Thinking Skills Assessment (TSA) Problem Solving (Section 1) Flashcards

24 sample cards from the Problem Solving (Section 1) deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. What is the "working backwards from a target" technique?

   Start from the known final state/value and reverse each operation in turn to recover the earlier states or the unknown starting value. Each forward operation is undone by its inverse.

2. If a number is doubled, then $5$ is added, giving $23$, how do you work backwards to the original?

   Reverse in opposite order: subtract $5$ ($23-5=18$), then halve ($18/2=9$). Original $=9$. In general undo $+5$ with $-5$ and undo $\times 2$ with $\div 2$.

3. What does "recognising shared structure" mean in problem solving?

   Identifying that two superficially different problems have the same underlying logical or mathematical form, so the same solution method applies to both.

4. How is "reasoning by analogy" used to solve a new TSA problem?

   Map the elements of the new problem onto a previously solved problem with the same relational structure, transfer the solution method, then translate the result back into the new problem's terms.

5. What is a risk when reasoning by analogy, and how is it avoided?

   A false analogy: the surface similarity may hide a structural difference. Verify that every relevant relation/constraint corresponds between the two problems before transferring the method.

6. What are "equivalent representations of data" in TSA?

   Different formats that encode the same information, e.g., a table, a bar chart, a pie chart, a list, or an equation. The skill is converting between them and recognising that they convey identical underlying values.

7. How do you convert a fraction of a total into a pie-chart angle?

   Multiply the fraction by $360^{\circ}$: angle $=\dfrac{\text{part}}{\text{whole}}\times 360^{\circ}$. For example a category that is $\tfrac14$ of the total occupies $90^{\circ}$.

8. How do you convert a category's value into its percentage of the whole for a chart?

   Percentage $=\dfrac{\text{category value}}{\text{total of all categories}}\times 100$.

9. What is "pattern equivalence in figures"?

   Recognising that two figures represent the same pattern despite transformations such as rotation, reflection, or translation, i.e., they are congruent up to those operations.

10. Which transformations preserve the equivalence (congruence) of a figure?

    Rotation, reflection (mirror), and translation preserve shape and size, so the figure remains equivalent. Scaling changes size (similar, not congruent); shearing distorts the shape.

11. How do you distinguish a rotation from a reflection of a figure?

    A rotation preserves the handedness/orientation order of features (clockwise stays clockwise); a reflection reverses handedness, producing a mirror image that cannot be obtained by rotation alone in the plane.

12. Give the order of operations to evaluate an arithmetic expression under time pressure.

    Use BIDMAS/BODMAS: Brackets, Indices (powers/roots), Division and Multiplication (left to right), then Addition and Subtraction (left to right).

13. What is a fast mental method to find $15\%$ of a quantity?

    Find $10\%$ (divide by $10$) and $5\%$ (half of the $10\%$), then add them: $15\%=10\%+5\%$. E.g. $15\%$ of $80=8+4=12$.

14. How do you quickly multiply a number by $25$ under time pressure?

    Multiply by $100$ and divide by $4$, since $25=\dfrac{100}{4}$. E.g. $36\times 25=\dfrac{3600}{4}=900$.

15. How do you compute average speed for a journey?

    $\text{average speed}=\dfrac{\text{total distance}}{\text{total time}}$. It is not the simple mean of speeds unless equal times are spent at each speed.

16. When interpreting a line graph, how do you read off the rate of change between two points?

    The rate of change equals the gradient: $\dfrac{\Delta y}{\Delta x}=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$, the change in the vertical quantity divided by the change in the horizontal quantity.

17. What common chart features must you check before reading values, to avoid errors?

    The axis scales and units, whether an axis starts at zero (a truncated axis exaggerates differences), the legend/key, and whether values are cumulative or per-interval.

18. On a cumulative frequency graph, how do you estimate the median?

    Find the value on the horizontal axis corresponding to the cumulative frequency equal to half the total, i.e., read across from $\dfrac{n}{2}$ on the vertical axis to the curve and down to the data axis.

19. What is spatial visualisation in the context of TSA problem solving?

    Mentally manipulating 2D or 3D shapes—folding nets, rotating solids, stacking cubes—to predict the result without physically moving them.

20. When a 2D net is folded into a cube, how do you find which faces end up opposite each other?

    On a cube, opposite faces are never adjacent in the net. Faces separated by exactly one face in a straight row of the net, or those that fold away from each other, become opposite; adjacent net faces become adjacent (sharing an edge).

21. How many small cubes form the surface vs interior of an $n\times n\times n$ cube?

    Interior (no painted faces) $=(n-2)^{3}$; surface cubes $=n^{3}-(n-2)^{3}$. For example, with $n=3$: interior $=1$, surface $=26$.

22. What is the general approach to a logical deduction puzzle (e.g., who-owns-what grids)?

    List all categories and possibilities, then apply each clue to a grid, marking forced eliminations and confirmations. Use the process of elimination iteratively until each item is uniquely determined.

23. In logic puzzles, how do you use the rule that each category value maps one-to-one?

    Once an item is confirmed for one entity, eliminate that item for all other entities and eliminate other items for that entity (a single mark in a row/column clears the rest), propagating constraints.

24. What is the difference between a valid deduction and a mere assumption in a logic puzzle?

    A valid deduction follows necessarily from the given clues with no alternatives; an assumption introduces information not entailed by the clues. Only deductions guarantee a correct, defensible answer.

What this deck covers

Problem Solving (Section 1) flashcards FAQ