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

## 1. | GCSE Higher |

(a) Solve 9m < 15m − 12

(b) On the number line below, show the set of values of \(x\) for which \( -4 \le x-1 \lt 5 \)

## 2. | GCSE Higher |

The graph of a quadratic function, \(y=f(x)\) is shown drawn accurately in the following diagram. Write down all the integer solutions of \(f(x) \le 0\).

## 3. | GCSE Higher |

The diagram below is a sketch of \(y = f(x)\) where \(f(x)\) is a quadratic function.

The graph intersects the x-axis where \(x=-2\) and \(x = 0.5\).

Which of the following is the solution of \(f(x) \le 0\) ?

- (a) \( x \ge -2 \) or \(x \ge 0.5\)
- (b) \( -2 \ge x \ge 0.5\)
- (c) \( x \ge -2 \) and \( x \le 0.5\)
- (d) \( x \le -2 \) and \( x \ge 0.5\)

## 4. | GCSE Higher |

Describe the unshaded (white) region by writing down three inequalities.

## 5. | GCSE Higher |

On the grid below indicate the region that satisfies all three of these inequalities.

$$y>-2$$ $$x+y<5$$ $$y-1 \le \frac{x}{2}$$## 6. | GCSE Higher |

A region on a coordinate grid is described by the following three inequalities:

$$x>-2$$ $$x+y<7$$ $$y \ge \frac{x}{3}+2$$By shading the **unwanted** regions show the region on the grid below.

## 7. | GCSE Higher |

By shading the unwanted regions, show the region satisfied by these three inequalities.

$$ y \le x + 3 $$ $$ y> 4-x $$ $$ x < 2.5 $$## 8. | GCSE Higher |

Solve the following inequalities then explain how the whole number solutions to A and B different.

$$A: 5 \le 5x \lt 30$$ $$B: 5 \lt 5x \le 30$$## 9. | GCSE Higher |

A region on a coordinate grid is described by the following three inequalities:

$$-8 \le x \le 6$$ $$2y \ge x + 1$$ $$2y+x \le 12$$(a) By shading the **unwanted** regions show the region on the grid below.

(b) Mr Mushnik says that the point with coordinates (-8, 10) does not satisfy all the inequalities because it does not lie in the region. Is Mr Mushnik correct? You must give a reason for your answer.

## 10. | GCSE Higher |

Show that you understand equations and inequalities by answering the following:

(a) Solve \(5x^2=80\)

(b) Solve \(8x + 2 \gt x + 7\)

(c) Write down the largest integer that satisfies \(8x - 2 \lt 25\)

(d) Solve the following pair of equations

$$3x + 5y = 21$$ $$8x - 5y = 1$$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.

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