Math 350!
Test 5 Review: Math! Prerequisite: Comple0on of prac0ce test 5G
Course Description
In this micro-course, we will review the most commonly missed math problems from test 5G. 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.!
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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.!
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Review Questions What is the average (arithmetic mean) value of the integers from –50 to 50, inclusive? (A) –
51 2
(B) –25 (C) 0 (D) 25 (E)
51 2
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Review Questions In a train, all 80 compartments are occupied by either 1, 2, or 4 people. If
1 2
of the compartments are occupied by more than
one person and
1 8
of the compartments that are occupied by
more than one person are occupied by 4 people, how many compartments are occupied by 2 people? (A) (B) (C) (D) (E)
10 25 30 35 40
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Review Questions B D A C Note: Figure not drawn to scale. Points B and C in the figure above are free to move as long as AB = 3, BC = 5, and angle ABC is always a right angle. What will be the length of AC when C lies on line AD? (A) 4 (B) 5 (C) 8 (D)
34 (approximately 5.83)
(E)
43 (approximately 6.56)
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Review Questions A cubical swimming pool measuring 4 yards by 4 yards by 4 yards is filled to capacity by a hose in
1 2
hour. How many
hours will it take to fill a cubical swimming pool measuring 8 yards by 8 yards by 8 yards to capacity, if it is filled by the same hose with water flowing at the same rate? (A) (B) (C) (D) (E)
1 2 4 8 32
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Review Questions A study of 400 fruit orchards showed that 250 of the orchards grew apples, 140 grew pears, 95 grew plums, 70 grew only apples and pears, 30 grew only apples and plums, 45 grew only pears and plums, and 10 grew all three. How many of the orchards grew only apples or plums? (A) (B) (C) (D) (E)
30 130 150 180 345
How many of the orchards grew no apples, pears, or plums? (A) (B) (C) (D) (E)
0 80 165 235 320
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Review Questions 0 5
1
4
2 3
On the dial shown above, the numbers are equally spaced. The arrow rotates clockwise at a constant rate through an angle of 240º every 20 seconds. If the arrow starts at 0, how many times will the arrow pass the number 4 on the dial in 100 seconds? (A) (B) (C) (D) (E)
Two Three Four Five Six
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Review Questions 4
If x13 = j and x12 = 9 , which of the following is an expression for x in terms of j ? 9 j 4 4 (B) j 9
(A)
(C) 4j (D) 9j (E) 13j
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Review Questions For nonzero numbers x and y, let the operations Ψ and ⌂ be defined by x Ψ y =
y x+ y and x ⌂ y = . x+ y xy
What is the value of 1 Ψ (2 ⌂ 3)?
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Review Questions How many different teams of 2 people each can Joshua select from a group of 5 people?
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Review Questions James used three pieces of ribbon, each 8 inches long, to tie up each of his presents. James had a 150-foot roll of ribbon when he started. If no ribbon was wasted, which of the following represents the number of feet of ribbon that was left on the roll after he wrapped up y presents? (12 inches = 1 foot) (A) 150 – 24y (B) 150 – 8y (C) 150 – 2y (D) 150 – y 1 (E) 150 – y 2
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Review Questions AB +BA 1 A4 In the correctly worked addition problem above, A and B represent two different digits. What digit does A represent? (A) (B) (C) (D) (E)
3 4 5 8 9
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Review Questions A page of a certain book is 12 inches high and 8 inches wide. The top and bottom margins on the page are each 2 inches wide, and the side margins are each 1 inch wide. The area on the page available for printing is what percent of the total area of the page? (A) (B) (C) (D) (E)
30% 35% 40% 45% 50%
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Review Questions For all positive integers x, let [x] be defined as the sum of positive integers from 1 to x, inclusive. For example, [5] = 1 + 2 + 3 + 4 + 5 = 15. Which of the following equals [11] – [9]? (A) (B) (C) (D) (E)
[2] [5] [6] [7] [8]
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Review Questions If
h 48 7
(A) (B) (C) (D) (E)
= 23 × 43 × 63 , then h =
3 7 9 21 63
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Review Questions a b + =x b a a b – =y b a
In the equations above, if a ≠ 0 and b ≠ 0, which of the following must be equal to x2 – y2? (A) 2 (B) 4 (C)
ab 2
a 2b2 (D) 2
(E) 4a2b2
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