Exam-Style Questions on Inequalities

Problems on Inequalities adapted from questions set in 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

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

3.

GCSE Higher

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

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

4.

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.

5.

GCSE Higher

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

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

6.

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

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

7.

GCSE Higher

John times how long it takes him to run around Hazelnut Park each Friday afternoon. The last three weeks his times, rounded to the nearest minute are $$p, q \; \text{and} \; r$$.

He notices that $$q$$ is 5% more than $$p$$ and $$r$$ is 5% less than $$q$$.

Indicate which of the following statements are true:

(a) $$r \lt p$$ and $$r \lt q$$

(b) $$r \gt p$$ and $$r \gt q$$

(c) $$r = p$$ and $$r \lt q$$

(d) $$p \gt q$$ and $$p = r$$

(e) $$p =q$$ and $$p \gt r$$

8.

GCSE Higher

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

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

Search for exam-style questions containing a particular word or phrase:

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

Kausar Begum Khan, Kenya

Friday, January 26, 2018

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

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."

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."

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.

For Students:

For All: