informationSOLUTION OF QUADRATIC EQUATIONS LESSON PLAN. A3 Topic Overview ALGEBRA
ALGEBRA A Topic Overview A SOLUTION OF QUADRATIC EQUATIONS This topic describes three methods of solving Quadratic equations. assumes you understand and have practised using the algebraic methods described
More informationSolve Quadratics Using the Formula
Clip 6 Solve Quadratics Using the Formula a + b + c = 0, = b± b 4 ac a ) Solve the equation + 4 + = 0 Give our answers correct to decimal places. ) Solve the equation + 8 + 6 = 0 ) Solve the equation =
More informationThe Grade Descriptors below are used to assess work and student progress in Mathematics from Year 7 to
Jersey College for Girls Assessment criteria for KS3 and KS4 Mathematics In Mathematics, students are required to become familiar, confident and competent with a range of content and procedures described
More informationBrockington College Mathematics Personal Learning Checklist
Brockington College Mathematics Personal Learning Checklist To help you use this personal learning checklist, the target levels for each topic have given to help you decide what to focus on for your tier
More informationRevision notes for Pure 1(9709/12)
Revision notes for Pure 1(9709/12) By WaqasSuleman A-Level Teacher Beaconhouse School System Contents 1. Sequence and Series 2. Functions & Quadratics 3. Binomial theorem 4. Coordinate Geometry 5. Trigonometry
More informationAlgebra Revision Guide
Algebra Revision Guide Stage 4 S J Cooper 1st Edition Collection of like terms... Solving simple equations... Factorisation... 6 Inequalities... 7 Graphs... 9 1. The straight line... 9. The quadratic curve...
More informationHIGHER MATHS REVISION CHECKLIST (Grades 9 4)
HIGHER MATHS REVISION CHECKLIST 2017+ (s 9 4) Geometry and Measures Circle theorems 8 Vector arguments and proof 8 Area of a triangle 7 Cosine Rule 7 Pythagoras and trig 2D and 3D 7 Sine Rule 7 Combined
More informationMathematics Revision Guide. Algebra. Grade C B
Mathematics Revision Guide Algebra Grade C B 1 y 5 x y 4 = y 9 Add powers a 3 a 4.. (1) y 10 y 7 = y 3 (y 5 ) 3 = y 15 Subtract powers Multiply powers x 4 x 9...(1) (q 3 ) 4...(1) Keep numbers without
More informationIntegers, Fractions, Decimals and Percentages. Equations and Inequations
Integers, Fractions, Decimals and Percentages Round a whole number to a specified number of significant figures Round a decimal number to a specified number of decimal places or significant figures Perform
More informationQ Scheme Marks AOs. Attempt to multiply out the denominator (for example, 3 terms correct but must be rational or 64 3 seen or implied).
1 Attempt to multiply the numerator and denominator by k(8 3). For example, 6 3 4 8 3 8 3 8 3 Attempt to multiply out the numerator (at least 3 terms correct). M1 1.1b 3rd M1 1.1a Rationalise the denominator
More informationPLC Papers Created For:
PLC Papers Created For: Year 11 Topic Practice Paper: Factorising Quadratics Factorising difficult quadratic expressions 1 Grade 7 Objective: Factorise a quadratic expression of the form ax 2 + bx + c
More informationRearrange m ore complicated formulae where the subject may appear twice or as a power (A*) Rearrange a formula where the subject appears twice (A)
Moving from A to A* A* Solve a pair of simultaneous equations where one is linear and the other is non-linear (A*) Rearrange m ore complicated formulae may appear twice or as a power (A*) Simplify fractions
More informationS4 (4.3) Quadratic Functions.notebook February 06, 2018
Daily Practice 2.11.2017 Q1. Multiply out and simplify 3g - 5(2g + 4) Q2. Simplify Q3. Write with a rational denominator Today we will be learning about quadratic functions and their graphs. Q4. State
More informationVerulam School Mathematics. Year 9 Revision Material (with answers) Page 1
Verulam School Mathematics Year 9 Revision Material (with answers) Page 1 Q1. (a) Simplify a 2 a 4 Answer... (b) Simplify b 9 b 3 Answer... (c) Simplify c 5 c c 5 Answer... (Total 3 marks) Q2. (a) Expand
