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INTERMEDIATE 2 – ADDITIONAL QUESTION BANK

INTERMEDIATE 2 – ADDITIONAL QUESTION BANK. Algebraic Operations. Quadratic Functions. UNIT 3 :. Further Trig. EXIT. INTERMEDIATE 2 – ADDITIONAL QUESTION BANK. You have chosen to study:. Algebraic Operations. UNIT 3 :. Please choose a question to attempt from the following:. 1. 2.

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INTERMEDIATE 2 – ADDITIONAL QUESTION BANK

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  1. INTERMEDIATE 2 – ADDITIONAL QUESTION BANK Algebraic Operations Quadratic Functions UNIT 3 : Further Trig EXIT

  2. INTERMEDIATE 2 – ADDITIONAL QUESTION BANK You have chosen to study: Algebraic Operations UNIT 3 : Please choose a question to attempt from the following: 1 2 3 4 5 6 7 8 Back to Unit 3 Menu EXIT

  3. ALGEBRAIC OPERATIONS : Question 1 Express (m  -7) as a single fraction in its simplest form. What would you like to do now? Get hint Reveal answer only Go to full solution Go to Comments Go to Algebraic Ops Menu EXIT

  4. Use the pattern ad + bc bd a + = c b d ALGEBRAIC OPERATIONS : Question 1 Express (m  -7) as a single fraction in its simplest form. What would you like to do now? Reveal answer only Go to full solution Go to Comments Go to Algebraic Ops Menu EXIT

  5. m2 - m = 2m + 14 ALGEBRAIC OPERATIONS : Question 1 Express (m  -7) as a single fraction in its simplest form. What would you like to do now? Try another like this Go to full solution Go to Comments Go to Algebraic Ops Menu EXIT

  6. Question 1 m2 + 7m - 8m = 2m + 14 m2 - m 1. Use the pattern = ad + bc 2m + 14 bd a + = c b d Express (m  -7) as a single fraction in its simplest form. m (m + 7) - (2 x 4m) = 2 (m + 7) Begin Solution Try another like this Comments Menu Back to Home

  7. Comments m2 + 7m - 8m = 2m + 14 m2 - m 1. Use the pattern = ad + bc ad + bc ad - bc 2m + 14 bd bd bd a a a - + + = = = c c c b b b d d d To add or subtract fractions use the results: m (m + 7) - (2 x 4m) 2 (m + 7) Try another Menu Back to Home

  8. ALGEBRAIC OPERATIONS: Question 1B Express (t  3) as a single fraction in its simplest form. What would you like to do now? Get hint Reveal answer only Go to full solution Go to Comments Go to Algebraic Ops Menu EXIT

  9. Use the pattern ad + bc bd a + = c b d ALGEBRAIC OPERATIONS: Question 1B Express (t  3) as a single fraction in its simplest form. What would you like to do now? Reveal answer only Go to full solution Go to Comments Go to Algebraic Ops Menu EXIT

  10. 7t2 + 19t = 10t – 30 ALGEBRAIC OPERATIONS: Question 1B Express (t  3) as a single fraction in its simplest form. What would you like to do now? Go to full solution Go to Comments Go to Algebraic Ops Menu EXIT

  11. Question 1B 7t2 – 21t +40t = 10t – 30 7t2 + 19t 1. Use the pattern = ad + bc 10t – 30 bd a + = c b d Express (t  3) as a single fraction in its simplest form. 7t (t – 3) + (10 x 4t) = 10 (t – 3) Begin Solution Continue Solution Comments Menu What would you like to do now? Back to Home

  12. Comments 7t2 – 21t +40t = 10t – 30 7t2 + 19t 1. Use the pattern = ad - bc ad + bc ad + bc 10t – 30 bd bd bd a a a + + - = = = c c c b b b d d d To add or subtract fractions use the results: 7t (t – 3) + (10 x 4t) = 10 (t – 3) Next Comment Menu Back to Home

  13. Comments 7t2 – 21t +40t = 10t – 30 7t2 + 19t 7t2 + 19t 1. Use the pattern = ad + bc 10t - 30 10t – 30 bd a + = c b d Note: Always check that you have cancelled as far as possible. This is the final result, it does not cancel further. 7t (t – 3) + (10 x 4t) = 10 (t – 3) Menu Back to Home

  14. ALGEBRAIC OPERATIONS: Question 2 Express as a single fraction in its simplest form. What would you like to do now? Get hint Reveal answer only Go to full solution Go to Comments Go to Algebraic Ops Menu EXIT

  15. ALGEBRAIC OPERATIONS: Question 2 Express as a single fraction in its simplest form. Multiply top line then bottom line. Cancel numbers then letters in alphabetical order. What would you like to do now? Reveal answer only Go to full solution Go to Comments Go to Algebraic Ops Menu EXIT

  16. 3b = 2a ALGEBRAIC OPERATIONS: Question 2 Express as a single fraction in its simplest form. What would you like to do now? Try another like this Go to full solution Go to Comments Go to Algebraic Ops Menu EXIT

