LemonmathSelf-study sheet

Grade 12 · Lesson 7.1

The exam format and how to tackle it

Name: Date: Time spent: min

Goals

Describe the three parts of the graduation maths exam and how each part is marked.
Work out the mark of a paper, especially the mark of a true/false question.
Plan the 90 minutes and choose a sensible order of work.
Round and write a short answer in the 4 boxes correctly.

Exercises

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. $1$ .

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.

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?

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. $x=2$ .

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

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.

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 $P(B)$ .

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?

Mini test

15 minutes, without looking back at the lesson. Part I: circle one letter; Part II: write T or F for each statement; Part III: write the answer in the box.

Part I. Multiple choice

Question 1. The greatest possible mark for Part II is

4

.B.

1

.C.

3

.D.

2

Question 2. The minimum value of

y=x^2-4x+5

[0, 3]

1

.B.

2

.C.

5

.D.

0

Question 3. The result of a short-answer question is

\dfrac73

, to be given to 1 decimal place. You write

2.3

.B.

2.4

.C.

2.33

.D.

2

Question 4. The integral

\displaystyle\int_0^1 3x^2\,dx

equals

1

.B.

3

.C.

6

.D.

-1

Part II. True or false

Question 1. In Part II, a student judges

4

3

1

0

statements correctly in the four questions.

a) The student gets $1$ mark for the first question.	T / F
b) The student gets $0.75$ for the second question.	T / F
c) The student gets $0.1$ for the third question.	T / F
d) The student's total for Part II is $1.6$ .	T / F

Part III. Short answer

Question 1. A student gets

11

questions right in Part I, exactly

3

statements right in every Part II question, and

3

questions right in Part III. What is the student's mark?

Question 2. Find

\displaystyle\int_0^1 e^x\,dx

. Give your answer to 2 decimal places.

Score: ........ / 10

Hints (only when stuck)

Exercise 1.

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.

Exercise 2.

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.

Exercise 3.

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.

Exercise 4.

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 $x\to+\infty$ .

Exercise 5.

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.

Exercise 6.

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 $t^3+2t$ .

Exercise 7.

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.

Exercise 8.

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 $4$ .

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