## Exam-Style Questions.## Problems adapted from questions set for previous Mathematics exams. |

## 1. | IB Standard |

Find the value of the following:

(a) \(log_464\);

(b) \(log_7\frac17\);

(c) \(log_{25}5\);

(d) Use the solutions to the previous parts of this question to help solve:

$$log_464+log_7\frac17-log_{25}5=log_4x$$## 2. | IB Standard |

Evaluate the following, giving your answers as integers.

(a) \(\log _5 25\)

(b) \(\log _6 3 + \log _6 12\)

(c) \(\log _2 12 - \log _2 6\)

## 3. | IB Standard |

Find the value of

(a) \(\log _4 2 + \log _4 8\)

(b) \(\log_2 60-\log_2 15\)

(c) \(27^{\log_3 4}\)

## 4. | IB Standard |

(a) Solve \(4x^2 - 8x - 5 = 0\)

(b) Hence solve \(4 \times 25^x - 8 \times 5^x = 5\)

## 5. | IB Standard |

Part of the graph of \(f(x) = {\log _b}(x + 4)\) for \(x > - 4\) is shown below.

The graph passes through A(4, 3) , has an x-intercept at (-3, 0) and has an asymptote at \(x = - 4\).

(a) Find the value of \(b\).The graph of \(f(x)\) is reflected in the line \(y = x\) to give the graph of \(g(x)\).

(b) Write down the y-intercept of the graph of \(g(x)\).

(c) Sketch the graph of \(g(x)\), noting clearly any asymptotes and the image of A.

(d) Find \(g(x)\) in terms of \(x\).

## 6. | IB Standard |

An arithmetic sequence has \(u_1 = \log_h(j)\) and \(u_2 = \log_h(jk)\), where \(h > 1\) and \(j, k \gt 0\).

(a) Show that the common difference, \(d = \log_h(k)\).

(b) Let \(j = h^5\) and \(k = h^7\). Find the value of \( \sum_{n=1}^{16} u_n \).

## 7. | IB Standard |

Consider the function \(f (x) = \log_p(24x - 18x^2)\) , for \(0 \lt x \lt 1\), where \(p \gt 0\).

The equation \(f (x) = 3\) has exactly one solution. Find the value of \(p\).

If you would like space on the right of the question to write out the solution try this Thinning Feature. It will collapse the text into the left half of your screen but large diagrams will remain unchanged.

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

The solutions to the questions on this website are only available to those who have a Transum Subscription.

Exam-Style Questions Main Page

To search the **entire Transum website** use the search box in the grey area below.

Do you have any comments about these exam-style questions? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.