Question Bank
Exam-style questions with the answer most students get wrong, the correct working step by step, and how to avoid the trap.
18 questions
When a Line Misses a Curve: Getting the Range of k the Right Way Round
The line never meets the curve, so the discriminant is negative. The critical values are easy; choosing between them or outside them is where marks go.
Try the question →Trig Equations: When sin x Is Negative, Where Are the Two Angles?
Solving sin x = −2/3 for 0° to 360°? The calculator gives −41.8°, and many students answer 41.8° and 138.2°. Here's how to find the right two angles.
Try the question →Enlargement and Area: Why You Multiply by k², Not k
A triangle is enlarged with scale factor 2.5. Its area does not go up 2.5 times. See why the area factor is k² and find the shaded area correctly.
Try the question →Half-Life With a Background Count: Subtract It First
The detector reads 660 counts/min and the background is 20. Halve the 660 and the answer is wrong. Here's how to correct for background radiation.
Try the question →Arithmetic Progressions: Counting the Terms Without Losing One
Finding the sum of all multiples of 8 between 150 and 450? Dividing the gap by 8 gives one term too few. Here's the reliable way to count.
Try the question →Conservation of Momentum: When Objects Move in Opposite Directions
Two skaters moving towards each other collide and hold on. Adding their momenta without a sign gives the wrong speed and force. Here's how to get both right.
Try the question →Rates of Change in a Cone: Why the Radius Isn't a Constant
Water filling a cone: treat the radius as fixed and your rate comes out three times too big. Write V in terms of h first, then differentiate.
Try the question →Probability Without Replacement: One of Each Colour Can Happen Two Ways
Picking two items without replacement and asked for one of each? Multiplying one pair of branches gives only half the answer. Here's why.
Try the question →Area of a Segment: Is Your Calculator in Radian Mode?
Finding a segment with an angle in radians? In degree mode, sin 1.2 gives a segment almost as big as the sector. Here's how to catch it.
Try the question →Specific Heat Capacity: Why the Time Must Be in Seconds
A heater runs for 6 minutes. Put 6 into E = Pt and your specific heat capacity comes out 60 times too small. Here's the full working.
Try the question →What Is the Acceleration at the Top of a Throw?
A ball thrown upwards stops for an instant at its highest point. Is its acceleration zero there? Many students say yes, and that's a trap.
Try the question →Area Under a Curve: When Part of It Is Below the x-Axis
Integrating y = x² − 3x from 0 to 4 in one go gives the wrong area. Split the integral where the curve crosses the x-axis.
Try the question →Solve x² = 5x: Why Dividing by x Loses an Answer
Most students answer x = 5 and lose a mark. The trap is dividing both sides by x, which throws away the root x = 0.
Try the question →Inverse Square Variation: Why a 50% Increase Isn't a 50% Decrease
If I varies inversely as d² and d goes up by 50%, I does not fall by 50%. Work out the multiplier properly to get the 55.6% decrease.
Try the question →Log Equations: The Answer You Must Reject
Solving log₂ x + log₂(x − 2) = 3 gives two values of x, but only one is allowed. Here's the trap and how to check.
Try the question →Refractive Index: Measure the Angles From the Normal
Using the angles with the surface in n = sin i divided by sin r gives a refractive index below 1. Measure both angles from the normal to get it right.
Try the question →Resistors in Parallel: The Step Students Forget
A 6 Ω and a 3 Ω resistor in parallel. Most students answer 9 Ω or 0.5 Ω. Here is why both are wrong and how to get 2 Ω every time.
Try the question →Speed–Time Graphs: Why You Can't Just Average the Two Speeds
Averaging the speeds on a speed–time graph gives the wrong average speed. Use total distance divided by total time, with the distance from the area.
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