PF M 334
Math 334!
Test 3 & 4 Review: Math! Prerequisite: Comple0on of prac0ce tests 3G and 4G
Course Description
In this micro-course, we will review the most commonly missed math problems from tests 3G and 4G. We will review math problem types including (but not limited to): exponent rules, multi-variable word problems, triangles (rule of 180, side length rules, and angle properties), minimum/maximum, least common factors, set problems, and other various problem types from arithmetic, geometry, algebra I and II.!
Math 334
2
Problem Solving Steps
The Strategy! ! Identify:! ALWAYS begin by determining the problem type. The most important step in solving a math! problem on the SAT does NOT involve your calculator.! ! Set Up:! Write down what you know is true. If there’s a diagram, label anything you can. Determine which equation(s) you will need to do the math. ! ! Make Sure:! What is the SPECIFIC answer they are asking for? Make sure you’re not falling for one of the SAT’s tricks.! ! Execute:! Plug in the information from the problem, carefully write out ALL STEPS, and solve the problem. After you’ve got an answer, check your work, and make sure your answer makes sense.!
Math 334
3
Review Questions If Set X is the set of all even integers from 1 to 100, and Set Y is the set of all multiples of 9 from 1 to 100, how many elements are there in the intersection of Sets X and Y ? (A) (B) (C) (D) (E)
5 6 11 12 44
Math 334
4
Review Questions E
A
B
C X
Y
D
F
Note: Figure not drawn to scale. The figure above shows two overlapping circles of identical size with centers at X and Y. The line segment with endpoints EF is a perpendicular bisector of the line through the centers of the circles. If EF = 12, and XY = 6, what is the radius of each circle? (A) (B) (C) (D) (E)
3 6 7 45 (approximately 6.71) 78.25 (approximately 8.85)
Math 334
5
Review Questions Tang-E drink contains 45 percent orange juice by volume. Which of the following expressions represents the percent of orange juice by volume in a mixture of t gallons of Tang-E drink and w gallons of water? (A) 45(t + w)% 45t % w t+w (C) % 45 45 % (D) t+w 45t (E) % t+w
(B)
Math 334
6
Review Questions L
T X
In the figure above, a three-foot by three-foot lattice is made of 24 one-foot pipes and 16 connectors of three types: 4 type L connectors that join 2 pipes, 8 type T connectors that join 3 pipes, and 4 type X connectors that join 4 pipes. Which of the following gives the correct number of the three types of connectors needed to make a four-foot by four-foot lattice from one-foot pipes in the same way? Type L (A) 6 (B) 6 (C) 4 (D) 4 (E) 4
Math 334
Type T Type X 10 10 12 8 10 9 12 9 14 10
7
Review Questions If g and h are positive integers and the ratio of g to h is the same as the ratio of g – 3 to h – 3, which of the following must be true? I. g = h II. g = 3 III. g = – 3h (A) None (B) I only (C) II only (D) III only (E) I and II
Math 334
8
Review Questions The last Wednesday of a 30-day month could be at most how many days after the first Tuesday of the same month?
Math 334
9
Review Questions For each positive integer n, let n☻ be defined by n
n n☻ = n + + 2 + . . . + 1. 2 2 For example, 16☻ = 16 + 8 + 4 + 2 + 1 = 31. What is the value of 512☻ – 128☻ ?
Math 334
10
Review Questions O 59°
P
N 93° 81° R M
50°
Q
Note: Figure not drawn to scale.
In ΔMOQ above, MP and NQ are line segments. All of the following are scalene triangles EXCEPT (A) ΔMNR (B) ΔMNQ (C) ΔMOQ (D) ΔMPQ (E) ΔMRQ
Math 334
11
Review Questions G
S
H
T I U Note: Figure not drawn to scale. F
In the figure above, FGHI is a rectangle with GF = 3 and GH = 12. Points S, T, and U are different points on a line (not shown) that is parallel to HI . Points S and T are symmetric about line GH and points T and U are symmetric about line FI. What is the length of SU ? (A) (B) (C) (D) (E)
4 6 9 12 18
Math 334
12
Review Questions x –7 If –3 = 16, then x = x (A) –2 1 2 3 (C) 2
(B)
(D) 2 (E) 4
Math 334
13
Review Questions y C (–x, 16) • E • • D (x, 16)
•
x
In the figure above, points C and D lie on the circle with center E and the graph of y = ax2, where a is a constant. If the circumference of the circle is 4π, what is the value of a ?
