Math Test

1. Marianne’s credit card has a simple interest rate of 21%. If she leaves a balance of $1500 on the card for one year, how much will she owe after two years?

a. $630
b. $1500
c. $2130
d. $2760
e. $3630

Sally head to her favorite bagel shop for breakfast. In how many different ways can she choose two bagels from a choice of whole wheat, plain, garlic, onion, everything, and cinnamon sugar?

a. 6 ways
b. 12 ways
c. 15 ways
d. 18 ways
e. 24 ways

3. Sammy surveyed 100 students in his school. He discovered that 61% of those households had at least one pet. Suppose he then asked 6 random families from his school if they had a pet. How many of those families could he expect to have a pet?

a. 1
b. 2
c. 3
d. 4
e. 6

4. A right triangle has one interior angle that measures 25°. What is the measurement of the unknown interior angle?

a. 25°
b. 35°
c. 65°
d. 90°
e. 115°

5. What is the distance between the two points (1, -4) and (6, 2)?

a. approximately 5.6 units
b. approximately 6.4 units
c. 7 units
d. approximately 7.8 units
e. approximately 9.4 units

6. Which quadrilateral has exactly one pair of parallel sides?

a. square
b. trapezoid
c. rhombus
d. rectangle
e. kite

7. A cone has a height of 12 meters and a base with a radius of 5 meters. What is the volume of the cone?

a. 117.75m
b. 188.4 m
c. 235.5 m
d. 471 m
e. 678 m

8. You are designing a poster to advertise a school dance. You start by drawing a prototype of your poser that is 12 inches high and 6 inches wide. The scale factor for the actual poster is 5:1. What will be the height and width of the actual poster?

h height: 2.4 inches, width 1.2 inches
b. height: 12 inches, width 6 inches
c. height: 17 inches, width 11 inches
d. height 25 inches, width 18 inches
e. height 60 inches, width 30 inches

9. What is the length of the tangent, t, in this diagram?


a. √112

b. 112
c. 4
d. √329

e. 329

10. What is the derivative with respect to x in this function:




f(x) = 6x9

a. 15x9
b. 9x6
c. 54x8
d. 54x9
e. 6x6







 
Answer Key:
C In order to find the simple interest rate, one must use the formula I = prt. In this equation, I is the interest rate, p is the principle, r is the interest rate per year, and t is the time in years. In this problem, the principle was $1500, the interest rate is 21%, and the length of time is 2 years. So now, I = prt is equal to (1500) (.21) (2) so I = 630. This is how much interested accrues over two years. This value needs to be added to the principle so the amount that she will need to pay after 2 years is 1500 + 630 or $2130. \
C One way to determine how many different possible combinations there are for choosing 2 different types of bagels out of a total of 6 is to make a list. The possible arrangements are: (wp), (wg), (wo), (we), (wc), (pw), (pg), (po), (pe), (pc), (gw), (gp), (go), (ge), (gc), (ow), (op), (og), (oe), (oc), (ew), (ep), (eg), (eo), (ec), (cw), (cp), (cg), (co), (ce). Crossing out the duplicate combinations we are left with 15 unique combinations.
D Sammy conducted a binomial experiment. This means that there is n number of independent trials, each trail can be a success (the family has a pet) or a failure (the family has no pets). The probability of success I p and the probability of failure is 1 – p. The equation to use is therefore P (k successes) = nCkpk(1-p)n-k
C The unknown angle has a measurement of 65°. The sum of all three interior angles of a right triangle is 180°. The known angles are 90° (the right angle), and 25°, leaving the unknown angle to be 65°.
D To find the distance between two points, use the formula:
d=√((x_2-x_1 )^2 )+〖(y_2-y_1)〗^2
B A trapezoid is a quadrilateral with exactly one pair of parallel sides.
D The volume of a cone can be found using the formula:
A= 1/2 Bh
E The posters will be similar figures. To find the height of the actual poster, multiply the height of the sketch by the scale factor. The same is true for the width- multiply the sketch width by the scale factor to get the actual width.
A To find the length of the tangent in a situation such as this use the formula:
C^2=E×(A+E) where C is the tangent, E is the secant and A is the diameter
C Solve the problem as follows:
df/dx=6(9x^8 )=54x^8