More informationFOUNDATION MATHS REVISION CHECKLIST (Grades 5 1)
FOUNDATION MATHS REVISION CHECKLIST 2017+ (s 5 1) Geometry and Measures Arc lengths and sectors 5 Derive triangle results 5 Enlargements and negative SF 5 Loci 5 Pythagoras 5 Similarity and Congruence
More informationFurther Mathematics SAMPLE. Marking Scheme
Further Mathematics SAMPLE Marking Scheme This marking scheme has been prepared as a guide only to markers. This is not a set of model answers, or the exclusive answers to the questions, and there will
More informationAS PURE MATHS REVISION NOTES
AS PURE MATHS REVISION NOTES 1 SURDS A root such as 3 that cannot be written exactly as a fraction is IRRATIONAL An expression that involves irrational roots is in SURD FORM e.g. 2 3 3 + 2 and 3-2 are
More informationAlgebra. Topic: Manipulate simple algebraic expressions.
30-4-10 Algebra Days: 1 and 2 Topic: Manipulate simple algebraic expressions. You need to be able to: Use index notation and simple instances of index laws. Collect like terms Multiply a single term over
More informationAssessment Report. Level 2, Mathematics
Assessment Report Level 2, 2006 Mathematics Manipulate algebraic expressions and solve equations (90284) Draw straightforward non-linear graphs (90285) Find and use straightforward derivatives and integrals
More informationWJEC LEVEL 2 CERTIFICATE 9550/01 ADDITIONAL MATHEMATICS
Surname Centre Number Candidate Number Other Names 0 WJEC LEVEL 2 CERTIFICATE 9550/01 ADDITIONAL MATHEMATICS A.M. MONDAY, 22 June 2015 2 hours 30 minutes S15-9550-01 For s use ADDITIONAL MATERIALS A calculator
More informationNot drawn accurately
Q1. A trapezium has parallel sides of length (x + 1) cm and (x + 2) cm. The perpendicular distance between the parallel sides is x cm. The area of the trapezium is 10 cm 2. Not drawn accurately Find the
More informationMesaieed International School
Mesaieed International School SUBJECT: Mathematics Year: 10H Overview of the year: The contents below reflect the first half of the two-year IGCSE Higher course which provides students with the opportunity
More informationThe Bridge to A level. Diagnosis Worked Solutions
The Bridge to A level Diagnosis Worked Solutions 1 1 Solving quadratic equations Solve x 2 + 6x + 8 = 0 (x + 2)(x + 4) = 0 x = 2 or 4 Solve the equation y 2 7y + 12 = 0 Hence solve the equation x 4 7x
More informationKS4: Algebra and Vectors
Page1 KS4: Algebra and Vectors Page2 Learning Objectives: During this theme, students will develop their understanding of Key Stage 4 algebra and vectors requiring algebraic manipulation. It will build
More informationMaths A Level Summer Assignment & Transition Work
Maths A Level Summer Assignment & Transition Work The summer assignment element should take no longer than hours to complete. Your summer assignment for each course must be submitted in the relevant first
More informationEDEXCEL NATIONAL CERTIFICATE UNIT 4 MATHEMATICS FOR TECHNICIANS OUTCOME 1
Learning outcomes EDEXCEL NATIONAL CERTIFICATE UNIT 4 MATHEMATICS FOR TECHNICIANS OUTCOME 1 TUTORIAL 3 - FACTORISATION AND QUADRATICS On completion of this unit a learner should: 1 Know how to use algebraic
More informationAlgebraic. techniques1
techniques Algebraic An electrician, a bank worker, a plumber and so on all have tools of their trade. Without these tools, and a good working knowledge of how to use them, it would be impossible for them
More informationThe degree of a function is the highest exponent in the expression
L1 1.1 Power Functions Lesson MHF4U Jensen Things to Remember About Functions A relation is a function if for every x-value there is only 1 corresponding y-value. The graph of a relation represents a function
More informationYou must have: Ruler graduated in centimetres and millimetres, pair of compasses, pen, HB pencil, eraser.
