Math 312!
Test 1 & 2 Review: Math! Prerequisite: Comple0on of prac0ce tests 1G and 2G
Course Description
In this micro-course, we will review the most commonly missed math problems from tests 1G and 2G. We will review math problem types including (but not limited to): slope, absolute value, logic word problems, triangles (rule of 180, Pythagorean formula, angle properties), weird symbol function problems, sequence/series, average, scientific notation, 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 If 7 and 13 are the lengths of two sides of a triangle, which of the following can be the length of the third side? I. 7 II. 17 III. 21 (A) (B) (C) (D) (E)
I only II only I and II only II and III only I, II, and III
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Review Questions If x is a positive integer, which of the following CANNOT be the units digit of 7x? (A) (B) (C) (D) (E)
1 3 5 7 9
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Review Questions Line g, line h, and point J lie in a plane. If line r in the same plane passes through point J and intersects line h but not line g, which of the following must be true? I. h is parallel to g. II. g is parallel to r. III. r is perpendicular to h. (A) (B) (C) (D) (E)
I only II only III only I and II II and III
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Review Questions If t is 30 percent of u and u is 6 percent of v, what percent of v is t? (A) (B) (C) (D) (E)
1.8% 5% 18% 50% 180%
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Review Questions y y = f (x)
3
O
1
x
The shaded region in the figure above is bounded by the x-axis, the line x = 1, and the graph of y = f(x). If the point (m, n) lies in the shaded region, which of the following must be true? I. m ≥ 1 II. n ≥ m III. f(m) ≥ n (A) (B) (C) (D) (E)
I only III only I and II only I and III only I, II, and III
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Review Questions The average (arithmetic mean) of four different positive integers is 9. If the first of these integers is 3 times the second integer and the second integer is 2 less than the third integer, what is the least possible value of the fourth integer? (A) (B) (C) (D) (E)
5 4 3 2 1
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Review Questions If 4
0). Which of the following represents the number of members in set C ? (A) (B) (C) (D) (E)
a+b+x a+b–x a + b + 2x a + b – 2x 2a + 2b + 2x
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Review Questions P M
N 5
L
21
O
Note: Figure not drawn to scale.
In the figure above, if the area of triangle OPL is equal to the area of the rectangle LMNO, what is the length of PN?
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Review Questions If the sum of consecutive integers from – 36 to n, inclusive, is 114, what is the value of n ?
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Review Questions 100 pounds of flour are divided into five piles so that the weight of the second pile is three times the weight of the first pile, the weight of the third pile is three times the weight of the second pile, the weight of the fourth pile is three times the weight of the third pile, and the weight of the fifth pile is 20 pounds. What is the weight, in pounds, of the smallest pile? (A) 2 (B) 3 1 2 1 5 (D) 2
(C) 3
(E) 20 Math 312
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Review Questions A right triangle has legs of lengths f and g and a hypotenuse of length h. If f 2 + g2 + h2 = 578, what is the value of h ? (A) 17 (B) 25.5 (C) 34 (D) 17 2 (E) 34 2
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Review Questions y O –1
2
y = mx + b x
The figure above shows the graph of the line y = mx + b, where m and b are constants. Which of the following best represents the graph of the line y = –2mx + b?
y (A)
O –2
–1
y
(B)
x
2 O
x
2 y
y (C)
(D) 1 O
O –1 1
x
1
x
y (E) O –1
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x
–1
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Review Questions w 11 x 7 y 9 = ; = ; and = . x 5 y 8 z 5
If w, x, y, and z in the equations above are positive integers, which of the following is true? (A) (B) (C) (D) (E)
w<x