WHICH IS TO THE LEFT OF 0.THE SUM AND PRODUCT OF SIGNED NUMBERS WIL...

3, which is to the left of 0.The sum and product of signed numbers will be positive or nega-In the figures, it can be determined thattive depending on the operation and the signs of the numbers; for● ABD and DBC are triangles.example, the product of a negative number and a positive number● Points A, D, and C lie on a straight line, so ABC is also ais negative.triangle.● Point D is a distinct point between points A and C.Division by zero is undefined; that is, x0 is not a real number for● Point E is the only intersection point of line segment BCany x.and the small curve shown.If n is a positive integer, then x

ⁿ

denotes the product of n factors● Points A and E are on opposite sides of line BD.of x; for example, 3

⁴

means (3)(3)(3)(3) = 81. If x 0, then x

⁰

= 1.● Point F is on line segment BD.Squaring a number between 0 and 1 (or raising it to a higher● The length of line segment AD is less than the length of

2

1line segment AC.power) results in a smaller number; for example, 1 = and39● The length of line segment AB is 10.(0.5)

³

= 0.125.● The measure of angle ABD is less than the measure ofAn odd integer power of a negative number is negative, andangle ABC.● The measure of angle ACB is 35 degrees.an even integer power is positive; for example, (2)

³

= 8 and● Lines m and n intersect the closed curve at three points:(2)

²

= 4.The radical sign means “the nonnegative square root of ;” forR, S, and T.example, 0 0 and 4 2. The negative square root of 4 isFrom the figures, it cannot be determined whether● The length of line segment AD is greater than the lengthdenoted by 4 2. If x 0, then x is not a real number;for example, 4 is not a real number.of line segment DC.● The measures of angles BAD and BDA are equal.The absolute value of x, denoted by |x|, is equal to x if x ≥ 0 and● The measure of angle ABD is greater than the measure ofequal tox if x < 0; for example, |8| = 8 and |8| = (8) = 8.angle DBC.If n is a positive integer, then n! denotes the product of all● Angle ABC is a right angle.positive integers less than or equal to n; for example,When a square, circle, polygon, or other closed geometric4! = (4)(3)(2)(1) = 24.figure is described in words with no picture, the figure is as-The sum and product of even and odd integers will be even orsumed to enclose a convex region. It is also assumed that such aodd depending on the operation and the kinds of integers; forclosed geometric figure is not just a single point. For example,example, the sum of an odd integer and an even integer is odd.a quadrilateral cannot be any of the following:If an integer P is a divisor (also called a factor) of another integerN, then N is the product of P and another integer, and N is said to bea multiple of P; for example, 3 is a divisor, or a factor, of 6, and 6 isa multiple of 3.A prime number is a positive integer that has only two distinct

(a single point)

(not convex)

(not closed)

positive divisors: 1 and itself. For example, 2, 3, 5, 7, and 11 areprime numbers, but 9 is not a prime number because it has threeWhen graphs of real-life data accompany questions, they arepositive divisors: 1, 3, and 9.drawn as accurately as possible so you can read or estimatedata values from the graphs (whether or not there is a note thatthe graphs are drawn to scale).Standard conventions apply to graphs of data unless other-wise indicated. For example, a circle graph represents 100 per-cent of the data indicated in the graph’s title, and the areas ofthe individual sectors are proportional to the percents they rep-resent. Scales, gridlines, dots, bars, shadings, solid and dashedlines, legends, etc., are used on graphs to indicate the data.Sometimes, scales that do not begin at zero are used, as well asbroken scales.Coordinate systems such as number lines and xy-planes aregenerally drawn to scale.ALGEBRAthe xy-plane. For example, the graph of the linear equation(including coordinate geometry)= −3 −25 and a y-intercept ofy 5x is a line with a slope of −3Questions that test algebra include those involving the follow-–2, as shown below.ing topics: rules of exponents, factoring and simplifyingalgebraic expressions, concepts of relations and functions,equations and inequalities, and coordinate geometry (includingslope, intercepts, and graphs of equations and inequalities).The skills required include the ability to solve linear and qua-dratic equations and inequalities, and simultaneous equations;the ability to read a word problem and set up the necessaryequations or inequalities to solve it; and the ability to applybasic algebraic skills to solve problems.Some facts about algebra that may be helpfulIf ab = 0, then a = 0 or b = 0; for example, if (x 1) (x + 2) = 0,it follows that either x 1 = 0 or x + 2 = 0; therefore, x = 1 or x = 2.Adding a number to or subtracting a number from both sidesGEOMETRYof an equation preserves the equality. Similarly, multiplying ordividing both sides of an equation by a nonzero number preservesQuestions that test geometry include those involving thethe equality. Similar rules apply to inequalities, except that multi-following topics: properties associated with parallel lines,plying or dividing both sides of an inequality by a negative numbercircles, triangles (including isosceles, equilateral, andreverses the inequality. For example, multiplying the inequality30˚60˚90˚ triangles), rectangles, other polygons, area,3x 4 > 5 by 4 yields the inequality 12x 16 > 20; however, mul-perimeter, volume, the Pythagorean Theorem, and angle mea-tiplying that same inequality by 4 yields 12x + 16 < 20.sure in degrees. The ability to construct proofs is not measured.The following rules for exponents may be useful. If r, s, x, and yare positive numbers, then1 ; for example, 5

^{– 3}

= =Some facts about geometry that may be helpful(a) x

^{– r}

=

3

1255x

^r

If two lines intersect, then the opposite angles (called vertical(b) (x

^r

)(x

^s

) = x

^r+s

; for example, (3

²

)(3

⁴

) = 3

⁶

= 729angles) are equal; for example, in the figure below, x = y.(c) (x

^r

)(y

^r

) = (xy)

^r

; for example, (3

⁴

)(2

⁴

) = 6

⁴

= 1,296(d) (x

^r

)

^s

= x

^rs

; for example, (2

³

)

⁴

= 2

¹²

= 4,096y˚ ^x˚

2

r

(e) x

s

=

^r–s

; for example, 44

5

= 4

^2–5

= 4

^–3

= 1x x

3

=644If two parallel lines are intersected by a third line, certain anglesThe rectangular coordinate plane, or xy-plane, is shown below.that are formed are equal. As shown in the figure below, if ,then x = y = z.zx

˚ ˚

y

˚

The sum of the degree measures of the angles of a triangle is