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Converting between Fractions, Decimals and Percentages
1 ticket
A student claims that 0.125, 12.5%, and 1/8 are all equivalent. Is the student correct? Justify your answer by converting between all three forms and explaining your reasoning.
Context: Auto-generated from Flow tool
Difference of Two Squares
1 ticket
A student claims that 4x² - 9y⁴ can be factored as (2x - 3y²)(2x + 3y²), but also claims that 16 - 25x⁶ can be factored as (4 - 5x³)(4 - 5x³). Are both factorizations correct? Explain why or why not, and identify any errors in the student's reasoning.
Context: Auto-generated from Flow tool
Direct and Inverse Proportion
1 ticket
A factory produces widgets using two machines. Machine A takes 4 hours to produce 100 widgets working alone. When Machine A and Machine B work together, they take 3 hours to produce 180 widgets. If the number of widgets produced is directly proportional to the number of hours worked, and the machines work at constant rates:
(a) How long would Machine B take to produce 100 widgets working alone?
(b) If Machine A breaks down and only Machine B is available, how many widgets would Machine B produce in 6 hours?
Context: Auto-generated from Flow tool
Exchange Rates and Currency Conversions
1 ticket
Sarah is traveling from the UK to Japan. She exchanges £150 to Japanese Yen when the exchange rate is £1 = ¥160. In Japan, she spends ¥18,400. When she returns to the UK, she exchanges her remaining Yen back to Pounds, but the exchange rate has changed to £1 = ¥155. How many Pounds does Sarah have left after converting her remaining Yen back to Pounds?
Context: Auto-generated from Flow tool
Expanding two brackets
1 ticket
Expand and simplify (2x - 3)(x² + 4x - 1). Explain why the final answer contains an x³ term but no x² term.
Context: Auto-generated from Flow tool
Multiplying decimals
1 ticket
A rectangular garden measures 2.5 meters by 3.8 meters. Calculate the area of the garden. Then, explain why your answer makes sense by comparing it to what the area would be if the garden measured 3 meters by 4 meters instead.
Context: Auto-generated from Flow tool
Probability tree diagrams
1 ticket
A bag contains 3 red marbles and 2 blue marbles. Two marbles are drawn from the bag without replacement. Using a probability tree diagram, find the probability that the two marbles are different colors. Show your work and explain why you multiply or add probabilities at each stage.
Context: Auto-generated from Flow tool
Product of prime factors
1 ticket
A number is expressed as 2² × 3 × 5³. Without calculating the actual number, explain whether it is divisible by 8, 9, 15, and 25. Justify your reasoning for each case using the prime factorisation.
Pythagoras' Theorem
1 ticket
A right-angled triangle has sides of length 6 cm and 8 cm. Is the hypotenuse necessarily 10 cm? Explain your reasoning with a diagram or calculation.
Context: Auto-generated from Flow tool
Simultaneous equations
1 ticket
Solve the simultaneous equations using the substitution method: y = 2x - 3 and 3x + 2y = 16. Explain why you chose to substitute one particular equation into the other, and what would happen if you made the opposite substitution choice.
Context: Focus on substitution method
completing the square
1 ticket
A student is asked to complete the square for the quadratic expression x² + 6x + 10. They write: x² + 6x + 10 = (x + 3)² + 1. Is their answer correct? Explain your reasoning by showing the correct method and identifying any errors in their working.
Context: Auto-generated from Flow tool
laws of indices
1 ticket
Simplify the expression (2x³y²)⁴ ÷ (4x²y⁵)² and explain why your answer cannot contain negative exponents.
Context: Auto-generated from Flow tool
multiplying fractio9ns
1 ticket
A recipe requires 2/3 cup of flour to make 12 cookies. If you want to make 3/4 of the recipe, how much flour will you need? Explain your reasoning.
quadratic equations
1 ticket
A student is solving the quadratic equation x² - 5x + 6 = 0. They correctly factor it as (x - 2)(x - 3) = 0, but then write the solutions as x = -2 and x = -3. Explain what misconception the student has, and show the correct method to find the solutions.
Context: Auto-generated from Flow tool
test
1 ticket
A student claims that when you multiply two negative numbers, the result is always negative. Is this correct? Explain your reasoning using a real-world example or mathematical principle.
Context: Auto-generated from Flow tool
the quadratic formula
1 ticket
A student solves the quadratic equation 2x² - 8x + 8 = 0 using the quadratic formula and gets x = 2. Another student says this is incorrect because quadratic equations should have two solutions. Who is right? Explain your reasoning using the quadratic formula and what it reveals about this specific equation.
Context: Auto-generated from Flow tool