The exam format and how to tackle it

Two students each get $8$ true/false statements right in Part II. Hà gets all $4$ statements right in two questions and none in the other two. Nam gets $2$ statements right in each of the four questions. Who scores more?

The answer lies in how Part II is marked, and it directly affects how you should work. This lesson describes the format of the specimen papers published by the Ministry of Education and Training from 2025, and the habits that stop you losing marks needlessly. The Ministry may adjust the format or the marking from year to year, so check its official announcement for your exam year.

Format and marking

The paper has three parts, lasts $90$ minutes, and is marked out of $10$ .

Part	Question type	Questions	Mark each	Total
I	Multiple choice (A, B, C, D)	$12$	$0.25$	$3$
II	True/false, each with $4$ statements a), b), c), d)	$4$	up to $1$	$4$
III	Short answer	$6$	$0.5$	$3$

Note The mark for a true/false question

In one Part II question, the number of statements you judge correctly decides the mark:

Correct statements	$0$	$1$	$2$	$3$	$4$
Mark	$0$	$0.1$	$0.25$	$0.5$	$1$

The mark rises steeply at the last statement: going from $3$ to $4$ correct doubles the mark. So every statement is worth checking carefully.

Back to the opening question: Hà scores $1+1=2$ , while Nam scores $4\cdot0.25=1$ . The same $8$ correct statements, but Hà scores twice as much.

Part I: multiple choice

Each question has exactly one correct option and wrong answers lose nothing. So never leave a question blank. Part I questions are usually short and test one formula or one step.

Three quick methods:

Solve directly, then match with the options.
Work backwards: put each option into the condition of the question (for example, differentiate an option to check an antiderivative).
Eliminate: wrong options usually come from a familiar mistake (wrong sign, missing coefficient, wrong formula). Spotting the mistake lets you rule them out quickly.

Part II: true or false

Each question gives a common setting (a function, a figure, a data table) followed by four statements. Later statements are usually harder.

Example A true/false question on a function

Let $f(x)=x^3-3x+2$ . a) $f'(x)=3x^2-3$ . b) The function is increasing on $(-1, 1)$ . c) The local maximum value of the function is $4$ . d) The equation $f(x)=0$ has three distinct roots.

Solution. We first work out the derivative and the values we need: $f'(x)=3(x-1)(x+1)$ , $f(-1)=4$ , $f(1)=0$ .

a) True: the derivative of $x^3$ is $3x^2$ , and of $-3x$ is $-3$ .

b) False: for $-1<x<1$ , $f'(x)<0$ , so the function is decreasing on $(-1, 1)$ .

c) True: $f'$ changes from $+$ to $-$ at $x=-1$ , and the local maximum value is $f(-1)=-1+3+2=4$ .

d) False: factorising, $f(x)=(x-1)^2(x+2)$ , so the equation has only two distinct roots, $x=1$ and $x=-2$ .

Key: T F T F.

Part III: short answers and the 4 boxes

Each answer is one number, written on the sheet in $4$ boxes. The minus sign and the decimal comma each take a box (the Vietnamese sheet uses a comma, not a point, as the decimal separator).

Writing the answer

-0.5

in 4 boxes

For example, $\dfrac{7}{4}=1.75$ is written 1,75 (all $4$ boxes); $-\dfrac{2}{3}$ to 1 decimal place is $-0.7$ (all $4$ boxes).

Time plan and checking

$90$ minutes for $22$ questions is tight. A suggested plan:

Task	Suggested time
Part I ( $12$ questions)	about $20$ – $25$ minutes
Part II ( $4$ questions)	about $25$ – $30$ minutes
Part III ( $6$ questions)	about $25$ – $30$ minutes
Checking, filling in the sheet	about $5$ – $10$ minutes

Work in order of difficulty, not necessarily in question order: on a first pass do every question you are sure of, mark the hard ones, then come back. Do not spend more than $5$ minutes on one Part I question.

Use your scientific calculator to check: evaluate a function at given points, compute definite integrals, solve quadratic and cubic equations. The calculator catches slips, but you still need reasoning to know what to compute.

Key terms

English	Tiếng Việt
multiple-choice question	trắc nghiệm nhiều phương án lựa chọn
true/false question	trắc nghiệm đúng/sai
short-answer question	trắc nghiệm trả lời ngắn
statement (claim)	ý (của câu đúng/sai)
distractor	phương án nhiễu
round to 1 decimal place	làm tròn đến hàng phần mười
round to 2 decimal places	làm tròn đến hàng phần trăm
answer sheet	phiếu trả lời
scientific calculator	máy tính cầm tay

Exercises

Each exercise comes with what you need and some steps to start. Try it yourself first, then open the solution.

Exercise 1 Multiple choice

In one true/false question you judge $3$ statements correctly. What mark do you get for that question? A. $0.5$ . B. $0.75$ . C. $0.25$ . D. $1$ .

What you need and how to start

What you need: the Part II scale: $1$ , $2$ , $3$ , $4$ correct statements give $0.1$ , $0.25$ , $0.5$ , $1$ .

Steps:

Read off the mark for $3$ correct statements.

Show solution

By the scale, $3$ correct statements give $0.5$ . Option B is the mistake $3\cdot0.25$ .

Answer. A.

Exercise 2 Written answer

Bình gets $9$ questions right in Part I; in Part II, $4$ , $4$ , $2$ , $1$ statements right; in Part III, $3$ questions right. Find Bình's mark.