Write your name here Surname Other names Pearson Edexcel Award Algebra Level 3 Calculator NOT allowed Centre Number Candidate Number Thursday 12 January 2017 Morning Time: 2 hours Paper Reference AAL30/01
More informationKing s Year 12 Medium Term Plan for LC1- A-Level Mathematics
King s Year 12 Medium Term Plan for LC1- A-Level Mathematics Modules Algebra, Geometry and Calculus. Materials Text book: Mathematics for A-Level Hodder Education. needed Calculator. Progress objectives
More informationLesson 9 Exploring Graphs of Quadratic Functions
Exploring Graphs of Quadratic Functions Graph the following system of linear inequalities: { y > 1 2 x 5 3x + 2y 14 a What are three points that are solutions to the system of inequalities? b Is the point
More informationScope and Sequence: National Curriculum Mathematics from Haese Mathematics (7 10A)
Scope and Sequence: National Curriculum Mathematics from Haese Mathematics (7 10A) Updated 06/05/16 http://www.haesemathematics.com.au/ Note: Exercises in red text indicate material in the 10A textbook
More informationQUADRATIC EQUATIONS M.K. HOME TUITION. Mathematics Revision Guides Level: GCSE Higher Tier
Mathematics Revision Guides Quadratic Equations Page 1 of 8 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier QUADRATIC EQUATIONS Version: 3.1 Date: 6-10-014 Mathematics Revision Guides
More informationDEPARTMENT OF MATHEMATICS
DEPARTMENT OF MATHEMATICS AS level Mathematics Core mathematics 1 C1 2015-2016 Name: Page C1 workbook contents Indices and Surds Simultaneous equations Quadratics Inequalities Graphs Arithmetic series
More informationUnit 3: Number, Algebra, Geometry 2
Unit 3: Number, Algebra, Geometry 2 Number Use standard form, expressed in standard notation and on a calculator display Calculate with standard form Convert between ordinary and standard form representations
More informationSample Assessment Materials
Edexcel Awards Mathematics Sample Assessment Materials Edexcel Level Award in Algebra (AAL0) Edexcel Level 3 Award in Algebra (AAL30) For first teaching from October 01 Pearson Education Limited is a registered
More informationChapter 1- Polynomial Functions
Chapter 1- Polynomial Functions Lesson Package MHF4U Chapter 1 Outline Unit Goal: By the end of this unit, you will be able to identify and describe some key features of polynomial functions, and make
More informationl Advanced Subsidiary Paper 1: Pure Mathematics Mark Scheme Any reasonable explanation.
l Advanced Subsidiary Paper 1: Pure athematics PAPER B ark Scheme 1 Any reasonable explanation. For example, the student did not correctly find all values of x which satisfy cosx. Student should have subtracted
More informationIntermediate Tier - Algebra revision
Intermediate Tier - Algebra revision Contents : Collecting like terms Multiplying terms together Indices Expanding single brackets Expanding double brackets Substitution Solving equations Finding nth term
More informationBook 4. June 2013 June 2014 June Name :
Book 4 June 2013 June 2014 June 2015 Name : June 2013 1. Given that 4 3 2 2 ax bx c 2 2 3x 2x 5x 4 dxe x 4 x 4, x 2 find the values of the constants a, b, c, d and e. 2. Given that f(x) = ln x, x > 0 sketch
More informationMEI STRUCTURED MATHEMATICS 4751
OXFORD CAMBRIDGE AND RSA EXAMINATIONS Advanced Subsidiary General Certificate of Education Advanced General Certificate of Education MEI STRUCTURED MATHEMATICS 475 Introduction to Advanced Mathematics
More information2 year GCSE Scheme of Work
2 year GCSE Scheme of Work Year 10 Pupils follow the 2 year Pearsons/Edexcel Scheme of Work FOUNDATION ROUTE HIGHER ROUTE YEAR 4 YEAR 5 YEAR 4 YEAR 5 GCSE (9-1) Foundation GCSE (9-1) Foundation GCSE (9-1)
More informationCore Mathematics 2 Trigonometry
Core Mathematics 2 Trigonometry Edited by: K V Kumaran Email: kvkumaran@gmail.com Core Mathematics 2 Trigonometry 2 1 Trigonometry Sine, cosine and tangent functions. Their graphs, symmetries and periodicity.