Math 334
14
Review Questions A company ordered $6,000 worth of chairs. Some of the chairs ordered cost $20 each and the others cost $40 each. If twice as many $20 chairs as $40 chairs were ordered, how many chairs were ordered altogether?
Math 334
15
Review Questions [4][5][6][7][8][9][10] [4][5][6][7][8][9][10] The figure above shows all the number cards that James, Tim, and Betty use to play a certain game. The cards are turned face down, mixed, and then each player is given exactly 3 cards. The player whose three cards add up to the highest sum wins. During one game, the sum of James’s three cards was 24 and the sum of Betty’s three cards was also 24. What is the maximum possible sum of Tim’s three cards for that game?
Math 334
16
Review Questions y° x° P
Note: Figure not drawn to scale.
In the figure above, point P is the center of a circle. If y is 35, what is the value of x ? (A) (B) (C) (D) (E)
80 90 100 110 120
Math 334
17
Review Questions If f ( x) = x 2 –
1 x, and g ( x) = x , then f ( g (18)) = 2
(A) 0 (B)
3 2 2
(C) 9 (D) 18 –
3 2 2
(E) 315
Math 334
18
Review Questions If w, x, y, and z are four nonzero numbers, then all of the following proportions are equivalent EXCEPT z
x
(A) w = y w y = x z y z = (C) w x x w (D) = z y
(B)
(E)
xy 1 = wz 1
Math 334
19
Review Questions ab c
• • • –2
d
•
ef
0
• •
g
•
2
On the number line above, which of the following corresponds to |a + e| ? (A) (B) (C) (D) (E)
b c d f g
Math 334
20
Review Questions Jeffrey’s e-mail password consists of 3 two-digit numbers. The combination satisfies the three conditions below. One number is a multiple of seven. One number is even. One number is the day of the month that Jeffrey’s rent is due. If each number satisfies exactly one of the conditions, which of the following could be the combination to the lock? (A) (B) (C) (D) (E)
12-35-15 12-28-15 14-19-11 21-42-21 33-35-20
Math 334
21
Review Questions 6
10
10 30°
30°
Note: Figure not drawn to scale.
What is the perimeter of the figure above? (A) (B) (C) (D) (E)
32 33 36 38 44
Math 334
22
Test 3 & 4 Review: Math! Prerequisite: Comple0on of prac0ce tests 3G and 4G
Course Description
In this micro-course, we will review the most commonly missed math problems from tests 3G and 4G. We will review math problem types including (but not limited to): exponent rules, multi-variable word problems, triangles (rule of 180, side length rules, and angle properties), minimum/maximum, least common factors, set problems, and other various problem types from arithmetic, geometry, algebra I and II.!
Math 334
2
Problem Solving Steps
The Strategy! ! Identify:! ALWAYS begin by determining the problem type. The most important step in solving a math! problem on the SAT does NOT involve your calculator.! ! Set Up:! Write down what you know is true. If there’s a diagram, label anything you can. Determine which equation(s) you will need to do the math. ! ! Make Sure:! What is the SPECIFIC answer they are asking for? Make sure you’re not falling for one of the SAT’s tricks.! ! Execute:! Plug in the information from the problem, carefully write out ALL STEPS, and solve the problem. After you’ve got an answer, check your work, and make sure your answer makes sense.!
Math 334
3
Review Questions If Set X is the set of all even integers from 1 to 100, and Set Y is the set of all multiples of 9 from 1 to 100, how many elements are there in the intersection of Sets X and Y ? (A) (B) (C) (D) (E)
5 6 11 12 44
Math 334
4
Review Questions E
A
B
C X
Y
D
F
Note: Figure not drawn to scale. The figure above shows two overlapping circles of identical size with centers at X and Y. The line segment with endpoints EF is a perpendicular bisector of the line through the centers of the circles. If EF = 12, and XY = 6, what is the radius of each circle? (A) (B) (C) (D) (E)
3 6 7 45 (approximately 6.71) 78.25 (approximately 8.85)
Math 334
5
Review Questions Tang-E drink contains 45 percent orange juice by volume. Which of the following expressions represents the percent of orange juice by volume in a mixture of t gallons of Tang-E drink and w gallons of water? (A) 45(t + w)% 45t % w t+w (C) % 45 45 % (D) t+w 45t (E) % t+w
(B)
Math 334
6
Review Questions L
T X
In the figure above, a three-foot by three-foot lattice is made of 24 one-foot pipes and 16 connectors of three types: 4 type L connectors that join 2 pipes, 8 type T connectors that join 3 pipes, and 4 type X connectors that join 4 pipes. Which of the following gives the correct number of the three types of connectors needed to make a four-foot by four-foot lattice from one-foot pipes in the same way? Type L (A) 6 (B) 6 (C) 4 (D) 4 (E) 4
Math 334
Type T Type X 10 10 12 8 10 9 12 9 14 10
7
Review Questions If g and h are positive integers and the ratio of g to h is the same as the ratio of g – 3 to h – 3, which of the following must be true? I. g = h II. g = 3 III. g = – 3h (A) None (B) I only (C) II only (D) III only (E) I and II
Math 334
8
Review Questions The last Wednesday of a 30-day month could be at most how many days after the first Tuesday of the same month?
