ALGEBRA 1 PRACTICE QUESTIONS FOR STAAR TEST WITH SOLUTIONS

Problem 1 :

Which expression is a factor of 10x2 - 19x + 6 ?

A) 10x - 3     B) 10x  - 1       C) 5x - 3      D) 5x - 2

Solution :

10x2 - 19x + 6

10x2 - 15x - 4x + 6

5x(2x - 3) - 2(2x - 3)

(5x - 2) (2x - 3)

So, option D) is correct.

Problem 2 :

The table shows the linear relationship between the distance in feet below sea level and the time in seconds traveled by a submarine.

Submarine

algebra-1-practice-questions-for-starr-test-q2

What is the rate of change of the distance in feet below sea level with respect to time that the submarine traveled ?

Record your answer and fill in the bubbles on your answer document. 

Solution :

The rate of change of distance with respect to time

difference between two consecutive observed distances/time taken

= (604 - 460)/(18 - 0)

= 144/18

= 8 feet/second

Problem 3 :

Which equation best represents the line shown on the grid ? 

algebra-1-practice-questions-for-starr-test-q3

A) y = 0      B) y = -6         C) x = 0        D) x = -6

Solution :

By observing the figure,

The equation of the line is y = -6

So, option B) is correct.

Problem 4 :

An insect population after x months can be modeled by the function g(x) = 18(1.3)x. Which statement is the best interpretation of one of the values in this function ?   

F) The inspect population increased by 13 insects each month.

G) The inspect population decreased by 13 insects each month.

H) The inspect population increased at a rate of 30% each month.

J) The inspect population decreased at a rate of 30% each month.

Solution :

g(x) = 18(1.3)x

Let x = 1 and x = 2

g(1) = 18(1.3)1

g(1) = 23.4 --- (1)

g(2) = 18(1.3)2

= 18 × 1.69

g(2)= 30.42 --- (2)

Subtract (2) and (1), we get

30.42 - 23.4 = 7.02

= 7.02 --- (3)

Statement F) and G) are false.

Let check the statement H) and J).

Dividing (3) and (1) we get, 

= 7.02/23.4

= 0.3

= 0.3 × 100

= 30%

The inspect population increased at a rate of 30% each month.

So, option H) is correct.

Problem 5 :

The graph of y = -(1/6)x - 4 is shown on the grid.

algebra-1-practice-questions-for-starr-test-q5

Which ordered pair is in the solution set of  y > -(1/6)x - 4 ?

A) (-8, 8)       B) (6, -5)         C) (4, -6)    D) (-2, -7)

Solution :

y > -(1/6)x - 4

Check the ordered pair that satisfy the inequality.

Point (-8, 8) ==> x = -8, y = 8

8 > -(1/6) × (-8) - 4

8 > 8/6 - 4

8 > 4/3  - 4

8 > (4 - 12)/3

8 > -8/3

(-8, 8) is a solution of y > -(1/6)x - 4.

y > -(1/6)x - 4

Check the ordered pair that satisfy the inequality.

Point (6, -5) ==> x = 6, y = -5

-5 > -(1/6) × 6 - 4

-5 > -1 - 4

-5 > -5

(6, -5) is not a solution of y > -(1/6)x - 4.

y > -(1/6)x - 4

Check the ordered pair that satisfy the inequality.

Point (4, -6) ==> x = 4, y = -6

-6 > -(1/6) × 4 - 4

-6 > -4/6 - 4

-6 > -2/3  - 4

-6 > (-2 - 12)/3

-6 > -14/3

(4, -6) is not a solution of y > -(1/6)x - 4.

y > -(1/6)x - 4

Check the ordered pair that satisfy the inequality.

Point (-2, -7) ==> x = -2, y = -7

-7 > -(1/6) × (-2) - 4

-7 > 2/6 - 4

-7 > 1/3  - 4

-7 > (1 - 12)/3

-7 > -11/3

(-2, -7) is not a solution of y > -(1/6)x - 4.

Then, the required solution is (-8, 8).

So, option A) is correct.

Problem 6 :

The conversion of degrees Celsius to degrees Fahrenheit can be  represented by a linear relationship. The graph shows the linear relationship between y, the temperature in degrees Fahrenheit, and x, the temperature in degrees Celsius from the freezing point of water.

algebra-1-practice-questions-for-starr-test-q6

Which equation best represents this situation ?

F) y = 5/9 x

H)  y = (5/9)x + 32

G) y = 9/5 x

J)  y = (9/5)x + 32

Solution :

algebra-1-practice-questions-for-starr-test-s5

Slope (m) = (y2 - y1)/(x2 - x1)

Two points (x1, y1) (x2, y2) = (0, 32) (40, 104)

= (104 - 32)/(40 - 0)

= 72/40

= 36/20

(m) = 9/5

y = mx + b

y = (9/5)x + 32

So, option J) is correct.

Problem 7 :

Which graph best represents the solution set for this system of inequalities ?

x + 2y < -2

y - x < 3

algebra-1-practice-questions-for-starr-test-q7

Solution :

In the given options , only option B and C will have dotted lines.

x + 2y < -2

y - x < 3

Select one of the points from the shaded region from B,

(2, 2)

2 + 2(2) < -2

8 < -2 (False)

So, option B is not correct.

Select one of the points from the shaded region from C,

(-2, -2)

-2 + 2(-2) < -2

-8 < -2 (True)

y - x < 3

-2 - (-2) < 3

-2 + 2 < 3

0 < 3 (True)

So, option C is correct.

Problem 8 :

Which graph best represents h(x) = (x + 1) (x - 3) ?

algebra-1-practice-questions-for-starr-test-q8

Solution :

 h(x) = (x + 1) (x - 3)

When h(x) = 0, x-intercepts are -1 and 3. Both options F and H are having the same x-intercepts.

Finding vertex :

h(x) = (x + 1) (x - 3)

h(x) = x2 - 2x - 3

h(x) = x2 - 2x(1) + 12 - 12 - 3

h(x) = (x - 1)2 - 4

Vertex is at (1, -4). So, option F is correct.

Problem 9 :

The first six terms in a geometric sequence are shown, where a1 = -4. 

-4

-16

-64

-256

-1,024

-4,096

Based on this information, which equation can be used to find the nth term in the sequence, an ?

A) an = -4n      B) an = -(4)n        C) an = -n2    D) an = (-4)n

Solution :

By observing all six terms are having negative signs, and it is geometric sequence,

Given, a1 = -4

a2 = -(4)2 = -16

a3 = -(4)3 = -64

 ⁞ 

an = -(4)n

So, option B) is correct.

Problem 10 :

What is the solution to 4(q + 56.5) = 30q - 112 ?

Record your answer and fill in the bubbles on your answer document.

Solution :

4(q + 56.5) = 30q - 112

4q + 226 = 30q - 112

4q - 30q = -226 - 112

-26q = -338

q = 338/26

q = 13

Problem 11 :

Which expression is equivalent to 36m2 - 100 ?

A) (9m - 20) (4m + 5)         B) 4(3m - 5) (3m + 5) 

C) 2(2m - 5) (9m + 10)        D) 4(3m - 5)2

Solution :

36m2 - 100 = 4(9m2 - 25)

= 4((3m)2 - 52)

= 4(3m + 5) (3m - 5)

So, option B) is correct.

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