More informationExaminer's Report Q1.
Examiner's Report Q1. For students who were comfortable with the pair of inequality signs, part (a) proved to be straightforward. Most solved the inequalities by operating simultaneously on both sets and
More informationA2 HW Imaginary Numbers
Name: A2 HW Imaginary Numbers Rewrite the following in terms of i and in simplest form: 1) 100 2) 289 3) 15 4) 4 81 5) 5 12 6) -8 72 Rewrite the following as a radical: 7) 12i 8) 20i Solve for x in simplest
More informationAlgebra 2 Khan Academy Video Correlations By SpringBoard Activity
SB Activity Activity 1 Creating Equations 1-1 Learning Targets: Create an equation in one variable from a real-world context. Solve an equation in one variable. 1-2 Learning Targets: Create equations in
More informationAlgebra. CLCnet. Page Topic Title. Revision Websites. GCSE Revision 2006/7 - Mathematics. Add your favourite websites and school software here.
Section 2 Page Topic Title 54-57 12. Basic algebra 58-61 13. Solving equations 62-64 14. Forming and solving equations from written information 65-67 15. Trial and improvement 68-72 16. Formulae 73-76
More informationAlgebra 2 Khan Academy Video Correlations By SpringBoard Activity
SB Activity Activity 1 Creating Equations 1-1 Learning Targets: Create an equation in one variable from a real-world context. Solve an equation in one variable. 1-2 Learning Targets: Create equations in
More informationPaper 1 Foundation Revision List
Paper 1 Foundation Revision List Converting units of length 692 Converting units of mass 695 Order of operations 24 Solving one step equations 178 Operations with negative numbers 39, 40 Term to term rules
More informationMATHEMATICS National Qualifications - National 5 Paper 1 (Non Calculator) Testing EF and REL
N5 Prelim Practice Paper B MATHEMATICS National Qualifications - National 5 Paper 1 (Non Calculator) Testing EF and REL Time allowed - 1 hour Fill in these boxes and read carefully what is printed below
More informationYear 12 Maths C1-C2-S1 2016/2017
Half Term 1 5 th September 12 th September 19 th September 26 th September 3 rd October 10 th October 17 th October Basic algebra and Laws of indices Factorising expressions Manipulating surds and rationalising
More informationEDEXCEL NATIONAL CERTIFICATE UNIT 4 MATHEMATICS FOR TECHNICIANS OUTCOME 1
Learning outcomes EDEXCEL NATIONAL CERTIFICATE UNIT 4 MATHEMATICS FOR TECHNICIANS OUTCOME 1 TUTORIAL 2 - LINEAR EQUATIONS AND GRAPHS On completion of this unit a learner should: 1 Know how to use algebraic
More informationINSIDE ALGEBRA CORRELATED WITH CALIFORNIA S COMMON CORE STANDARDS HIGH SCHOOL ALGEBRA
We CA Can COMMON Early Learning CORE STANDARDS Curriculum PreK Grades 8 12 INSIDE ALGEBRA CORRELATED WITH CALIFORNIA S COMMON CORE STANDARDS HIGH SCHOOL ALGEBRA May 2011 www.voyagersopris.com/insidealgebra
More informationEvaluation. Simplification + 3 KU. Factorisation. a 9b Evaluate 30 3p 2 q where p = 1 and q = 6 2 KU. 2. Simplify 4(3x 2 KU
. Algebra 1 Basic algebraic operations Evaluation... 1 Simplification, removing brackets, FOIL, squares... 1 Factorisation, common factor, difference of two squares, quadratic (trinomial)... 1 Solving
More informationYou must have: Ruler graduated in centimetres and millimetres, pair of compasses, pen, HB pencil, eraser.
