Senior Secondary (HKDSE) · Mathematics

More about equations: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on More about equations.

10 questions28 marksFree, no account

Question 1

1 mark

Solve the equation $$6(x + 1) = -2x + 14$$.

Question 2

1 mark

Solve the equation \( 3^{2x+2} - 10 \cdot 3^x + 1 = 0 \).

Question 3

1 mark

Solve the fractional equation:
$$\frac{2x}{x-1} - \frac{1}{x+1} = \frac{4}{x^2-1}$$

Question 4

1 mark

Solve the equation \(2 \cos^2 \theta + \cos \theta - 1 = 0\) for \(0^\circ \le \theta \le 180^\circ\).

Question 5

1 mark

Solve the equation \( 2^{2x+2} - 5 \cdot 2^x + 1 = 0 \).

Question 6

4 marks

Solve the equation \(25^x - 6 \cdot 5^x + 5 = 0\).

Write your answer out first, then check it against the worked solution.

Question 7

5 marks

Solve the fractional equation $$\frac{1}{x-3} + \frac{2}{x+4} = 2$$.

Write your answer out first, then check it against the worked solution.

Question 8

5 marks

Solve the fractional equation $$\frac{4}{x+3} + \frac{1}{x-2} = 1$$.

Write your answer out first, then check it against the worked solution.

Question 9

4 marks

The sum of a non-zero real number \( x \) and twice its reciprocal is \( 3.3 \).

(a) Form an equation in \( x \) to represent the above information and show that it can be transformed into \( 10x^2 - 33x + 20 = 0 \).
(b) Solve the equation in (a) to find the possible values of \( x \).

Write your answer out first, then check it against the worked solution.

Question 10

5 marks

Solve the equation $$ \log_3 (x+4) + \log_3 (x-2) = \log_3 7 $$ for real values of $$x$$.

Write your answer out first, then check it against the worked solution.

* The content provided by thinka is generated by AI and may not always be accurate or up-to-date. Please use it as a supplementary resource and verify with official materials.

You've seen the model answer. Now get yours marked.

This page can show you how a good answer looks. It cannot tell you what your answer was missing. thinka marks your written work against the real mark scheme in about 15 seconds.

Get My Answers Marked Back to the notes

Want more questions like these? Get a fresh set on this topic, marked as you go.