Solution:
(24 + 5)/8 + [ ] = (64 + 3)/16
29/8 + [ ] = 67/16
[ ] = 67/16 – 29/8
[ ] = 67/16 – 58/16
[ ] = 9/16
Therefore, the missing number is 9/16.
Question 2
Adam thinks of a number. He divides this number by 13 and then adds 23. His answer is 32. What was his original number?
Solution:
Let the original number be x.
x/13 + 23 = 32
x/13 = 32 – 23
x/13 = 9
x = 9 x 13
x = 117
Therefore, his original number was 117.
Question 3
Find the area of this shape:
Solution:
The shape is made up of a rectangle and a triangle.
Area of rectangle = length x breadth = 10 x 4 = 40 m²
Height of triangle = 12m – 4 m = 8 m
Area of triangle = 1/2 x base x height = 1/2 x 10 x 8 = 40 m²
Total area = 40 + 40 = 80 m²
Therefore, the total area of the shape is 80 m².
Question 4
50 children are going on a school trip. The trip costs £4.75 including lunch. However the students may pay only £3.25 and bring their own packet lunch if they wish. The total cost of the trip is £207.5. How many of the students took a packed lunch?
Solution:
Let x be the number of students who took a packed lunch.
Number of students who bought lunch = 50 – x
Total cost = 4.75 x (50 – x) + 3.25 x
207.5 = 4.75 x (50 – x) + 3.25 x
207.5 = 237.5 – 4.75 x + 3.25 x
207.5 = 237.5 – 1.5 x
1.5 x = 30
x = 20
Therefore, 20 students took a packed lunch.
Question 5
Find the value of x.
5 – 3x = 3x + 11
Solution:
5 – 3x = 3x + 11
5 – 11 = 3x + 3x
-6 = 6x
x = -1
Therefore, the value of x is -1.
Bonus Questions
11plus Daily Free Practice Paper
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