Math 9 · Unit 9: Sequences and functions · Cambridge Lower Secondary Maths Stage 9

Questions

1. 1. Complete the outputs for this function machine. Put a number in each empty box.

   Fill the blanks with these.

   • 25
   • 8
   • 10
   • 16
   Check

2. 2. Complete the outputs for this function machine. Put a number in each empty box.

   Fill the blanks with these.

   • 12
   • 64
   • 16
   • 125
   Check

3. 3. Complete the table of values for each function machine. Put a number in each empty cell.

   Fill the blanks with these.

   • 8
   • 10
   • 15
   • 16
   • 25
   • 125
   • 64
   • 4
   Check

4. 4. Question 1 used a squaring machine and a cubing machine with inputs 2, 4 and 5. Question 2a uses the same two machines with x = 2, 4 and 5. What do you notice about your answers to 2a compared with Question 1?

   • They are all smaller than the outputs in Question 1.
   • They are the same as the outputs in Question 1.
   • They are double the outputs in Question 1.
   • There is no link between them.
   Check

5. 5. Complete the equation for each function in part a. Put the power in each empty box.

   Fill the blanks with these.

   • 1
   • 4
   • 2
   • 3
   Check

6. 6. These mapping diagrams are for the functions in part a: i y = x² and ii y = x³. Each shows the arrow from x = 2. Where do the arrows from x = 4 and x = 5 go?

   • i 4 → 16 and 5 → 25; ii 4 → 16 and 5 → 25
   • i 4 → 8 and 5 → 10; ii 4 → 12 and 5 → 15
   • i 4 → 64 and 5 → 125; ii 4 → 16 and 5 → 25
   • i 4 → 16 and 5 → 25; ii 4 → 64 and 5 → 125
   Check

7. 7. Complete the table of values for each two-step function machine. Put a number in each empty cell.

   Fill the blanks with these.

   • 65
   • 64
   • 36
   • 37
   • 998
   • 25
   Check

8. 8. Complete the equation for each function in part a: i y = x□ + □ and ii y = x□ − □.

   • i y = x² + 1; ii y = x³ + 2
   • i y = x² + 1; ii y = x³ − 2
   • i y = (x + 1)²; ii y = (x − 2)³
   • i y = 2x + 1; ii y = 3x − 2
   Check

9. 9. Complete the table of values for each two-step function machine. What are the y-values, in order, for the three machines?

   • i −16, 4, 36; ii −9, 81, 144; iii 0, 9, 25
   • i −8, 4, 12; ii 3, 27, 48; iii 0, 9, 15
   • i 16, 4, 36; ii 9, 81, 144; iii 0, 27, 125
   • i 64, 16, 144; ii 3, 27, 48; iii 0, 9, 65
   Check

10. 10. Complete the equation for each function in part a.

    • i y = 4x²; ii y = (3x)²; iii y = (x + 1)³
    • i y = (4x)²; ii y = 3x²; iii y = x³ + 1
    • i y = (4x)²; ii y = (3x)²; iii y = x³ + 1
    • i y = x² + 4; ii y = 3x²; iii y = (x + 1)³
    Check

11. 11. Complete the table of values for each two-step function machine. What are the y-values, in order, for the three machines?

    • i 36, 16, 64; ii 14, 9, 5¼; iii −9½, −2, 1
    • i 36, 16, 64; ii 14, 9, 5¼; iii −27½, −⅝, −⅜
    • i −6, −4, 8; ii 14, 9, 5¼; iii −27½, −⅝, −⅜
    • i 36, 16, 64; ii 4, 49, 30¼; iii −27½, −⅝, −⅜
    Check

12. 12. Write each function in part a as an equation.

    • i y = x² − 4; ii y = (x + 5)²; iii y = (x − ½)³
    • i y = (x − 4)²; ii y = x² + 5; iii y = x³ − ½
    • i y = x² − 4; ii y = x² + 5; iii y = (x − ½)³
    • i y = (x − 4)²; ii y = (x + 5)²; iii y = x³ − ½
    Check

13. 13. Which step comes first in the function machine for y = (2x)²?

    • either step
    • squaring
    • multiplying by 2
    • adding 2
    Check

14. 14. For y = (2x)², what are the y-values when x = 1/8, 1/4, 1/2 and 2?

    • 1/4, 1/2, 1, 4
    • 1/32, 1/8, 1/2, 8
    • 1/16, 1/4, 1, 16
    • 1/64, 1/16, 1/4, 4
    Check

15. 15. Work out the missing values in the tables. The missing x-values are all negative. What are the missing values, reading the empty cells from left to right?

    • i 2, −4, −18, −10; ii 64, −3, −144, −7
    • i 2, −4, 18, −10; ii 64, −3, 144, −7
    • i 2, −4, 18, −10; ii 64, −3, 144, 1
    • i 2, 4, 18, 10; ii 64, 3, 144, 7
    Check

16. 16. Write each function in part a as an equation.

    • i y = (x ÷ 2)²; ii y = (x + 3)²
    • i y = x² ÷ 2; ii y = x² + 3
    • i y = (x ÷ 2)²; ii y = x² + 3
    • i y = x² ÷ 2; ii y = (x + 3)²
    Check

17. 17. Sofia and Zara each make a conjecture about their function machine. Is Zara correct?

    • Yes
    • No
    Check

18. 18. How can you check that a reverse equation is correct?

    • Make sure the answer is positive.
    • Put an output back in and see if you get the original input.
    • Check that it has the same numbers as the first equation.
    • Square both sides.
    Check

19. 19. What is the equation and its reverse equation for this function machine?

    • y = x⁴ and x = y⁴
    • y = 4x and x = y/4
    • y = x⁴ and x = ⁴√y
    • y = x + 4 and x = y − 4
    Check

20. 20. What is the equation and its reverse equation for this function machine?

    • y = x + 5 and x = y − 5
    • y = x⁵ and x = y/5
    • y = x⁵ and x = ⁵√y
    • y = 5x and x = y/5
    Check