National 5 Mathematics

Transcription

1 St Andrew s Academ Mathematics Department National 5 Mathematics UNIT 4 ASSESSMENT PREPARATION St Andrew's Academ Maths Dept

2 Practice Unit Assessment 4A for National 5 1. Simplif, giving our answer in surd form: 3. (a) Simplif (i) (ii) 4 The number of people attending a football match was If each person paid 7, how much was collected? Give ou answer in Scientific Notation. 3. The diagram shows the parabola with 40 equation k. 35 What is the value of k? The equation of the quadratic function whose graph is shown below is of the form = ( + a) + b, where a and b are integers. Write down the values of a and b St Andrew's Academ Maths Dept

3 5. Sketch the graph = ( 1)( + 3) on plain paper. Mark clearl where the graph crosses the aes and state the coordinates of the turning point. 6. A parabola has equation = ( 3) + 4. (a) Write down the equation of its ais of smmetr. Write down the coordinates of the turning point on the parabola and state whether it is a maimum or minimum. (4 )( 4) 7. Write ( 4) ( 4) in its simplest form. 8. Write each of the following as a single fraction: 3 5 (a) ( a, b 0) a b f e ( g 0) 5 g St Andrew's Academ Maths Dept

4 Practice Unit Assessment 4B for National 5 1. Simplif, giving our answer in surd form: (a) Simplif (i) (ii) 3 1 The number of people attending a musical was If each person paid 34, how much was collected. Give ou answer in Scientific Notation. 3. The diagram shows the parabola with equation k. 16 What is the value of k? The equation of the quadratic function whose graph is shown below is of the form = ( + a) + b, where a and b are integers Write down the values of a and b St Andrew's Academ Maths Dept

5 5. Sketch the graph = ( 5)( 7) on plain paper. Mark clearl where the graph crosses the aes and state the coordinates of the turning point. 6. A parabola has equation = ( + 4) 3. (a) Write down the equation of its ais of smmetr. Write down the coordinates of the turning point on the parabola and state whether it is a maimum or minimum. (3 1)( ) 7. Write ( 3) ( ) in its simplest form. 8. Write each of the following as a single fraction: 5 7 (a) ( c, d 0) c d k k ( h 0) 7 h St Andrew's Academ Maths Dept

6 Practice Unit Assessment 4C for National 5 1. Simplif, giving our answer in surd form: 147. (a) Simplif (i) 3 8 (ii) A factor produces cakes ever da. How man cakes will it produce in the month of April? Give ou answer in Scientific Notation. 3. The diagram shows the parabola with equation k 4 What is the value of k? The equation of the quadratic function whose graph is shown below is of the form = ( + a) + b, where a and b are integers. Write down the values of a and b St Andrew's Academ Maths Dept

7 5. Sketch the graph = ( 4)( + ) on plain paper. Mark clearl where the graph crosses the aes and state the coordinates of the turning point. 6. A parabola has equation = 5 ( + 3). (a) Write down the equation of its ais of smmetr. Write down the coordinates of the turning point on the parabola and state whether it is a maimum or minimum. ( 5)( 7) 7. Write ( 5) ( 5) in its simplest form. 8. Write each of the following as a single fraction: 4 9 (a) ( m, n 0) m n 4 k ( h 0) k l St Andrew's Academ Maths Dept

8 Practice Unit 4A: Marking Scheme Points of reasoning are marked # in the table. Question Main points of epected responses 1 start of process 16 (or equivalent) simplified surd 4 (a) (i) simplif numerator 10 correct answer 7 (ii) correct coefficient 0 4 simplif indices in answer 0 5 calculation of amount epress in standard form = correct value of k k = 5 4 find value of a find value of b a = 1 b = 5 identif and annotate roots and -intercept identif and annotate turning point draw correct shape of graph 6 (a) ais of smmetr 3, 1 and (0, 3) ( 1, 4) = 3 correctl annotated graph turning point nature ( 3, 4) minimum turning point 7 reduce to simplest form (a) 4 denominator correct numerator correct multipl b inversion of fraction correct answer 4 /// ab 3b 5a ab g e fg 5e St Andrew's Academ Maths Dept

9 Practice Unit 4B: Marking Scheme Points of reasoning are marked # in the table. Question Main points of epected responses 1 simplif surd 3 6 (a) (i) simplif numerator 4 correct answer (ii) correct coefficient 6 4 simplif indices 4 5 in answer calculation of amount = epress in standard form correct value of k k = 4 find value of a find value of b a = 1 b = 4 5 identif and annotate roots and -intercept identif and annotate turning point draw correct shape of graph 6 (a) ais of smmetr 5, 7 and (0, 35) (6, 1) correctl annotated graph = 4 turning point nature ( 4, 3) minimum turning point 7 reduce to simplest form (a) 4 denominator correct numerator correct multipl b inversion of fraction correct answer 4 k 7 /// cd 5d 7c cd h k St Andrew's Academ Maths Dept

10 Practice Unit 4C: Marking Scheme Points of reasoning are marked # in the table. Question Main points of epected responses 1 simplif surd 7 3 (a) (i) simplif numerator 10 correct answer 13 (ii) correct coefficient 18 4 simplif indices in answer calculation of distance epress in standard form = correct value of k k = 3 4 find value of a find value of b 5 identif and annotate roots and -intercept identif and annotate turning point draw correct shape of graph a = 1 b = 3, 4 and (0, 8) (1, 9) correctl annotated graph 6 (a) ais of smmetr = 3 turning point nature ( 3, 5) maimum turning point 7 reduce to simplest form (a) 4 denominator correct numerator correct multipl b inversion of fraction correct answer 4 /// mn 4n 9m mn l k 4l k St Andrew's Academ Maths Dept