## 2018 Grade 9 Math Challenge Elimination Level Questions – Part 1

This is the 2018 Grade 9 Math Challenge Elimination Level Questions – Part 1 with answers. Questions in the previous years can be accessed on the Past Tests page and all questions can be found in the All Posts page.

1.) Find the value of k that will make $x^2 + 16x + k$ a perfect square.

2.) A number and its reciprocal have a sum of $\dfrac {34}{15}.$ Find the smaller of these two numbers.

3.) Solve for x in $9x^2 - 10 = 6.$

4.) Solve for x in $(x^2 - 4)^2 - 2(x^2 - 4) = 15.$

5.) Solve the inequality $x^2 + 2x - 15 \geq 0$ for x.

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## 2015 Grade 9 Math Challenge Elimination Level Questions – Part 2

This is the 2015 Grade 9 Math Challenge Elimination Level Questions – Set 2. Answers and solutions will be posted later. Questions in the previous years can be accessed on the Past Tests page and all questions can be found in the All Posts page.

Instruction: Write your answer on the space provided before each item. Give all fractions in lowest terms, and all equations of lines in the form ax + by = c where a, b and c are relatively prime integers, with a > 0.

26.) If 4 men can paint a house in 5 days, in how many days can 10 men paint the same house?

27.) If y is proportional to the cube x and x is proportional to the fourth power z, then y is proportional to which power of z?

28.) Running at uniform speed in a race, Allan can beat Ben by 20 m, Ben can beat Carlo by 10 m and Allan can beat Carlo by 28 m. How long is the race?

29.) Find the measure of the vertex angle of an isosceles triangle whose base angles measure 65°.

30.) Find x if the angles of a quadrilateral measure $x^\circ, (2x + 10)^\circ, (3x + 20)^\circ$ and $(4x - 30)^\circ.$

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## 2015 Grade 9 Math Challenge Elimination Level Questions – Part 1

This is the 2015 Grade 9 Math Challenge Elimination Level Questions – Set 1. Answers and solutions will be posted later. Questions in the previous years can be accessed on the Past Tests page and all questions can be found in the All Posts page.

Instruction: Write your answer on the space provided before each item. Give all fractions in lowest terms, and all equations of lines in the form ax + by = c where a, b and c are relatively prime integers, with a > 0.

1.) Simplify: $\sqrt{\dfrac{3}{2}} = \sqrt{\dfrac{2}{3}}$

2.) Evaluate: $\dfrac{20^0 + 2^{-1}}{2^{-2} + 2^{-3}}$

3.) Simplify: $\sqrt{\dfrac{1}{9} + \dfrac{1}{16}}$

4.) Simplify: $\dfrac{x^{-1} - y^{-1}}{x^{1/3} - y^{1/3}}$

5.) If a, b and c are real numbers such that $\dfrac{b}{a} = 5$ and $\dfrac{b}{c} = 2,$ what is the value of $\dfrac{a + b}{b + c}?$

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## Mock MTAP Math Challenge Year 4 Questions – Set 1

This is the 2018 Mock MTAP Math Challenge Year 4 questions – Individual Written Competition Set 1. Answers and solutions will be posted later. Questions in the previous years can be accessed on the Past Tests page and all questions can be found in the All Posts page.

Part I. Solve each problem and write the answer on the answer sheet provided. Give lines as ax + by + c = 0. Leave answers in simplifi ed radicals and use base 10 unless otherwise stated. [2 points each]

1.) Find the vertex of the parabola $y = 2x^2 - 8x - 5.$

2.) What is the remainder when $3x^3 - 5x^2 + x - 2$ is divided by $x - 2?$

3.) Find the domain of $f(x) = log \sqrt{3x^2 - 5x + 2}.$

4.) Determine all real numbers x such that $|5x - 6| \leq 7.$

5.) In right triangle ABC with $\angle C = 90^{\circ}$ AB = 15 cm and AC = 12 cm. Find the length of the altitude to AB.

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## 2017 Grade 8 Math Challenge Sectoral Level (Questions with answer)

This is the 2017 MTAP Grade 8 Math Challenge questions Sectoral Level. Questions in the previous years can be accessed on the Past Tests page and all questions can be found in the All Posts page

Easy

1.) If $f(x) = \dfrac {9x^2 - 25}{3x - 5},$ compute $f(-6)$.

2.) If the volume of a cube is 20% more than its surface area, what is the side length of the cube?

3.) How many digits does the quotient $\dfrac {2.5 \times 10^{-4}}{5 \times 10^{-2}}$ have?

4.) What is the cube root of $6.4 \ times 10^{-8}$?

5.) If two dice are rolled, what is the probability that the product of the two numbers that come out is even?

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