 # Exam-Style Questions.

## Problems adapted from questions set for previous Mathematics exams.

### 1.

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 $$f(x) \le 0$$. ### 2.

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 $$x \ge 0.5$$

### 3.

GCSE Higher

Describe the unshaded (white) region by writing down three inequalities. ### 4.

GCSE Higher

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

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

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. ### 6.

GCSE Higher

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

$$y \le x + 3$$ $$y> 4-x$$ $$x < 2.5$$ ### 7.

GCSE Higher

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

$$A: 5 \le 5x \lt 30$$ $$B: 5 \lt 5x \le 30$$

### 8.

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

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

### 9.

GCSE Higher

Solve $$2x^2 + 7x - 15 <0$$

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