## 2018 Grade 10 Math Challenge Questions 26-50 (with PDF)

This is the 2018 MTAP Grade 10 Math Challenge questions 26 to 30. Questions 1-25 including can be found here. The pdf can be downloaded here. Solutions and answer will be posted later. More reviewers can be found on the Past Tests and All Posts pages.

Questions

26.) Find the radius of the circle with equation $x^2 + y^2 + 4x - 3y + 5 = 0$.

27.) Give the equation (in center-radius form) of the circle having as a diameter the segment with endpoints $(-2, 10)$ and $(4, 2)$.

28.) The center of a circle is on the x-axis. If the circle passes through $(0,5)$ and $(6,4)$, find the coordinates of its center.

29.) If $\theta$ is an angle in a triangle and $\sec \theta = \frac{7}{5}$, find $\tan \theta$Continue reading

## 2018 Grade 10 Math Challenge Questions 1-25

This is the 2018 MTAP Grade 10 Math Challenge questions 1 to 25. Questions  26 to 50 (including the pdf of Questions 1-50) can be found here. Solutions and answers will be posted later. More reviewers can be found on the Past Tests and All Posts pages.

Questions

1.) The average of a number and $\sqrt{7} + \sqrt{5}$ is $\sqrt{7} - \sqrt{5}$. Find the number.

2.) Find $n$ if $27.63%$ of $349$ is \$latex  2.763%4 of $n$.

3.) Simplify: $\dfrac{101!}{99!}$.

4.) If $3^n = 90$, find the integer closest to $n$.

5.) Find the largest positive integer $n$ such that $(n - 18)^{4036} \leq 99^{2018}.$

6.) How many integers between 60 and 600(inclusive) are divisible by 2 or by 3?  Continue reading

## 2015 Grade 10 MTAP Sectoral Level

This is the 2015 Metrobank-MTAP-NCR Math Challenge Sectoral Level for  Grade 10. Please inform me if you see any errors.

More past tests can be found here. If you have old tests, kindly send it to mtapreviewers@gmail.com, so we can share it here with answers/solutions.

Easy

1.) What is the next term in the arithmetic sequence whose first two terms are −18 and then 19?

2.) Express $-3 + \log_2 x + 3 \log_2 y$ as a single logarithm with base $2$.

3.) What should be the value of $c$ if the point where $f(x) = -x^2 + 2x + c$ attains its maximum, is also a zero of $f$?

4.) What is the reciprocal of $\sqrt{9}- 2$ in simplest terms?

5.) If $\log_x25 = 4$, what is $\log_25x$Continue reading

## 2015 Grade 9 MTAP Sectoral Level

This is the 2015 Metrobank-MTAP-NCR Math Challenge Sectoral Level for  Grade 9. Please inform me if you see any errors.

More past tests can be found here. If you have old tests, kindly send it to mtapreviewers@gmail.com, so we can share it here with answers/solutions.

Easy

1.) If $\displaystyle \frac {x}{y} = 2$, find $\frac {x^2 - y^2}{x^2 + y^2}$.

2.) In a cube with sides of length 1 cm, one vertex is denoted by A. What is the sum of the distances from A to each of the other vertices of the cube?

3.) Find two positive numbers in the ratio 7:12 so that the bigger number exceeds the smaller by 10.

## 2016 MTAP Elimination Questions with Solutions

I am happy to announce that I have acquired a copy of the 2016 MTAP Elimination Questions with complete solutions for Grade 7, 8, 9, and 10.