Math Knowledge

Look at the figures below.Square B is 2 times Square A.Square C is 2 times Square B.If square B = 3, what is the sum of the three squares? A. 10 1⁄2 B. 9 1⁄2 C. 6 1⁄3 D. 6 1⁄2

---A. 10 1⁄2 B. 9 1⁄2 C. 6 1⁄3 D. 6 1⁄2 Each square is 2 times the size of the previous square. If square B = 3, then square C = 6, and square A would be half square B, or 11⁄2. Adding up the values, 11⁄2 + 3 + 6 = 101⁄2.

If 6 + x + y = 20 and x + y = k, then 20 - k = A. 6 B. 0 C. 14 D. 20

---A. 6 B. 0 C. 14 D. 20 6 + x + y = 20x + y = 14 = k; now substitute 20 - 14 = 6

If 2x = y, then find the value of (2x - y)4 + 6 A. 6 B. 20x-10y C. 8x-4y+ 6 D. 8x-y+ 6

---A. 6 B. 20x-10y C. 8x-4y+ 6 D. 8x-y+ 6 If 2x = y, then substitute either one into the equation for the other. So, for example: (2x - 2x) 4 + 6= (0) 4 + 6 = 6

If m ∠ 2 = 80° in figure below, m ∠ 4 = A. 80º B. 100º C. 120º D. None of the above

---A. 80º B. 100º C. 120º D. None of the above ∠ 2 and ∠ 1 are supplementary angles. m ∠ 1 = 100°. ∠ 1 and ∠ 4 are supplementary. m ∠ 4 =80°

If A2 + B2 = A2 + X2, then B equals A. ±X B. X2-2A2 C. ±A D. A2+X2

---A. ±X B. X2-2A2 C. ±A D. A2+X2 Subtract A2 from both sides of the equation: B2 = X2, therefore B = ± X.

104⁄10 = A. 10^3 B. 10^4 C. 20^3 D. 20^4

A. 10^3 ---B. 10^4 C. 20^3 D. 20^4 104⁄10 = 10000⁄10 = 1000 = 103The base remains unchanged. (10^4)

In the figure below m is parallel to n. If m∠ 2=120°, then what is m∠ 3? A. 120° B. 60° C. 30° D. 90°

A. 120° ---B. 60° C. 30° D. 90° If m∠ 2=120°, then m∠ 1 = 60° because they are a linear pair (add to 180°) m∠ 1 = m∠ 3 because they are corresponding angles. So, m∠ 3 = 60°.

A box contains 3 black, 4 red, and 5 white marbles. If one marble is to be picked at random, what is the probability that it will be red? A. 1⁄5 B. 1⁄2 C. 1⁄3 D. 1⁄4

A. 1⁄5 B. 1⁄2 ---C. 1⁄3 D. 1⁄4 There are 12 marbles in the box. 4 out of 12 are red = 1 out of 3 are red. The probability of picking a red marble is 1⁄3.

Look at the figures below.Triangle R is 3 times triangle S.Triangle S is 3 times triangle T.If triangle S = 1, what is the sum of the three triangles? A. 2 1⁄3 B. 3 1⁄3 C. 4 1⁄3 D. 6

A. 2 1⁄3 B. 3 1⁄3 --C. 4 1⁄3 D. 6 S = 1 R = 3 × 1+ T = 1⁄3 41⁄3

The perimeter of a rectangle is 90. One side of the rectangle is twice the length of the other.What is the length of the longer side? A. 20 B. 25 C. 30 D. 35

A. 20 B. 25 ---C. 30 D. 35 Let x equal shorter side; 2x equals length of longer side. 6x = 90; x = 15; longer side = 2x = 30.

In the figure below, the sides of ABC are respectively parallel to the sides of DEF. If the complement of C is 40°, then the complement of F is A. 20º B. 50º C. 40º D. 60º

A. 20º B. 50º ---C. 40º D. 60º If the sides are parallel, the angles are congruent.

Which is NOT a prime number? A. 23 B. 37 C. 87 D. 53

A. 23 B. 37 ---C. 87 D. 53 87 can be divided by 3 as well as by 1 and itself.

How many different combinations of jackets and pants are possible from a wardrobe that contains 3 jackets and 5 pairs of pants? A. 3 B. 5 C. 8 D. 15

A. 3 B. 5 C. 8 ---D. 15 Each jacket can be worn with 5 pairs of pants. 3 × 5 = 15

If you multiply x + 3 by 2x + 5, what will the coefficient of x be? A. 3 B. 6 C. 9 D. 11

A. 3 B. 6 C. 9 ---D. 11 x + 3 X 2x + 5 2x^2 + 6x 5x + 15 2x^2 + 11x + 15

√745 is a number between A. 30 and 40 B. 40 and 50 C. 70 and 80 D. 20 and 30

A. 30 and 40 B. 40 and 50 C. 70 and 80 ---D. 20 and 30 Since 202 = 400 and 302 = 900, then √400 = 20 and √900 = 30, then √745 is between those values.

