Download ANSWER KEY for HSPA-PREP Assignment #4

ANSWER KEY for HSPA-PREP Assignment #4
 Part-I: Pre-Algebra and Algebra basic material
 Open-ended HSPA questions: Assignment pages 5, 8 and 11.
 PSAT/SAT material: Begins on page 12
PART-I
Practice with Patterns and Numbers
1.
C
49
(use x-3)
2.
C
6
3.
16, 19, 21
4.
94, 90
(use x-2): 96-2=94; 92-2=90
5.
1,625
(use 5x): (3)(5)=15; (15)(5)=75; (75)(5)=325; (325)(5)=1625
6.
125, 62.5, 31.25
Divide by 2 or multiply by 0.5
7.
multiply by -2
(3)(-2)= -6; (-6)(-2)=12; (12)(-2)= -24
8.
multiply by -0.5 or divide by -2
9.
multiply by -4
(2)(-4)= -8; (-8)(-4)=32; (32)(-4)= -128
10.
82, 244, 730
(28)(3)-2 = 84-2 = 82; (82)(3)-2=246-2=244; (244)(3)-2=732-2=730
11.
256; 65,536
(use x2): 2(2)=4, 4(4)=16, (16)(16)=256; (256)(256)=65,536
12.
677
(use x2 +1): (26)2 +1 = 676 +1=677
Practice Solving Linear Equations
1.
B
x = -7
2.
C
a=8
3.
A
b = -3
4.
D
x=4
5.
B
w = 15
6.
B
x = 12/9 which reduces to 4/3
7.
C
-9 = a
8.
C
Z = 80
9.
D
x = -16
10.
A
y = -80
Practice Recognizing Lines and Slopes
1.
Sketches will vary but slopes should be the same 2/2 or 1
They are perpendicular because the slope of one line is the negative reciprocal of the slope
of the other line.
2.
C
Two lines are parallel
3.
A
Parallel
2y – 4x = 12 can become y – 2x = 12, then y = 2x + 12 which is
parallel to the line y = 2x +5 (the coefficient of x is the slope and they
are both 2).
4.
B
3
2y = 6x + 10; divide both sides by 2 and get y = 3x +10; slope is 3
5.
B
6
6.
B
2
y-2x = 14; add 3x to both sides and get y = 2x +14; slope is 2
7.
A
4
1
slope =
8.
B and D
9.
y1  y 2
40 4
=
=
2  3 1
x1  x2
3  4 1
1 4
 3 1



and D.
52
3
5  4
9
3
Table A:
input x = 4
output (2)(4)+1 =
9
input x = 7
output (2)(7)+1 =
15
2
2
Table B:
input x = 3
output X = 3 =
9
Input x = 5
output X2 = 52 =
25
If you deposit $50 and use Table A; 2(50)+1 =
101 You would have $101.
If you deposit $50 and use Table B; (50)2 = (50)(50) = 2,500 You would have $2,500.
B.
Sample correct response: In Table A Bank the amount you deposit is only multiplied by 2
and $1 added; but in Table B Bank your money grows exponentially; the $50 is multiplied
times itself and (50)(50) gives you a much larger amount.
10.
Equation for perimeter:
2(x-2) + 2(x+5) = 22 or x-2 + x-2 + x+5 + x + 5 = 22
Solving for x: x =4
Longer side is x + 5 = 4 + 5 = 9; Shorter side is x – 2 = 4 – 4 = 2
Check: 2 (x-2) + 2 (x+5) = 2 (4-2) + 2(4+5) = 2(2) + 2(9) = 4 + 18 = 22 correct
Area of rectangle is (length)(width); (9)(2) = 18 square units
11.
Equation for perimeter of triangle would be 2(3x+2) +2x = 100 or 3x+2 + 3x+3 + 2x = 100
Solving the equation you find that x = 12
Base = 2(x) = 2(12) = 24
Each side = 3x+2 = 3(12)-2 = 36-2 = 38
Check: 38 + 38 + 24 = 100 correct it matches the original equation and perimeter given
12.
Equation for perimeter of the equilateral triangle is 3(x+6) = 108
Solving the equation you find that x =30
Each side is x+6 or 30 + 6 which = 36
Check: 3 (x+6) = 3 (30+6) = 3(36) = 108, correct
13.
Equation: x + 2x + 3x = 180o
x = 180/6 = 30 o
Angle B = 2x = (2)(30) = 60 o
Angle C = 3X = 3(30) = 90 o
Side AB is largest because it is opposite the largest angle.
Practice with Expressions and Equations
1.
D
4n-6
2.
A
3.
D
4.
A
10n = .20n
Real-Life Applications
1.
C
A = P (1 + .029)3
Remember, you write 2.9% as .029
A = 5300(1.029) 3
A = 5300(1.08954…)
A = $5,774.60
Mixed Practice
1.
geometric series
2.
C
add 34 to both sides
3.
D
In example A: 4a=48 and a = 12
In example B: -2b=-24 and b = 12
In example C: 3x = 36 and x = 12
In example D: 3y = -12 and y = -12 not 12
4.
B
14.55 per hour
40x + 10(2x) = 873; 40x +20x = 873; 60x = 873; x = 14.55
5.
D
$9.00
2(3x) + 3x = 6x + 3x = 9x = 27; x =3 Adult ticket = 3x = (3)(3) =9
2
6.
A
5 =n-6
7.
D
same slope
8.
B
y = 1/3x -4/3
b4
9
C
c=
a
10.
A
x=6
2x+3(x-2)=24; 2x+3x–6=24; 5x = 30, x = 6
11.
C
3
y = 4x +3
slope is 4
y = 4x
slope is 4
3y=x,
slope is ¼
16x-4y=24; becomes 4y=16x-24, then y = 4x-6
slope is 4
y + 4x =6; becomes y = -4x +6, then slope is -4
Open-ended question 13
 x + 2x + 4 + 3x = 100cm = perimeter
 x = 16
6x + 4 = 100; 6x = 96; x = 16
 AB = x = 16cm
 BC = 2x + 4 = 3 + 4 = 36cm
 CA = 3x = 3(16) = 48cm
(b)( h)
(36)(8)
 (36)(4) = 144 sq. cm.
 Area =
=
2
2
Open-ended question 14
PART-III
HSPA/PSAT/SAT QUESTIONS
13.
B
20
(Remember to divide by x or 10)
14.
C
32
(See which ones you can eliminate first)
15.
D
½
(Remember, you can substitute x for r+s and then solve for x.)
16.
A
12
(Note: if 2u + 2v = 60; then u + v = 30 and you can substitute that into the
other equation: t + u + v = 42, or t + 30 = 42; then just solve for t.
17.
E
56
18.
B
-1
19.
A
10
20.
C
3
8
You should notice that the line has a negative slope. So you can eliminate D
and E. Look at the two coordinates given and you see that the slope is
2
2
or
which is -1.
2
2
Put the two equations in the correct form so you can compare them.
Y = ax + 5
Here ‘a’ is the slope.
3x + 8y = 10; becomes 8y = -3x + 10; then y = -3/8x +10/8
21.
A
-8
Just solve for x in the first equation: 2x + 4 = 10, 2x = 6, x =3
Then substitute 3 for x in the next expression: 4(x)-20 = 4(3)-20 = 12-20 = -8
22.
2x = ½ or 0.5 (Notice you can use substitution again.) If yz = 10, then substitute 10 for yz
in the other equation.
2xyz = 5 then becomes 2x(10) = 5; then 2x = 5/10 or 1/2