## Exam-Style Questions on Simultaneous Equations## Problems on Simultaneous Equations adapted from questions set in previous Mathematics exams. |

## 3. | GCSE Higher |

A rectangular sheet of paper can be cut into two identical rectangular pieces in two different ways, either by cutting along line A or by cutting along line B.

When the original sheet of paper is cut along line A, the perimeter of each of the two pieces is 56 cm.

When the original sheet of paper is cut along line B, the perimeter of each of the two pieces is 64 cm.

What is the perimeter of the original sheet of paper?

## 4. | GCSE Higher |

Two numbers are chosen so that the sum of their squares is 25.

If those numbers are represented by \(x\) and \(y\) they will also satisfy the equation:

$$y-3x=13$$Use an algebraic method to find two possible values of \(x\) and \(y\) .

## 5. | GCSE Higher |

The prices of two watches are in the ratio \(a:b\).

When the prices are both increased by £10, the ratio becomes \(5 : 7\).

When the prices are both reduced by £10, the ratio becomes \(1 : 3\).

Express the ratio \(a:b\) in its lowest terms.

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? 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.

Kausar Begum Khan, Kenya

Friday, January 26, 2018

"This is a fabulous website! I cannot thank you enough."

Aruna Upadhyayula, Bahrain

Tuesday, November 6, 2018

"Transum is so resourceful. The resources are so child-friendly that my students love its usage.It has a wide range of topics and caters to most of my needs. 'Thankyou" will be too small a word to express my gratitude to the content developers of this site."

Ahmed Jaja, Ghana

Thursday, November 22, 2018

"It was very useful for me.I recommend it to every math student.Thank you."

Madiwa Otieno, Kenya

Tuesday, February 5, 2019

"A very great site.Nice questions."

Yuli, Woodmansterne

Tuesday, April 2, 2019

"This website is amazing it helps me with my maths to get good marks in my upcoming test. Thanks."