WESTMOOR Math Comp Practice

Algebra

100

The sum of two numbers is 20 and their difference is 4. What is the larger number?

12

200

The roots of x²−8x+k=0 are equal. Find k.

Discriminant = 0

k=16

300

If one root of x²-7x+10=0 is 5 what is the other root?

2

400

x+1/x=2  

find x¹⁰+1/x¹⁰

2

500

x+1/x=3

find x⁶+1/x⁶

322

Combinatorics

100

The number of ways to arrange the 6 different scoops of ice cream (6!)

What is 720

200

The number of 3-digit numbers that can be formed using digits 2, 5, and 9 exactly once.

What is 6

300

Binary strings use only 0s and 1s. How many 7-character binary strings end with 11?

What is 32

400

Binary strings use only 0s and 1s. 

How many 6-character binary strings Exist?

What is 64

500

The number of non-negative integer solutions to a+b+c< 17 where a<b<c

What is 123

Statisitics

100

The probability of an impossible event is always this number.

What is 0?

200

The average of five numbers is 12. Four of the numbers are 8, 10, 14, and 15. What is the fifth number?

What is 11

300

You toss 4 fair coins. What is the probability that 3 or more of them are heads?

What is 5/16

400

If the mean score on a math test is 80 with a standard deviation of 5, approximately 95% of students scored between these two numbers.

What are 70 and 90?

500

A box contains 3 red, 4 blue, and 5 green balls. A random sample of 3 balls is drawn without replacement. What is the probability all 3 are different colors?

What is 3/11

Geometry

100

Triangle ABC has sides of lengths 7, 24, and 25. What is the area of the triangle?

What is 84

200

A square is inscribed in a circle with radius 5. What is the area of the square?
 

Answer: What is 50?

300

The points A(−6,−2) and B(0,4) are endpoints of a diameter of a circle. Find the radius of the circle.
 

What is 3√2?

400

A right triangle has legs of lengths 6 and 8. A square is inscribed in the triangle so that one side of the square lies along the triangle’s hypotenuse. What is the side length of the square?

What is 120/37

500

The points A(-6, -2) and B(0, 4) lie on a circle. Find the coordinates of the center of the circle if the line segment AB is a diameter.

What is (-3,1)

Calculus (not on test)

100

What is the derivative of f(x)= e^x

e^x

200

lim_x->2(8-3x+12x²)

50

300

derivative of e^-x

-1/e^x

400

This equation's derivative is: 25x3 - 12x² + X. Find its intergral...

What is  25x⁴/4 - 4x³ + x²/2?

500

Find the area enclosed by y=x² and the y-axis between [0,3] is revolved around the y-axis.

What is 9/2pi