Write your name here Surname Other names Pearson Edexcel Award Algebra Level 3 Calculator NOT allowed Centre Number Candidate Number Tuesday 10 May 2016 Morning Time: 2 hours Paper Reference AAL30/01 You
More information5.6 Logarithmic and Exponential Equations
SECTION 5.6 Logarithmic and Exponential Equations 305 5.6 Logarithmic and Exponential Equations PREPARING FOR THIS SECTION Before getting started, review the following: Solving Equations Using a Graphing
More informationYear 12 Maths C1-C2-S1 2017/2018
Half Term 1 5 th September 12 th September 19 th September 26 th September 3 rd October 10 th October 17 th October Basic algebra and Laws of indices Factorising expressions Manipulating surds and rationalising
More informationCore A-level mathematics reproduced from the QCA s Subject criteria for Mathematics document
Core A-level mathematics reproduced from the QCA s Subject criteria for Mathematics document Background knowledge: (a) The arithmetic of integers (including HCFs and LCMs), of fractions, and of real numbers.
More informationPLC Papers. Created For:
PLC Papers Created For: t followed by close scrutiny of the marking scheme followed by reassessing every 3 days to attain at least 8 out o Approximate solutions to equations using iteration 1 Grade 9 Objective:
More informationYou must have: Ruler graduated in centimetres and millimetres, pair of compasses, pen, HB pencil, eraser.
Write your name here Surname Other names Pearson Edexcel Award Algebra Level 3 Calculator NOT allowed Centre Number Candidate Number Monday 8 May 017 Morning Time: hours Paper Reference AAL30/01 You must
More informationPrelim Examination 2010 / 2011 (Assessing Units 1 & 2) MATHEMATICS. Advanced Higher Grade. Time allowed - 2 hours
Prelim Examination 00 / 0 (Assessing Units & ) MATHEMATICS Advanced Higher Grade Time allowed - hours Read Carefully. Calculators may be used in this paper.. Candidates should answer all questions. Full
More informationPure Mathematics P1
1 Pure Mathematics P1 Rules of Indices x m * x n = x m+n eg. 2 3 * 2 2 = 2*2*2*2*2 = 2 5 x m / x n = x m-n eg. 2 3 / 2 2 = 2*2*2 = 2 1 = 2 2*2 (x m ) n =x mn eg. (2 3 ) 2 = (2*2*2)*(2*2*2) = 2 6 x 0 =
More informationA marks are for accuracy and are not given unless the relevant M mark has been given (M0 A1 is impossible!).
NOTES 1) In the marking scheme there are three types of marks: M marks are for method A marks are for accuracy and are not given unless the relevant M mark has been given (M0 is impossible!). B marks are
More informationQuadratic Equations. All types, factorising, equation, completing the square. 165 minutes. 151 marks. Page 1 of 53
Quadratic Equations All types, factorising, equation, completing the square 165 minutes 151 marks Page 1 of 53 Q1. (a) Factorise x 2 + 5x 24 Answer... (2) (b) Solve x 2 + 5x 24 = 0 Answer... (1) (Total
More information2005 Mathematics. Intermediate 2 Units 1, 2 and 3. Finalised Marking Instructions
2005 Mathematics Intermediate 2 Units 1, 2 and 3 Finalised Marking Instructions These Marking Instructions have been prepared by Examination Teams for use by SQA Appointed Markers when marking External
More informationA Level Summer Work. Year 11 Year 12 Transition. Due: First lesson back after summer! Name:
A Level Summer Work Year 11 Year 12 Transition Due: First lesson back after summer! Name: This summer work is compulsory. Your maths teacher will ask to see your work (and method) in your first maths lesson,
More informationVariables and Expressions
Variables and Expressions A variable is a letter that represents a value that can change. A constant is a value that does not change. A numerical expression contains only constants and operations. An algebraic
More informationPerth Academy Mathematics Department Intermediate 2 Unit 3 Revision Pack. Contents:
Perth Academ Mathematics Department Intermediate Unit Revision Pack Contents: Algebraic Operations: Fractions Fractions Formulae Surds Indices Quadratic Functions: Y = a Y = a + b Y = ( + a) + b Turning
More informationWhat you may need to do: 1. Formulate a quadratic expression or equation. Generate a quadratic expression from a description or diagram.
