Problem Solving — Drills
Problem Solving has 6 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 6 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Net — A 3-D shape unfolded flat.
- Vertex — A flat surface; a line where two faces meet; a corner point.
- Perfect square — A number that is some whole number squared: 1, 4, 9, 16, 25, …
- Diagonal — A segment joining two non-adjacent vertices.
- Adjacent — The side next to that angle which is not the hypotenuse.
- Height — The perpendicular distance from the base to the opposite corner.
Working backwards
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A number is multiplied by 4, then 10 is added, giving 30. Find the number.
Worked answer
5
30 - 10 = 20
20 ÷ 4 = 5
Check: 5 × 4 + 10 = 30 ✓
Problem 2
A number is multiplied by 3, then 2 is added, giving 29. Find the number.
Worked answer
9
29 - 2 = 27
27 ÷ 3 = 9
Check: 9 × 3 + 2 = 29 ✓
Pattern
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
What comes next in 3, 6, 12, 24, …?
Worked answer
48
Each term is 2 times the one before
24 × 2 = 48
Problem 2
What comes next in 6, 14, 22, 30, …?
Worked answer
38
It grows by 8
30 + 8 = 38
Counting
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
You have 5 shirts and 6 pairs of trousers. How many different outfits?
Worked answer
30
5 × 6 = 30
Problem 2
You have 6 shirts and 5 pairs of trousers. How many different outfits?
Worked answer
30
6 × 5 = 30
Simpler
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
How many diagonals does a polygon with 14 sides have?
Worked answer
77
Each vertex gives 14 - 3 = 11 diagonals
14 × 11 = 154, counting each twice
154 ÷ 2 = 77
Problem 2
At a gathering of 6 people, everyone shakes hands with everyone else once. How many handshakes?
Worked answer
15
Each of 6 shakes 5 hands: 30
Each handshake was counted twice
30 ÷ 2 = 15
Guesscheck
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Adult tickets cost $12 and child tickets $5. 19 tickets sold for $151. How many adults?
Worked answer
8
All 19 as children: $95
We need $151, which is $56 more
Each swap adds 12 - 5 = 7
56 ÷ 7 = 8 adults
Problem 2
Adult tickets cost $8 and child tickets $5. 27 tickets sold for $153. How many adults?
Worked answer
6
All 27 as children: $135
We need $153, which is $18 more
Each swap adds 8 - 5 = 3
18 ÷ 3 = 6 adults
Consecutive
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Two consecutive whole numbers add to 51. What is the smaller one?
Worked answer
25
2n + 1 = 51
n = 25
They are 25 and 26.
Problem 2
Two consecutive whole numbers add to 71. What is the smaller one?
Worked answer
35
2n + 1 = 71
n = 35
They are 35 and 36.