Math 334
9
Review Questions For each positive integer n, let n☻ be defined by n
n n☻ = n + + 2 + . . . + 1. 2 2 For example, 16☻ = 16 + 8 + 4 + 2 + 1 = 31. What is the value of 512☻ – 128☻ ?
Math 334
10
Review Questions O 59°
P
N 93° 81° R M
50°
Q
Note: Figure not drawn to scale.
In ΔMOQ above, MP and NQ are line segments. All of the following are scalene triangles EXCEPT (A) ΔMNR (B) ΔMNQ (C) ΔMOQ (D) ΔMPQ (E) ΔMRQ
Math 334
11
Review Questions G
S
H
T I U Note: Figure not drawn to scale. F
In the figure above, FGHI is a rectangle with GF = 3 and GH = 12. Points S, T, and U are different points on a line (not shown) that is parallel to HI . Points S and T are symmetric about line GH and points T and U are symmetric about line FI. What is the length of SU ? (A) (B) (C) (D) (E)
4 6 9 12 18
Math 334
12
Review Questions x –7 If –3 = 16, then x = x (A) –2 1 2 3 (C) 2
(B)
(D) 2 (E) 4
Math 334
13
Review Questions y C (–x, 16) • E • • D (x, 16)
•
x
In the figure above, points C and D lie on the circle with center E and the graph of y = ax2, where a is a constant. If the circumference of the circle is 4π, what is the value of a ?
Math 334
14
Review Questions A company ordered $6,000 worth of chairs. Some of the chairs ordered cost $20 each and the others cost $40 each. If twice as many $20 chairs as $40 chairs were ordered, how many chairs were ordered altogether?
Math 334
15
Review Questions [4][5][6][7][8][9][10] [4][5][6][7][8][9][10] The figure above shows all the number cards that James, Tim, and Betty use to play a certain game. The cards are turned face down, mixed, and then each player is given exactly 3 cards. The player whose three cards add up to the highest sum wins. During one game, the sum of James’s three cards was 24 and the sum of Betty’s three cards was also 24. What is the maximum possible sum of Tim’s three cards for that game?
Math 334
16
Review Questions y° x° P
Note: Figure not drawn to scale.
In the figure above, point P is the center of a circle. If y is 35, what is the value of x ? (A) (B) (C) (D) (E)
80 90 100 110 120
Math 334
17
Review Questions If f ( x) = x 2 –
1 x, and g ( x) = x , then f ( g (18)) = 2
(A) 0 (B)
3 2 2
(C) 9 (D) 18 –
3 2 2
(E) 315
Math 334
18
Review Questions If w, x, y, and z are four nonzero numbers, then all of the following proportions are equivalent EXCEPT z
x
(A) w = y w y = x z y z = (C) w x x w (D) = z y
(B)
(E)
xy 1 = wz 1
Math 334
19
Review Questions ab c
• • • –2
d
•
ef
0
• •
g
•
2
On the number line above, which of the following corresponds to |a + e| ? (A) (B) (C) (D) (E)
b c d f g
Math 334
20
Review Questions Jeffrey’s e-mail password consists of 3 two-digit numbers. The combination satisfies the three conditions below. One number is a multiple of seven. One number is even. One number is the day of the month that Jeffrey’s rent is due. If each number satisfies exactly one of the conditions, which of the following could be the combination to the lock? (A) (B) (C) (D) (E)
12-35-15 12-28-15 14-19-11 21-42-21 33-35-20
Math 334
21
Review Questions 6
10
10 30°
30°
Note: Figure not drawn to scale.
What is the perimeter of the figure above? (A) (B) (C) (D) (E)
32 33 36 38 44
Math 334
22