What you need and how to start

What you need: Part I $0.25$ per question; Part II by the scale; Part III $0.5$ per question.

Steps:

Work out each part.
Add the three parts.

Show solution

Part I: $9\cdot0.25=2.25$ . Part II: $1+1+0.25+0.1=2.35$ . Part III: $3\cdot0.5=1.5$ .

Answer. $2.25+2.35+1.5=6.1$ .

Exercise 3 Short answer

A short-answer question asks for 1 decimal place, and the exact result is $-\dfrac{2}{3}$ . What do you write in the 4 boxes? Why does the question not ask for 2 decimal places?

What you need and how to start

What you need: the minus sign and the comma each take a box.

Steps:

Work out $-\dfrac23\approx-0.667$ and round to 1 decimal place.
Count the characters if rounded to 2 decimal places.

Show solution

$-\dfrac23\approx-0.667$ , which to 1 decimal place is $-0.7$ : four characters "−", "0", ",", "7". To 2 decimal places it would be $-0.67$ , which needs $5$ boxes and cannot be written.

Answer. $-0.7$ .

Exercise 4 Multiple choice

The horizontal asymptote of the graph of $y=\dfrac{2x+1}{x-1}$ is A. $y=2$ . B. $x=1$ . C. $y=-1$ . D. $x=2$ .

What you need and how to start

What you need: a horizontal asymptote has the form $y=b$ with $b=\lim\limits_{x\to\pm\infty}y$ .

Steps:

Rule out the options of the form $x=\dots$ straight away.
Find the limit as $x\to+\infty$ .

Show solution

Options B and D are vertical lines, so they are ruled out. $\lim\limits_{x\to\pm\infty}\dfrac{2x+1}{x-1}=2$ . Option C takes the ratio of the constant terms $\dfrac{1}{-1}$ .

Answer. A.

Exercise 5 True/False

Given $\displaystyle\int_0^2 f(x)\,dx=3$ and $\displaystyle\int_0^2 g(x)\,dx=-1$ .

a) $\displaystyle\int_0^2\left[f(x)+g(x)\right]dx=2$ .

b) $\displaystyle\int_0^2 2f(x)\,dx=6$ .

c) $\displaystyle\int_2^0 g(x)\,dx=1$ .

d) $\displaystyle\int_0^2 f(x)g(x)\,dx=-3$ .

What you need and how to start

What you need: the integral of a sum is the sum of the integrals; a constant factor comes outside; swapping the limits changes the sign. There is no rule for the integral of a product.

Steps:

Judge each statement with exactly one property.

Show solution

a) True: $3+(-1)=2$ .

b) True: $2\cdot3=6$ .

c) True: swapping the limits changes the sign, $-(-1)=1$ .

d) False: the integral of a product is not the product of the integrals. For instance $f(x)=\dfrac32$ and $g(x)=-x+\dfrac12$ satisfy the conditions, but $\displaystyle\int_0^2 f(x)g(x)\,dx=-\dfrac32$ .

Answer. a) True; b) True; c) True; d) False.

Exercise 6 Short answer

A car moves with velocity $v(t)=3t^2+2$ (m/s), with $t$ in seconds. Find the distance it travels in the first $3$ seconds, in metres.

What you need and how to start

What you need: the distance is the integral of the velocity when $v(t)\ge0$ .

Steps:

Write $s=\displaystyle\int_0^3(3t^2+2)\,dt$ .
Use the antiderivative $t^3+2t$ .

Show solution

$s=\int_0^3(3t^2+2)\,dt=\Big[t^3+2t\Big]_0^3=27+6=33.$

Answer. $33$ .

Exercise 7 Short answer

Two events $A$ , $B$ have $P(A)=0.4$ , $P(B\mid A)=0.3$ and $P(B\mid\overline{A})=0.5$ . Find $P(B)$ .

What you need and how to start

What you need: the law of total probability $P(B)=P(A)P(B\mid A)+P(\overline A)P(B\mid\overline A)$ .

Steps:

Find $P(\overline A)=1-0.4$ .
Substitute into the formula.

Show solution

$P(B)=0.4\cdot0.3+0.6\cdot0.5=0.12+0.3=0.42.$

Answer. $0.42$ .

Exercise 8 Challenge

Minh plans the $90$ -minute paper: the last $5$ minutes for checking, $2$ minutes for each Part I question and $5$ minutes for each Part III question. The remaining time is shared equally among the $4$ Part II questions. How many minutes does each Part II question get?

What you need and how to start

What you need: Part I has $12$ questions and Part III has $6$ .

Steps:

Work out the time for Parts I and III.
Subtract everything from $90$ and divide by $4$ .

Show solution

Part I: $12\cdot2=24$ minutes; Part III: $6\cdot5=30$ minutes. That leaves $90-5-24-30=31$ minutes for Part II, so $\dfrac{31}{4}=7.75$ minutes per question.

Answer. $7.75$ minutes (about $7$ minutes $45$ seconds).

Format and marking

Part I: multiple choice

Part II: true or false

Part III: short answers and the 4 boxes

Time plan and checking

Key terms

Exercises

Mini test

Part I. Multiple choice

Part II. True or false

Part III. Short answer

a) The student gets $1$ mark for the first question.	True	False
b) The student gets $0.75$ for the second question.	True	False
c) The student gets $0.1$ for the third question.	True	False
d) The student's total for Part II is $1.6$ .	True	False