# FREE IB Mathematics Questions and Answers

#### Since Paul expects 9% returns, how long will it take for his $37,353 investment to double?

Use the Rule of 72 to mentally compute the result.

72 divided by the growth rate. In this case, Paul's wealth would increase by twofold in eight years (72/9). An easy method for estimating how long it would take for an investment to double in value is the rule of 72.

#### The town of Homeville saw an increase in population last year of about 0.5%. What was the approximate population at the end of the year if there were 2,460 people living there at the start of the year?

You must determine the difference of 2,460 in a percentage of a half. To perform this mentally, first calculate 1 percent of the starting value, then divide that by 2. 1% of 2,460 in this instance equals 24.6, and half of that is 12.3. We may calculate the population increase as 12 individuals since you cannot have 3/10 of a person. The new population is 2,472 when that is added to the initial 2,460.

#### Theoretically, an observation is characterized as having a weight equal to _____ to its variance (standard error squared).

Theoretically, an observation's weight is defined as having an inverse relationship to its variance. Accordingly, the observation should be given more weight because it will be more exact and precise with a reduced observation error.

#### A car that usually costs $29,600 has been reduced to $22,100. What is the estimated discount percentage?

First, calculate the dollar value of the markdown: 29,600 – 22,100 = 7,500. The result is 0.2533 when you divide the total reduction of $7,500 by the original price of $29,600. To find out that the markdown is somewhat more than 25%, move the decimal point two places to the right.

#### A whole deck of playing cards without jokers is used to draw one card for each round of the game. The gambler doubles his bet if the card is a club or a queen. If not, the dealer keeps the cash. How much better in this game are the odds for the dealer?

In a game where the dealer keeps the gambler's bet if he draws any card other than a club or queen, his chances of winning the money are 38% better than the gambler's. A deck of cards has 52 cards, with 13 cards in each suit, including clubs. Each deck has four queens, but since the queen of clubs has already been tallied, the gambler's list of winning cards only includes the queens of hearts, diamonds, and spades. The gambler's odds of winning are 31% because he must draw one of the 16 cards to succeed. If his odds are 31%, the gambler has far better odds of 69%, which is an improvement of 38%.

#### 12 softballs may be produced by Jane's Softball Production Company in one hour. How many softballs can they make in a day and a half?

168 softballs. Although this is not a difficult problem and could be calculated mentally, perhaps by multiplying 14 by 10 (140), then adding 2 more 12s to the answer.

However, there is a trick that allows you to multiply numbers close to ten together within seconds.

First, consider the problem: 14 x 12

Using the 2 in 12, add it to 14: 16 (these are the first two digits of the answer).

Using the 2 in 12, multiply it by the 4 in 14: 8 (this is the last digit of the answer).

Thus, the answer to 14 x 12 is 168.

It works for larger numbers in the teens, but those involve “carrying”.

Consider the problem: 17 x 14.

Using the 4 in 14, add it to 17: 21

Using the 4 in 14, multiply it by the 7 in 17 (28). The 8 is the last digit of the answer. Carry the 2 over, and add it to the 21 from the previous step to get 23.

The answer to 17 x 14 is 238.

#### Over the previous week, sales for Seven/Twelve have totaled $4 million. What were the daily sales on average?

$571,000. $4 million divided by 7 days is an average of $571,429 per day.

#### How many minutes does it take a car traveling at 200 km/h to cover 60 km?

The quickest way to do this problem is to divde 60 by 200.

You can quickly reduce that to 3/10. Then multiply 3/10 by 60 to get 18 minutes.

#### Miller's Auto Shop generated $460,000 in gross sales the previous year. Their gross sales climbed astonishingly this year by 25%. How much money was made this year in total?

To find 25% of a given number, simply halve the number, then halve it again. In this example, half of 460,000 is 230,000, then half of 230,000 is 115,000. Therefore, 25% of $460,000 is $115,000. Add $115,000 to the original $460,000 to find the gross revenue for the year - $575,000.

#### What is the greatest approach to bear in mind when coming up with answers to market-sizing questions?

The ability to estimate and round figures is essential for answering inquiries as fast as feasible.

Take some time to carefully select your numbers before coming up with your solution. Choose rounded numbers that go well together and will make your math much easier.

#### Which of the following right angle trigonometric functions is incorrect?

Secant cannot be equal to 1/sine, as stated. Secant is equal to 1/cosine, where cosine is the hypotenuse or neighboring side of a right triangle.