2. LEARN SPECIAL MATH STRATEGIES
Strategy #6: Recognize “Figure not drawn to scale” –
assume the picture is misleading, closest answer to visual is
incorrect, you should redraw the figure
In the figure below, AB = BC. If x = 30 , what is
the degree value of m?
B
x
A. 75
B. 105
C. 130 m
D. 135 A C
E. 150 Note: Figure not drawn to scale
3. LEARN SPECIAL MATH STRATEGIES
Strategy #7: Test the extremes – given a range of values
(4 < x < 9), tests the extremes (4 and 9) and not the
numbers in between; the answer should be obvious
If y = 4x – 3 and 0 < x < 3, then y is between
A. -3 and 9
B. -2 and 10
C. 0 and 12
D. 1 and 5
E. 1 and 9
4. LEARN SPECIAL MATH STRATEGIES
Strategy #8: Find a pattern – try a few numbers to see
a pattern that will help you answer the question
If n is a positive integer, which of the following
cannot be the units digit of .
A. 1
B. 3
C. 5
D. 7
E. 9
5. LEARN SPECIAL MATH STRATEGIES
Strategy #9: Don’t by misled by generic answers – if you
find you’re guessing, ignore choices like “None of the above” or
“It cannot be determined from the information given”
If x, y, and z are positive numbers and
2x = 3y = 4z, then the value of x + y + z is how
many times the value of x?
A.
B.
C.
D.
E. It cannot be determined from the information given
6. LEARN SPECIAL MATH STRATEGIES
Strategy #10: Do the math – don’t go searching for wild
gimmicks and tricks; it is a math test so sometimes you
just need to do the math and solve the problem
What is the area of the shaded region in the figure
below?
(3, 10)
A. 30
B. 21 (0, 4)
C. 18
D. 12
(3, 0)
E. 9
Editor's Notes
Since AB=BC, triangle ABC is an isosceles triangle so angles A and C must be equal.Since the angles in a triangle sum to 180, the other two angles (which must be equal) are 75 (180 – 30=150; 150/2 = 75).We are trying to find the exterior angle of angle A which is 75, so 180-75 = 105.
(A). y= 4(0)-3 = 0-3 = -3; y= 4(3)-3 = 12-3 = 9
(C).7^1 = 7, 7^2 = 49, 7^3 = 343, 7^4 = 2401, 7^5 = 16807, 7^6 = 117649, 7^7 = 823543, 7^8 = 5764801As you can see from the pattern above, the units digits are 7, 9, 3, 1 and then the units digits begin to repeat. The only number they do not reach is 5.
(A).Since 2, 3, and 4 are all factors of 12 (in fact this is the least common multiple of the three numbers), we can find x, y, and z such that each product (2x, 3y, and 4z) is equal to 12. Therefore, x=6, y=4, and z=3. So x+y+z=13.If x=6 and x+y+z=13, then this sum is 13/6 times the value of x which is 6.To check, (13/6)*6=13, the sum of the three variables.
(B). The shape in the shaded region forms a trapezoid, so we can use this area formula if we know it, but it is not one of the formulas listed at the beginning of the math section. We can cut the figure into a rectangle and triangle and use the given area formulas to find these two areas and finally the sum of the areas.The dimensions of the rectangle is 3 x 4 so the area of the rectangular part is 12.The base of the triangle is 10-4 = 6, and the height is 3 (same as the rectangle). So the area of the triangle is (1/2)*6*3 = 9Therefore the total area of the shaded region is 12+9 = 21.