  17. Question 2 15b2 4a3 2a2 x 5b 30a2b2 3b = = 20a3b 2a 1. Multiply top line then bottom line. Express as a single fraction in its simplest form. 3 b 2 a 2. Cancel numbers then letters in alphabetical order. Begin Solution Try another like this What would you like to do now? Comments Menu Back to Home

  18. Comments ac = bd 15b2 4a3 2a2 x 5b 30a2b2 3b = = 20a3b 2a a x c b d To multiply fractions use the result: 1. Multiply top line then bottom line. 3 b 2 a 2. Cancel numbers then letters in alphabetical order. Next Comment Menu Back to Home

  19. Comments 15b2 4a3 2a2 3b 2a 30a2b2 20a3b x = = 5b 30a2b2 3b = = 2a 20a3b To simplify final answer write out in full and cancel: 1. Multiply top line then bottom line. 30.a.a.b.b 20.a.a.a.b 3 b 2 a 2. Cancel numbers then letters in alphabetical order. Try another Menu Back to Home

  20. ALGEBRAIC OPERATIONS: Question 2B Express as a single fraction in its simplest form. What would you like to do now? Get hint Reveal answer only Go to full solution Go to Comments Go to Algebraic Ops Menu EXIT

  21. ALGEBRAIC OPERATIONS: Question 2B To divide by a fraction : turn it upside down and multiply. Express as a single fraction in its simplest form. Multiply top line then bottom line. Cancel numbers then letters in alphabetical order. What would you like to do now? Reveal answer only Go to full solution Go to Comments Go to Algebraic Ops Menu EXIT

  22. vw2 = 3 ALGEBRAIC OPERATIONS: Question 2B Express as a single fraction in its simplest form. What would you like to do now? Go to full solution Go to Comments Go to Algebraic Ops Menu EXIT

  23. Question 2B w3 = 6v 2v2 2v2  x w w w3 6v vw2 2v2w3 = = 3 6vw • To divide by a fraction : turn it upside down and multiply. Express as a single fraction in its simplest form. 2. Multiply top line then bottom line. v 1 w2 3 Begin Solution 3. Cancel numbers then letters in alphabetical order. Continue Solution Comments Menu What would you like to do now? Back to Home

  24. Comments w3 = 6v 2v2 2v2 ad  x = = w w bc w3 6v 2v2w3 vw2 = = 3 6vw a a x ÷ d c b b d c To divide fractions use the result: • To divide by a fraction : turn it upside down and multiply. 2. Multiply top line then bottom line. v 1 w2 3 3. Cancel numbers then letters in alphabetical order. Next Comment Menu Back to Home

  25. Comments w3 = 6v 2v2 2v2 2v2w3 6vw  x = w w w3 6v 2.v.v.w.w.w 6.v.w vw2 vw2 2v2w3 = = = 6vw 3 3 To simplify final answer write out in full and cancel: • To divide by a fraction : turn it upside down and multiply. 2. Multiply top line then bottom line. v 1 w2 3 3. Cancel numbers then letters in alphabetical order. Next Comment Menu Back to Home

  26. ALGEBRAIC OPERATIONS: Question 3 Simplify What would you like to do now? Get hint Reveal answer only Go to full solution Go to Comments Go to Algebraic Ops Menu EXIT

  27. ALGEBRAIC OPERATIONS: Question 3 Deal with numbers and then apply laws of indices: when dividing subtract the powers. Simplify Remember subtracting negative is like adding. What would you like to do now? Reveal answer only Go to full solution Go to Comments Go to Algebraic Ops Menu EXIT

  28. ALGEBRAIC OPERATIONS: Question 3 = 3d2 Simplify What would you like to do now? Try another like this Go to full solution Go to Comments Go to Algebraic Ops Menu EXIT

  29. Question 3 1. Deal with numbers and then apply laws of indices: when dividing subtract the powers. Simplify . 24d5/4  8d–3/4 = 3d5/4-(–3/4) 2. Remember subtracting negative is like adding. = 3d8/4 = 3d2 Begin Solution Try another like this Comments Menu Back to Home

  30. Comments Learn Laws of Indices: 1. Deal with numbers and then apply laws of indices: when dividing subtract the powers. 24d5/4  8d–3/4 e.g. = 3d5/4-(–3/4) 2. Remember subtracting negative is like adding. = 3d8/4 = 3d2 Try another Menu Back to Home

  31. ALGEBRAIC OPERATIONS: Question 3B Simplify What would you like to do now? Get hint Reveal answer only Go to full solution Go to Comments Go to Algebraic Ops Menu EXIT

  32. ALGEBRAIC OPERATIONS: Question 3B Deal with top row first. Apply laws of indices: when dividing subtract the powers & when multiplying add powers. Simplify Now divide remembering subtracting negative is like adding. What would you like to do now? Reveal answer only Go to full solution Go to Comments Go to Algebraic Ops Menu EXIT

  33. ALGEBRAIC OPERATIONS: Question 3B Simplify = a3 What would you like to do now? Go to full solution Go to Comments Go to Algebraic Ops Menu EXIT

