Algebra 3b: Mastery Questions
Guidance Notes - To answer each question, click on the letter that corresponds to the correct answer. You then need to click the 'Check' button to see if you are correct. If your answer is incorrect, you will be given a hint on how to get the correct answer. You then need to click the 'Try again' button to attempt the question once more.
1. Which of these tables shows that y is directly proportonal to x?

  A  
  B  
  C  
  D  
    
2. In the following table, y is directly proportional to x. What is the constant of proportionality?

  x  
  2.5  
  5  
  10  
  20  
y
7.5
15
30
60

  A  
  B  
  C  
  D  
2
3
5
10
    
3. If y is directly proportional to x, which of these statements could not be true?

  A  
  B  
  C  
  D  
yx = 5
xy = 7
y6 = x
4y = x
    
4. Which of these graphs shows that y is directly proportonal to x?

  A  
  B  
  C  
  D  
    
5. Which of these points lies on the graph of y = 2.5x ?

  A  
  B  
  C  
  D  
(2.5, 1)
  (5, 2)  
(3, 7.5)
(7.5, 3)
    
6. If you were asked to plot the the graph of y = 4x for -3 ≤ x ≤ 3 on a pair of suitable axes, which of these would be the correct range of values for y?

  A  
-3 ≤ y ≤ 3
   B  
-6 ≤ y ≤ 6
  C  
-9 ≤ y ≤ 9
  D  
-12 ≤ y ≤ 12
    
7. If you were asked to plot the line y = 5x - 3 which of these points would not lie on the line?

  A  
  B  
  C  
  D  
 (2, 7) 
(3, 12)
(6, 32)
(8, 37)
    
8.
 
The axes opposite have two different graphs. You are given one of the equations. What is the eqaution of the other graph?

  A  
y = x − 3
   B  
y = 2x − 3
  C  
y = -2x + 3
  D  
y = -2x − 3
    
9.

Mrs Pearson pays one rate for 100 units of electricity she uses and a diferent rate for any additonal units used as shown by the graph above
How much must she pay for using 900 units of electricity?

  A  
  B  
  C  
  D  
£180
£100
£126
£116
    
10. Will is n years old. Layla is 3 years older than Will. Luke is twice as old as Layla. The total of their ages is 61. Work out the age of each person.
Which of these equatons can be used to solve this queston?

  A  
  B  
  C  
  D  
3n + 3 = 61
4n + 3 = 61
4n + 6 = 61
4n + 9 = 61
    
11. Look at this function machine. Which of these equations does it represent?

n →   × 4    →   − 2    →   × 3   → 78

  A  
3(4n − 2) = 78
   B  
4(3n − 2) = 78
  C  
4n − 6 = 78
  D  
4n − 2 × 3 = 78
    

12.
This function machine represents the equation 
7n − 2
 + 8 = 32
4

n →         →         →         →        → 32

Which operation belongs in the third box?

  A  
  B  
  C  
  D  
× 7
÷ 4
+ 8
− 2
    
13. Which option gives you the correct method for solving this equation?

5n − 6 = 74

  A  
Add 6, divide by 5
  B  
Divide by 5, add 6
  C  
Add 6, multiply by 5
  D  
Subtract 6, divide by 5
    
14. Which option gives you the correct method for solving this equation?

a
 − 3 = 15
4

  A  
Subtract 3, divide by 4
  B  
Add 3, divide by 4
  C  
Multiply by 4, add 3
  D  
Add 3, multiply by 4
    
15. Solve the equation 5(x − 2) + 6 = 31.

  A  
  B  
  C  
  D  
x = 4
x = 5
x = 6
x = 7
    

16.
Solve the equation 
x + 3
 − 1 = 3
3

  A  
  B  
  C  
  D  
x = 3
x = 6
x = 9
x = 12
    
17. Which option is correct in making x the subject of the formula y = 7x + 4?

  A  
Subtract 4, divide by 7
  B  
Divide by 7, subtract 4
  C  
Multiply by 7, subtract 4
  D  
Subtract 4, multiply by 7
    
18. Which option is correct in making a the subject of the formula v = u + at?

  A  
Divide by t, subtract u
  B  
Divide by u, subtract t
  C  
Subtract u, divide by t
  D  
Subtract u, divide by a
    
19. Expand 3(2x − 5)

  A  
  B  
  C  
  D  
5x − 8
6x − 8
6x − 15
6x − 5
    
20. Expand and simplify 4y − 2(y − 3)

  A  
  B  
  C  
  D  
2y − 6
2y + 6
3y − 6
3y + 6
    
21. Expand and simplify 3(5a − 2) + (a − 4)

  A  
  B  
  C  
  D  
9a − 10
16a − 6
18a − 18
16a − 10
    
22. Factorise 5x + 20

  A  
  B  
  C  
  D  
5(x + 4)
5(x + 20)
  25x  
5 + x + 20
    
23. Factorise fully 24y − 72

  A  
  B  
  C  
  D  
8(3y − 9)
3(8y − 24)
12(2y− 6)
24(y − 3)
    
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