This is the 2014 MTAP Grade 8 Math Challenge questions 1 to 25 with answer key. More reviewers can be found on the **Past Tests** and **All Posts** pages.

1.) Simplify: 1 – 2 +3 – 4 + … + 49 – 50 + 49 – 48 + 47 – 46 + … + 1

2.) Simplify:

3.) In the proportion , what is *x*?

4.) Between what two consecutive integers does lie?

5.) What is the area of a rectangle whose sides are twice as long as the sides of a smaller rectangle whose area is

6.) What is the medium of the following numbers:

7.) Let *U* = {1, 2, 3, …, 12} be the universal set, and *A* = {10, 11, 12}, *B* = {1, 3, 5, 7, 9, 11}, and *C* = {4, 5, … ,11}. What is

8.) With the same sets given in Item 7, what is

9.) With the same sets given in Item 7, how many elements does have?

10.) With the same sets given in Item 7, how many elements does have?

11.) If and , find the value of

12.) Simplify:

13.) Perform the indicated operations:

14.) Simplify:

15.) Twelve less than three times a number is *3x*, what is the number?

16.) Simplify:

17.) The legs of a right triangle are (3*x* – 2) cm and 2*x* cm long. If *x* = 3, how long is its hypotenuse?

18.) The product of two numbers is If one number is twice the other, what is their product?

19.) Christ walked *x* km at a constant rate of *y* m/hr. How many minutes did he walk?

20.) If the length of a rectangle is cm and its area is how much longer is its length that its width?

21.) Solve for x in the equation

22.) What is the largest integral value of *x* If “=” in Item 21 is replaced by “<”?

23.) Solve for *x* in the equation |3 – 2*x*| = 3.

24.) Solve for x in the inequality |3 – 2*x*| > 2.

25.) In 2005, Cora was three times as old as her son Jayson. Four years back then, she was four times as old as Jayson. In what year was Jayson born?

Answer key:

1.) 0

2.)

3.) 6

4.) -5 and -4

5.)

6.) 0

7.) {11}

8.) {2, 4, 6, 8}

9.) 2

10.) 144

11.) 6

12.)

13.)

14.) -x – 4

15.) x + 4

16.) 4027

17.)

18.)

19.)

20.) (x + 6)cm

21.) 3

22.) 2

23.) 0 and 3

24.) or

25.) 1993

View Part 2 here: 2014 Grade 8 Math Challenge Elimination Questions with answers – Part 2