Show model answer and explanation
7
3x=21.
University admission · Other / specialist pathway · Mathematics
Mathematics for the chosen programme
Apply functions, algebra and probability with explicit conditions.
About this lesson and its coverage
Original Model Test for Exam unit. These questions and suggested practice times are independent Kidemy material, not an official or past paper. Choose modules for the target programme; all listed subjects are not required for every applicant.
Learn the idea
Check domain restrictions before cancelling or taking logarithms. A root solves an equation; not every algebraic manipulation preserves equivalence at excluded inputs. Probability calculations require a clear outcome set and assumptions about independence.
Worked example
For x≠1, (x²−1)/(x−1)=x+1. The simplified expression has a value at 1, but the original fraction does not. The restriction must remain.
- State restrictions.
- Show a valid transformation.
- Check candidate solutions in the original problem.
Your written practice
Show your working on paper. Check your answer, then choose Next.
Show model answer and explanation
2
10²=100.
Show model answer and explanation
1/3
Two of six equally likely outcomes: 5 or 6.
Write in your own words. A guardian or teacher should review this response.
Show model answer and explanation
At x=1, the denominator is zero, so cancellation does not restore the original domain.
Keep the restriction after simplifying.
Write in your own words. A guardian or teacher should review this response.
Show model answer and explanation
3x²+2 gives the local rate of change of the function with respect to x.
Differentiate both terms and define rate.
Progress and browser storage
Notebook challenge, sources and further study
Mathematics model test
Solve the tasks and verify a result by substitution or a second method.
Review with a guardian or teacher
- Keep domains.
- Show working.
- Explain probability assumptions.
Keep your work on paper or in a local file. This page does not upload it or automatically grade the project.
Teacher-led lessons, schedules and prices for this outline are upcoming. You can use any starter practice above now without booking.
Your next step
Solo practice works without an account. Sign in to save a practice record to your learner profile.
Keep practising
Exact lesson links and related activities are labelled separately. Return-to-course links retain your selected learning path.