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IB Maths: Functions and Graphs – Practice Paper 4 (10 Questions)
IB Maths: Functions and Graphs – Practice Paper 4 (10 Questions)
Paper 4 is a mixed review of the chapter: function notation and substitution, domain and range, vertex and completing the square, composite and inverse functions, and solving backwards from a function value.
Quick answer Ten items, about twenty-five minutes. Items 01 to 04 cover substitution, squaring, completing the square and a domain; items 05 to 07 cover composites, an inverse and a range; items 08 and 09 are an equation and a minimum; item 10 redoes the missing equality in a root domain.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 questions |
| Suggested time | 25 minutes |
| Difficulty mix | Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1 |
| Chapter | Chapter: IB Maths: Functions and Graphs – Tutor Lesson Plan |
| Level | IB SL |
02 Questions (10 items)
- FoundationGiven f of x equals two x minus five, find f of four.
- FoundationGiven g of x equals x squared plus one, find g of minus two.
- FoundationFind the vertex of f of x equals x squared minus six x plus five.
- FoundationFind the domain of f of x equals one over x plus two.
- IntermediateWith f of x equals three x plus two and g of x equals x squared minus one, find f of g of two.
- IntermediateWith f of x equals x cubed minus two, find the inverse function and its value at six.
- IntermediateFor y equals x minus one squared plus three, find the range.
- ChallengeWith f of x equals two x plus one and g of x equals x minus three, solve f of g of x equals eleven.
- ChallengeFor f of x equals x squared minus four x plus one, find the minimum and the x that gives it.
- Error redoA student answers x greater than five for the domain of the square root of x minus five. Give the correct answer.
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | f of four is three | Substitute four: two times four minus five is three. |
| 2 | g of minus two is five | Square first: minus two squared is four, then add one. |
| 3 | the vertex is three comma minus four | Completing the square gives x minus three squared minus four, so the vertex is three, minus four. |
| 4 | all real numbers except minus two | The denominator cannot be zero, so x plus two must not be zero. |
| 5 | f of g of two is eleven | First g of two is three, then f of three is eleven. |
| 6 | the inverse is the cube root of x plus two, and it gives two at six | Rearranging gives the cube root of y plus two, and eight has cube root two. |
| 7 | y is at least three | The square is never negative, so the smallest value is three. |
| 8 | x is eight | Substituting gives two times x minus three plus one equals eleven, so x is eight. |
| 9 | the minimum is minus three at x equals two | Completing the square gives x minus two squared minus three, which is smallest when the square is zero. |
| 10 | x is at least five | The expression under the root may equal zero, so five is included. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.
