Expression Structure Test Answer Key with Scoring – Algebra 1

Question 1 Parts of an expression (2 points)

Terms: 9y², −4y, 11.

Coefficients: 9 and −4. Constant term: 11.

3 terms; coefficients 9 and −4; constant 11

Scoring: 1 point for the three terms, 1 point for the coefficients (including the sign) and the constant.

Question 2 Name the factors (2 points)

Factors: 3, a and (b + 4).

The sum factor is (b + 4).

Scoring: 1 point for the three factors, 1 point for identifying (b + 4).

Question 3 Rational or irrational (2 points)

(a) √81 = 9, rational. (b) √45 = 3√5, irrational. (c) 0.375 = 3/8, rational. (d) 3π, a nonzero rational times π, irrational.

(a) rational (b) irrational (c) rational (d) irrational

Scoring: 0.5 point each.

Question 4 Kayak rental (3 points)

(a) 18 is a fixed fee; 9.5 is the charge in dollars per hour.

(b) 18 + 9.5(3.5) = 18 + 33.25 = 51.25.

(c) The term 9.5h, which equals $33.25.

$51.25

Scoring: 1 point per part.

Question 5 Growth of an investment (3 points)

(a) Starting value $1,500; growth factor 1.06; rate 6% per year.

(b) 1.06² = 1.1236, so 1,500 × 1.1236 = $1,685.40.

(c) After 1 year: 1,500(1.06) = 1,590, so growth is $90.

(b) $1,685.40 (c) $90

Scoring: 1 point per part.

Question 6 Sum with a root (2 points)

If 7 + √10 were rational, subtracting 7 would make √10 rational. But √10 is irrational, since 10 is not a perfect square.

7 + √10 is irrational.

Scoring: 1 point for the answer, 1 point for the justification.

Question 7 Making rational results (2 points)

(a) Example: √5 and −√5 give a sum of 0. Another valid pair is 2 + √3 and 4 − √3, sum 6.

(b) Example: √3 and √12 give √36 = 6. Another valid pair is √2 and √2, product 2.

Any valid pairs with the correct sum or product

Scoring: 1 point per part; accept any correct example.

Question 8 Rectangle structure (3 points)

(a) 2(x + 7 + 4) = 2x + 22.

(b) Area = 4(5 + 7) = 48.

(c) The factor 4 is the width: the area is 4 strips, each of length x + 7.

(a) 2x + 22 (b) 48 square units

Scoring: 1 point per part.

Question 9 Area of a circle (1 point)

The area is 25π, a nonzero rational number times π.

Irrational

Scoring: 1 point for the answer with the explanation.