Download Wildwood School Summer 2009 Math Problem Set for Incoming

Wildwood School Summer 2009 Math Problem Set for Incoming Juniors
Name: ____________________________________________
This assignment is due on the first day of math class. Write neatly; show your work. If you cannot solve a
problem within five minutes, skip it and go on to the next one.
A. Numerical Calculations
Evaluate:
3 7 8
1. - + − = ?
5 4 3
⎛ 3 ⎞⎛ 7 ⎞⎛ 8 ⎞
2. ⎜− ⎟⎜ ⎟⎜− ⎟ = ?
⎝ 5 ⎠⎝ 4 ⎠⎝ 3 ⎠
⎛ 3⎞ ⎛ 7 ⎞
3. ⎜− ⎟ ÷ ⎜ ⎟ = ?
⎝ 5⎠ ⎝ 4 ⎠
4.
5.
6.
7.
8.
9.
10.
B. Algebra:
Combine, simplify or solve.
1. 2x − 5(3x − 4) + (8 − x) =
2. 2x − 5(3x − 4) + (8 − x) = 45
3. 2x + 3y = 13
3x + 2y = 12
⎛ 3 ⎞−1
⎜− ⎟ = ?
⎝ 5⎠
The GCF of 15 and 21 is ?
73% of 28 is ?
28 is 73% of ?
The prime factors of 420 are :
4.
2x − 4 = 8
5.
If m = -3 and n = 5, m2 − n = ?
6.
7.
156787.2 ≈ 1.57 ×10?
53
=?
.871
8.
9.
10.
C. Linear Graphs
1. Slope between (-2, 4) and (5, 7) = ?
x 2 y 3z 4
=?
x 4 y 3z 2
x 4 y −1
=?
x −3 y −2
(5x - 3) (3x + 5)
+
=?
2
3
(5x - 3) (3x + 5)
=
2
3
(x −1)(x − 2)(x − 3) = ?
D. Factor
1.
45x + 36y
2. For y = 3x - 7, slope = ?, y - int = ?
2. 15x 2 − 3x
3. Eqn for a line parallel to y = 3x - 7 :
3. 3x 2 y 3 − 6x 3 y 2
2
4. Eqn for a line perpendicular to y = 3x - 7 : 4. x + 4 x + 3
5. Eqn for slope = -.3 and y - int = 3.1:
5.
x 2 − 3x − 40
6. Eqn for x - int = -3 and y - int = 4 :
7. Eqn through (1,-2) with slope = 7 :
6.
25x 2 − 49
7.
4 x 2 − 20x + 25
8. Eqn through (1,-2) and (3, 5) :
8.
2x 2 + 3x − 35
9.
x 4 −1
9. Slope of y = -5 is ?
10. Slope of x = 3 is ?
10. 24 x 2 −101x −144
E. Quadratics
Solve
F. Geometry
For right triangle ABC with a = 5 and b = 12
x2 − x − 6 = 0
1.
hypotenuse c = ?
2. 2x −11x + 5 = 0
2.
altitude to c = ?
3.
3x + 4 x − 6 = 0
3.
sin A = ?
4.
3x 2 + 4 x + 6 = 0
4.
cos B - ?
5. x 2 −14 x + 49 = 0
5.
perimeter = ?
6. minimum value of
6.
7.
area = ?
dimensions of a
1.
2
2
y = x 2 − 2x + 7
triangle that is congruent :
7. maximum value of
y = −2x 2 + 2x + 3
8.
dimensions of a
triangle that is similar :
G. Word Problems
1. What are three consecutive even numbers that add to 72?
2. If five pounds of seed are needed for a lawn of 72 square feet, how many pounds of seed are
needed for a lawn of 200 square feet?
3. If one side of a square is increased by 2 and the other side decreased by 2, the resulting
rectangle’s area is 32. What was the length of the side of the square?
4. If I invest a sum of money at 6% for one year and twice as much at 7% for two years and my
total simple interest earned is $50, how much did I invest in each?
5. If two drivers are 150 miles apart and drive toward each other, one at 50mph and the other at
60mph, how much time will be needed till they meet?
6. If one worker can complete a job in 2 hours and another can complete it in 3 hours, then how
long would it take them to complete it working together?
7. What is the length of the side of an isosceles right triangle whose hypotenuse is 10?
8. A triangle’s largest angle is three times the smallest and the other angle is twice the smallest.
What are the angles? What kind of triangle is this?
9. The angles of a triangle can be represented by 3x+25, 4x+10 and 2x+10. What are the angles?
What kind of triangle is this?
10. To the nearest hundredth, what is the radius of a circle whose area is equal to a square’s with side
6?