  34. Question 3B = a3/3 = a5/3 –2/3 a-2 a-2 a5/3 x a–2/3 a-2 1. Deal with top row first. Apply laws of indices: when dividing subtract the powers & when multiplying add powers. Simplify . 2. Now divide remembering subtracting negative is like adding. Begin Solution = a1-(-2) Continue Solution Comments = a3 Menu Back to Home

  35. Comments = a5/3 –2/3 = a3/3 a-2 a-2 a5/3 x a–2/3 a-2 Learn Laws of Indices: 1. Deal with top row first. Apply laws of indices: when dividing subtract the powers & when multiplying add powers. e.g. 2. Now divide remembering subtracting negative is like adding. Next Comment = a1-(-2) Menu = a3 Back to Home

  36. Comments = a5/3 –2/3 = a3/3 a-2 a-2 a5/3 x a–2/3 a-2 Learn Laws of Indices: 1. Deal with top row first. Apply laws of indices: when dividing subtract the powers & when multiplying add powers. e.g. 2. Now divide remembering subtracting negative is like adding. Next Comment = a1-(-2) Menu = a3 Back to Home

  37. ALGEBRAIC OPERATIONS: Question 4 Simplify giving your answer with positive indices. What would you like to do now? Get hint Reveal answer only Go to full solution Go to Comments Go to Algebraic Ops Menu EXIT

  38. ALGEBRAIC OPERATIONS: Question 4 Deal with numbers and then apply laws of indices: when dividing subtract the powers. Simplify giving your answer with positive indices. Remember subtracting negative is like adding. What would you like to do now? Reveal answer only Go to full solution Go to Comments Go to Algebraic Ops Menu EXIT

  39. = m2 + 1 m ALGEBRAIC OPERATIONS: Question 4 Simplify giving your answer with positive indices. What would you like to do now? Try another like this Go to full solution Go to Comments Go to Algebraic Ops Menu EXIT

  40. Question 4 = m2 + 1 m 1. Multiply out brackets remembering to apply laws of indices: when multiplying add the powers. Simplify giving your answer with positive indices. m1/3( m5/3 + m-4/3 ) = m6/3 + m-3/3 = m2 + m-1 2. Negative powers become positive on bottom line. Begin Solution Try another like this What would you like to do now? Comments Menu Back to Home

  41. Comments = m2 + 1 m Learn Laws of Indices: 1. Multiply out brackets remembering to apply laws of indices: when multiplying add the powers. m1/3( m5/3 + m-4/3 ) = m6/3 + m-3/3 e.g. = m2 + m-1 2. Negative powers become positive on bottom line. Try another Menu Back to Home

  42. ALGEBRAIC OPERATIONS: Question 4B Simplify giving your answer without indices. What would you like to do now? Get hint Reveal answer only Go to full solution Go to Comments Go to Algebraic Ops Menu EXIT

  43. ALGEBRAIC OPERATIONS: Question 4B Multiply out brackets remembering to apply laws of indices: when multiplying add the powers. Simplify giving your answer without indices. Zero power is 1 and ½ power is square root. What would you like to do now? Reveal answer only Go to full solution Go to Comments Go to Algebraic Ops Menu EXIT

  44. ALGEBRAIC OPERATIONS: Question 4B = 1 - w Simplify giving your answer without indices. What would you like to do now? Go to full solution Go to Comments Go to Algebraic Ops Menu EXIT

  45. Question 4B 1. Multiply out brackets remembering to apply laws of indices: when multiplying add the powers. Simplify giving your answer without indices. w-1/4( w1/4 - w3/4 ) = w-1/4+1/4 - w-1/4+3/4 = w0 - w1/2 2. Zero power is 1 and ½ power is square root. = 1 - w Begin Solution Continue Solution Comments Menu Back to Home

  46. Comments Learn Laws of Indices: 1. Multiply out brackets remembering to apply laws of indices: when multiplying add the powers. w-1/4( w1/4 - w3/4 ) = w-1/4+1/4 - w-1/4+3/4 = w0 - w1/2 e.g. 2. Zero power is 1 and ½ power is square root. = 1 - w Next Comment Menu Back to Home

  47. ALGEBRAIC OPERATIONS: Question 5 Evaluate 7c3/4 when c = 16 What would you like to do now? Get hint Reveal answer only Go to full solution Go to Comments Go to Algebraic Ops Menu EXIT

  48. ALGEBRAIC OPERATIONS: Question 5 Evaluate 7c3/4 when c = 16 Deal with indices first. Power ¾ is 4th root cubed. Evaluate root before power What would you like to do now? Reveal answer only Go to full solution Go to Comments Go to Algebraic Ops Menu EXIT

  49. = 56 ALGEBRAIC OPERATIONS: Question 5 Evaluate 7c3/4 when c = 16 What would you like to do now? Try another like this Go to full solution Go to Comments Go to Algebraic Ops Menu EXIT

  50. Question 5 = 56 • Deal with indices first. Power ¾ is 4th root cubed. Evaluate 7c3/4 when c = 16 c3/4 = (4c)3 = (416)3 = (2)3 = 8 So 7c3/4 = 7 x 8 Begin Solution Try another like this Comments What would you like to do now? Menu Back to Home

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