Dealing with a quadratic What it is: A quadratic expression is an algebraic expression containing an x 2 term, as well as possibly an x term and/or a number, but nothing else - eg, no x 3 term. The general
More informationCAMBRIDGE IGCSE MATHS EXAMINATION BOARD COVERAGE
CAMBRIDGE IGCSE MATHS EXAMINATION BOARD COVERAGE TIER TOPIC HEADING SUB HEADING Both Number Integers Ordering numbers Both Number Integers Rounding numbers Both Number Integers Adding and subtracting whole
More informationLESMAHAGOW HIGH SCHOOL Mathematics Department. National 5. Relationships Scheme of Work
LESMAHAGOW HIGH SCHOOL Mathematics Department National 5 Relationships Scheme Work Relationships Main Resource (Supplementary resource Int 2 Credit Book 1/2) Applying algebraic skills to linear equations
More informationHOW TO PASS NATIONAL 5 MATHS
HOW TO PASS NATIONAL MATHS Name: Homework 9 0 Score Homework Sheet Evaluate Find the equation of the straight line passing through these points: (,-) and (,9). Simplify m x m -9 Change the subject of the
More informationCore 1 Module Revision Sheet J MS. 1. Basic Algebra
Core 1 Module Revision Sheet The C1 exam is 1 hour 0 minutes long and is in two sections Section A (6 marks) 8 10 short questions worth no more than 5 marks each Section B (6 marks) questions worth 12
More informationUnderstand the difference between truncating and rounding. Calculate with roots, and with integer and fractional indices.
The assessments will cover the following content headings: 1. Number 2. Algebra 3. Ratio, and rates of change 4. Geometry and measures 5. Probability 6. Statistics Higher Year 7 Year 8 Year 9 Year 10 Year
More informationCandidates are expected to have available a calculator. Only division by (x + a) or (x a) will be required.
Revision Checklist Unit C2: Core Mathematics 2 Unit description Algebra and functions; coordinate geometry in the (x, y) plane; sequences and series; trigonometry; exponentials and logarithms; differentiation;
More informationPaper collated from year 2007 Content Pure Chapters 1-13 Marks 100 Time 2 hours
1. Paper collated from year 2007 Content Pure Chapters 1-13 Marks 100 Time 2 hours 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. Mark scheme Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question
More information*P43632A0120* Algebra Level 3 Calculator NOT allowed. Pearson Edexcel Award AAL30/01. P43632A 2014 Pearson Education Ltd.
