Question 1

Which of the following is the correct algebraic expression for 'three more than the quotient of a number and 11'?

Accepted Answer

$$\frac{x}{11} + 3$$

Question 2

Evaluate the expression $$5(x + 7)$$ for $$x = 4.$$

Accepted Answer

$$55$$

Question 3

Which of the following is a solution to the equation $$2(z + 1) = 5(z - 2)$$?

Accepted Answer

$$z = 3$$

Question 4

Translate the sentence: 'Nine less than 4 times a number gives 26' into an algebraic equation.

Accepted Answer

$$4x - 9 = 26$$

Question 5

If $$x = 2$$ and $$y = 5$$, what is the value of $$3x + 2y$$?

Accepted Answer

$$16$$

Question 6

Which of the following is the correct order of operations for evaluating $$2 + 3 	imes (4 - 1)$$?

Accepted Answer

Subtract, multiply, add

Question 7

A mathematical model for the percentage of marriages ending in divorce after $$n$$ years, when the wife is under 18 at marriage, is $$d = 4n + 5. $$What is $$d$$ when $$n = 10$$?

Accepted Answer

$$45$$

Question 8

Given the formula $$d = 2.3n + 1.5$$ for the percentage of marriages ending in divorce after $$n$$ years when the wife is over 25, what is the percentage after 15 years?

Accepted Answer

$$36.0$$

Question 9

Which of the following is NOT a variable?

Accepted Answer

$$7$$

Question 10

If $$6x + 16 = 46$$, what is the value of $$x$$?

Accepted Answer

$$x = 5$$

Question 11

Which of the following best describes a mathematical model?

Accepted Answer

A formula that describes a real-world phenomenon

Question 12

What is the algebraic expression for 'twice a number, decreased by 6'?

Accepted Answer

$$2x - 6$$

Question 13

If the product of 8 and a number is 48, what is the number?

Accepted Answer

$$x = 6$$

Question 14

Which of the following is an equation?

Accepted Answer

$$8x = 48$$

Question 15

A cricket chirps 50 times per minute. If the formula for temperature is $$T = 0.2C + 20$$, where $$C is $$the number of chirps per minute, what is the temperature?

Accepted Answer

$$T = 30$$

Question 16

Which of the following is the correct translation for 'ten less than a number'?

Accepted Answer

$$x - 10$$

Question 17

If $$d = 4n + 5$$ overestimates the actual percentage of marriages ending in divorce by 5% after 15 years, what is the actual percentage?

Accepted Answer

$$60\%$$

Question 18

Which of the following is the correct way to determine if a number is a solution to an equation?

Accepted Answer

Substitute the number for the variable and check if both sides are equal

Question 19

What is the value of $$5 + 3x$$ when $$x = 4$$?

Accepted Answer

$$17$$

Question 20

Which of the following is an example of an algebraic expression?

Accepted Answer

$$2x - 6$$

Chapter 1: Variables, Real Numbers, and Mathematical Models – Study Notes

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