√75= A. 3√5 B. 5√3 C. 5√15 D. 15√5

A. 3√5 ---B. 5√3 C. 5√15 D. 15√5 √75 = √3 × 25 = 5√3

The sum of the measures of the angles of a hexagon is A. 540º B. 720º C. 900º D. 1,080º

A. 540º ---B. 720º C. 900º D. 1,080º A hexagon has 6 sides. (n - 2) × 180° = (6 - 2) × 180° = 720°.

∠1 and ∠2 form a linear pair and therefore are supplementary angles. If m∠ 1 = 6x + 19 and m∠ 2 = 5x - 4, then m∠ 1 = A. 71° B. 109° C. 45° D. 91°

A. 71° ---B. 109° C. 45° D. 91° Angles that are a linear and/or are supplementary add up to 180°. So,6x + 19 + 5x - 4 = 18011x + 15 = 18011x = 165x = 15Plug x back in to find m∠ 1. 6(15) + 19 = 109°.

∠ 1 and ∠ 2 form a linear pair and therefore are supplementary angles. If m ∠ 1 = 7x - 6 and m ∠ 2 = 5x + 18, m ∠ 2 = A. 78º B. 82º C. 85º D. 88º

A. 78º B. 82º C. 85º ---D. 88º 7x − 6 + 5x +18 = 12x + 12 = 180° 12x = 180° − 12 = 168° x = 14 5 × 14 +18 = 70 + 18 = 88°

If x = y, find the value of 8 + 5(x - y). A. 8 + 5x - 5y B. 8 + 5xy C. 13x - 13y D. 8

A. 8 + 5x - 5y B. 8 + 5xy C. 13x - 13y ---D. 8 8 + 5(x - y) = 8 + 5x - 5y Since x = y, 5x = 5y and 5x - 5y = 0 Substituting: 8 + 0 = 8

The area of the figure below can be determined by the formula A. ac ÷ b B. 1⁄2bh C. bc ÷ a D. bh2

A. ac ÷ b ---B. 1⁄2bh C. bc ÷ a D. bh2 The formula for the area of a triangle is one half the base times the height.

A quadrilateral is a rectangle only if A. it has four congruent sides. B. it has opposite sides equal in length. C. it has four right angles and four congruent sides. D. it has four right angles and opposite side equal in length.

A. it has four congruent sides. B. it has opposite sides equal in length. C. it has four right angles and four congruent sides. ---D. it has four right angles and opposite side equal in length. The definition of a rectangle is a polygon with four sides, four right angles, and opposite sides equal in length. So, a quadrilateral is a rectangle only if it has four right angles and opposite sides equal in length.

A quadrilateral is a square only if A. it has four right angles. B. it has at least one pair of parallel sides. C. it has four right angles and four congruent sides. D. both pairs of its opposite sides are parallel.

A. it has four right angles. B. it has at least one pair of parallel sides. ---C. it has four right angles and four congruent sides. D. both pairs of its opposite sides are parallel. By definition, a square must have four equal sides and four right angles.

A is older than B. With the passage of time, the A. ratio of the ages of A and B remains unchanged. B. ratio of the ages of A and B increases. C. ratio of the ages of A and B decreases. D. difference in their ages varies.

A. ratio of the ages of A and B remains unchanged. B. ratio of the ages of A and B increases. ---C. ratio of the ages of A and B decreases. D. difference in their ages varies. With the passage of time, the ratio of the ages of A and B decreases. Pick a pair of ages and try for yourself. A is 4; B is 2; the ratio of their ages is 4:2 or 2:1. In two years, A is 6 and B is 4. The ratio of their ages is 6:4 or 3:2.

(x + 3)(x + 2) = A. x2+ 5x+ 5 B. x2+ 5x+ 6 C. x2 + 6x+ 5 D. x2+ 6x+ 6

A. x2+ 5x+ 5 ---B. x2+ 5x+ 6 C. x2 + 6x+ 5 D. x2+ 6x+ 6 x + 3 × x + 2 x^2 + 3x 2x + 6 x^2 + 5x + 6