Staar Released Algebra

• 92

Answer explanation

Factor 184:  {1, 2, 4, 8, 23, 46, 92, 184}
4 is the largest perfect square
 $\sqrt{4\ \cdot\ 46}\ =\ \sqrt{4}\cdot\sqrt{46}\ =2\sqrt{46}$  

Given g(x) = x² − 6x − 16, which statement is true?

• The zeros are -8 and 2, because the factors of g are (x + 8) and (x − 2).

• The zeros are -8 and −2, because the factors of g are (x + 8) and (x + 2).

• The zeros are -2 and 8, because the factors of g are (x + 2) and (x − 8).

• The zeros are 2 and 8, because the factors of g are (x − 2) and (x − 8)

Answer explanation

1. B & D are wrong because -16 requires a + and - factor and the negative is larger

2. Factor 16 and get two numbers whose difference is 6. {1,2,4,4,8,16} so 2 & 8 and

What is the equation in slope-intercept form of the line that passes through the points (−26, −11) and (39, 34)?

• y = (-9/13)x + 7

• y = (-9/13)x - 7

• y = (9/13)x + 7

• y = (-9/13)x - 7

Answer explanation

1. Find the slope m= (-11-34)/(-26-39) = (-45)/(-65) = 9/13

2. Use Point-Slope

[y-(-11)] = (9/13)[x-(-26)]

y + 11 = (9/13)(x + 26)

y + 11 = (9/13)x + 18

-11 -11

y = (9/13)x + 7

Which expression is equivalent to

(x⁹yz⁴)⁵

• x¹⁴y⁶z⁹

• x¹⁴y⁵z⁹

• x⁴⁵yz²⁰

• x⁴⁵y⁵z²⁰

Answer explanation

(x⁹yz⁴) is used five times so each power (9,1,4) is multiplied by 5

What is the solution to

4(y − 3) + 19 = 8(2y + 3) + 7?

• -1/2

• 1/2

• -2

• 2

Answer explanation

PEMDAS

4(y − 3) + 19 = 8(2y + 3) + 7

4y - 12 + 19 = 16y +24 + 7

4y + 7 = 16y + 31

-4y -31 -4y -31

-24 = 12y

-2 = y

Given p(x) = −4(x − 15)² + 2, what is the value of p(7)?

• 3574

• -3574

• -254

• 254

Answer explanation

−4(7 − 15)² + 2

-4(-8)² + 2 = -4(64) + 2 = -256 + 2 = -254

A customer paid a total of $6.00 for 68 copies at a print shop. Some of the copies were black-and-white copies, and the rest were color copies.

• Each black-and-white copy cost $0.08.

• Each color copy cost $0.15.

Which system of equations can be used to find b, the number of black-and-white copies, and c, the number of color copies that the customer paid for at the print shop?

• b + =c 6.00

  0.08b + 0.15c = 68

• b + c = 68

  0.15b + 0.08c = 6.00

• b + c = 6.00

  0.15b + 0.08c = 68

• b + c = 68

  0.08b + 0.15c = 6.00

Answer explanation

6.00 = 0.08b + 0.15c

68 = b + c

Which expression is a factored form of

2x² − 25x + 63

• (x + 9)(2x + 7)

• (x − 9)(2x − 7)

• (x + 7)(2x + 9)

• (x − 7)(2x − 9)

Answer explanation

Factor 2 and 63: {1,2} and {1,3,7,9,21,63}

Because -25 is negative one of these must use negative factors and we must factor in the 2.

(x − 9)(2x − 7)

What is the equation in standard form of the line that passes through the point (6, −1) and is parallel to the line represented by 8x + 3y = 15?

• 8x + 3y = −45

• 8x − 3y = −51

• 8x + 3y = 45

• 8x − 3y = 51

Answer explanation

8(6) + 3(-1) = 48 - 3 = 45

Which value of x is a solution to this equation?

3x² − 30x − 72 = 0

• x = −12

• x = −4

• x = −2

• x = −6

Answer explanation

3x² − 30x − 72 = 0 (divide everything by 3)

x² − 10x − 24 = 0

Factor 24 and look for 2 with a difference of 10 as the larger one must be negative.

{1,2,3,4,6,8,12,24) .... 2 and -12

(x − 12)(x + 2)