Topic 1 - Solving Equations and Inequalities

To which subset of the real number system does the number 1.555... belong?

• whole numbers

• natural numbers

• rational numbers

• irrational numbers

Which of the following must be an irrational number?

• the sum of two irrational numbers

• the product of two irrational numbers

• the sum of a rational number and an irrational number

• the product of a rational number and an irrational number

Which numbers in Set A = {−7, −4, 2, 14, 21, 34, 42} are elements of both

Set B and Set C , shown below?

Set B = {even numbers} Set C = {multiples of 7}

​ (a)   and ​ (b)   (Please drag the smaller number at the front as the order matters)

• 14
• 42
• -7
• -4
• 2
• 21
• 34

An airport shuttle charges a $5 flat rate plus $1.50 per mile driven. Alex’s last trip to the airport cost $41. Write and solve an equation to find the number of miles of Alex’s trip.

​ (a)   x + ​ (b)   = ​ (c)  

The trip was ​ (d)   miles

• 1.5
• 5
• 41
• 24

Six friends all use $2-off coupons to buy themselves movie tickets. They spend a total of $42. What is the price of one movie ticket without the coupon?

• $5

• $7

• $9

• $11

Venetta buys 2 pounds of pistachios and 3 pounds of almonds. The pistachios cost $4 more per pound than the almonds. She pays a total of $48. Select all the correct statements about this situation. (Hint: Make an equation that relates the total cost of pistachios and almonds then solve for either p or a by expressing one in terms of the other)

• One pound of pistachios plus 1 pound of almonds cost $20.

• The pistachios cost twice as much per pound as the almonds.

• Reducing the number of pounds of almonds by one results in a total cost of $40.

• The cost a , in dollars, of 1 pound of almonds is modeled by the equation

  2(a − 4) + 3a = 48 .

• The cost p , in dollars, of 1 pound of pistachios is modeled by the equation

  2p + 3(p − 4) = 48 .

How many solutions does the equation 4x + 2(x − 5) = 3(2x − 4) have?

• no solution

• exactly one solution

• at least two solutions

• infinitely many solutions

Cranberry juice costs $6.30 per quart and apple juice costs $3.60 per quart. Terrence wants to make a cranberry-apple juice mixture that costs $4.50 per quart. He wants to know how many quarts q of cranberry juice he should mix with 4 quarts of apple juice. Which equation below represents the situation?

• 3.60(q − 4) + 25.20 = 4.50q

• 3.60q + 25.20 = 4.50(q + 4)

• 6.30(q − 4) + 14.40 = 4.50q

• 6.30q + 14.40 = 4.50(q + 4)

Mathematical Equivalence

ON

The formula a = m − n represents the actual cost, a , of an item with original price m after a coupon for n dollars off is applied. Solve the formula for the amount of the coupon.

• n = a + m

• n = m − a

• n = a − m

• n = −m − a