Write your name here Surname Other names Pearson Edexcel Award Algebra Level 3 Calculator NOT allowed Centre Number Candidate Number Monday 12 May 2014 Morning Time: 2 hours Paper Reference AAL30/01 You
More informationMaths Assessment Framework Year 10 Higher
Success Criteria for all assessments: Higher Tier 90% 9 80% 8 70% 7 60% 6 50% 5 Please note the GCSE Mathematics is one of the first GCSEs which will be graded by number rather than A*, A, B, C etc. Roughly,
More information56 CHAPTER 3. POLYNOMIAL FUNCTIONS
56 CHAPTER 3. POLYNOMIAL FUNCTIONS Chapter 4 Rational functions and inequalities 4.1 Rational functions Textbook section 4.7 4.1.1 Basic rational functions and asymptotes As a first step towards understanding
More information1 Solving equations 1.1 Kick off with CAS 1. Polynomials 1. Trigonometric symmetry properties 1.4 Trigonometric equations and general solutions 1.5 Literal and simultaneous equations 1.6 Review 1.1 Kick
More informationYEAR 10 PROGRAM TERM 1 TERM 2 TERM 3 TERM 4
YEAR 10 PROGRAM TERM 1 1. Revision of number operations 3 + T wk 2 2. Expansion 3 + T wk 4 3. Factorisation 7 + T wk 6 4. Algebraic Fractions 4 + T wk 7 5. Formulae 5 + T wk 9 6. Linear Equations 10 +T
More information1.2. Indices. Introduction. Prerequisites. Learning Outcomes
Indices 1.2 Introduction Indices, or powers, provide a convenient notation when we need to multiply a number by itself several times. In this Section we explain how indices are written, and state the rules
More informationAQA Level 2 Certificate in Further Mathematics. Worksheets - Teacher Booklet
AQA Level Certificate in Further Mathematics Worksheets - Teacher Booklet Level Specification Level Certificate in Further Mathematics 860 Worksheets - Teacher Booklet Our specification is published on
More informationGCSE (9 1) Mathematics
GCSE (9 1) Mathematics New topics sample questions (1MA1) First teaching from September 2015 First certification from June 2017 Issue 2 Contents About this booklet 3 1. Number 5 2. Algebra 8 3. Ratio,
More informationYear 12 into 13 Maths Bridging Tasks
Year 1 into 13 Maths Bridging Tasks Topics covered: Surds Indices Curve sketching Linear equations Quadratics o Factorising o Completing the square Differentiation Factor theorem Circle equations Trigonometry
More information4751 Mark Scheme June Mark Scheme 4751 June 2005
475 Mark Scheme June 2005 Mark Scheme 475 June 2005 475 Mark Scheme June 2005 Section A 40 2 M subst of for x or attempt at long divn with x x 2 seen in working; 0 for attempt at factors by inspection
More informationUNIT 3 MATHEMATICAL METHODS ALGEBRA
UNIT 3 MATHEMATICAL METHODS ALGEBRA Substitution of Values Rearrangement and Substitution Polynomial Expressions Expanding Expressions Expanding Expressions by Rule Perfect Squares The Difference of Two
More informationTwitter: @Owen134866 www.mathsfreeresourcelibrary.com Prior Knowledge Check 1) Simplify: a) 3x 2 5x 5 b) 5x3 y 2 15x 7 2) Factorise: a) x 2 2x 24 b) 3x 2 17x + 20 15x 2 y 3 3) Use long division to calculate:
More informationMethod marks are awarded for a correct method which could lead to a correct answer.
Pre Paper 3F Question Bank Answers November 2017 GCSE Mathematics (AQA style) Foundation Tier This set of answers is not a conventional marking scheme; while it gives a basic allocation of marks, its main
More informationCore Mathematics C1 Advanced Subsidiary
Paper Reference(s) 666/0 Edexcel GCE Core Mathematics C Advanced Subsidiary Monday 0 January 0 Morning Time: hour 0 minutes Materials required for examination Mathematical Formulae (Pink) Items included
More informationAlgebra II Unit #2 4.6 NOTES: Solving Quadratic Equations (More Methods) Block:
Algebra II Unit # Name: 4.6 NOTES: Solving Quadratic Equations (More Methods) Block: (A) Background Skills - Simplifying Radicals To simplify a radical that is not a perfect square: 50 8 300 7 7 98 (B)
More informationC-1. Snezana Lawrence
C-1 Snezana Lawrence These materials have been written by Dr. Snezana Lawrence made possible by funding from Gatsby Technical Education projects (GTEP) as part of a Gatsby Teacher Fellowship ad-hoc bursary
More information