Teacher edition (with key)← Advanced Math 6

Advanced Math 6 — every item

Singapore Dimensions Math 6A / 6B · 65 items

One section per unit, in course order. For review and for a year of homework sheets.

01Whole numbers: primes, GCF, and LCMgcf-lcm-grade6

1.
Write $84$ as a product of primes. How many distinct prime factors does it have?
Answer: ______________
2.
Using $84 = 2^2 \cdot 3 \cdot 7$ and $120 = 2^3 \cdot 3 \cdot 5$ , find $\text{GCF}(84, 120)$ .
Answer: ______________
3.
Using $84 = 2^2 \cdot 3 \cdot 7$ and $120 = 2^3 \cdot 3 \cdot 5$ , find $\text{LCM}(84, 120)$ .
Answer: ______________
4.
Two buses leave the depot together at 8:00. Bus A leaves every $12$ minutes and Bus B every $18$ minutes. When do they next leave together?
1. (A)
  8:06
2. (B)
  8:30
3. (C)
  8:36
4. (D)
  11:36
5.
A ribbon $84$ cm long and a ribbon $120$ cm long are each cut into pieces of the same length, as long as possible, with nothing left over. How many pieces are there in total?
1. (A)
  12
2. (B)
  17
3. (C)
  24
4. (D)
  204
5. (E)
  840

02Fractions: division and multi-step storiesfraction-operations-6

1.
$\dfrac{1}{2} \div \dfrac{1}{8} = \ ?$
1. (A)
  $\dfrac{1}{16}$
2. (B)
  $\dfrac{1}{4}$
3. (C)
  $4$
4. (D)
  $16$
2.
Compute $3\dfrac{1}{2} \div \dfrac{3}{4}$ . Give your answer as a fraction or mixed number.
Answer: ______________
3.
A jug holds $6$ cups of juice. How many $\dfrac{3}{4}$ -cup servings can be poured from it?
Answer: ______________
4.
Compute $2\dfrac{2}{3} \times 1\dfrac{1}{2}$ .
Answer: ______________
5.
Mia spent $\dfrac{2}{5}$ of her money on a book, then $\dfrac{1}{3}$ of the remainder on lunch. She had $24 left. How much money did she start with, in dollars?
Answer: ______________

03Decimals: terminating and repeatingdecimals-terminating-repeating

1.
Write $\dfrac{7}{8}$ as a decimal.
Answer: ______________
2.
Which fraction has a terminating decimal?
1. (A)
  $\dfrac{1}{3}$
2. (B)
  $\dfrac{1}{6}$
3. (C)
  $\dfrac{1}{8}$
4. (D)
  $\dfrac{1}{9}$
3.
Compute $4.2 \times 0.35$ .
Answer: ______________
4.
Compute $7.2 \div 0.08$ .
Answer: ______________
5.
The decimal form of $\dfrac{3}{11}$ repeats. Enter the two-digit block that repeats.
Answer: ______________

04Negative numbers and absolute valueintegers-absolute-value

1.
A submarine is at an elevation of $-250$ metres. How far is it from the surface, in metres?
Answer: ______________
2.
Which list is in order from least to greatest?
1. (A)
  $-\dfrac{3}{2},\ -2,\ -2.5,\ 0,\ \dfrac{1}{2}$
2. (B)
  $0,\ \dfrac{1}{2},\ -\dfrac{3}{2},\ -2,\ -2.5$
3. (C)
  $-2.5,\ -2,\ -\dfrac{3}{2},\ 0,\ \dfrac{1}{2}$
4. (D)
  $-2,\ -2.5,\ -\dfrac{3}{2},\ 0,\ \dfrac{1}{2}$
3.
At 6 a.m. the temperature was $-7^\circ$ C. At noon it was $-3^\circ$ C. Which statement is correct?
1. (A)
  $-7 > -3$ , so 6 a.m. was warmer.
2. (B)
  $-3 > -7$ , so noon was warmer.
3. (C)
  $\lvert -7 \rvert < \lvert -3 \rvert$ , so 6 a.m. was warmer.
4. (D)
  Both are below $0$ , so they are equally cold.
4.
Compute $\lvert -4 \rvert + \lvert 3 \rvert - \lvert -2 \rvert$ .
Answer: ______________
5.
On a number line, point $A$ is at $-6$ and point $B$ is at $-1$ . How many units apart are $A$ and $B$ ?
Answer: ______________

05Ratiosratios-grade6

1.
A recipe uses flour and sugar in the ratio $5:2$ . If you use $35$ cups of flour, how many cups of sugar do you need?
Answer: ______________
2.
Share $84 between two people in the ratio $2:5$ . How many dollars does the person with the larger share receive?
Answer: ______________
3.
Share $84$ marbles among three children in the ratio $2:3:7$ . How many marbles does the child with the smallest share get?
Answer: ______________
4.
In a bag, the ratio of red to blue marbles is $3:4$ . There are $28$ blue marbles. How many red marbles are there?
1. (A)
  $12$
2. (B)
  $21$
3. (C)
  $36$
4. (D)
  $84$
5.
In a class the ratio of boys to girls is $2:3$ . After $4$ more boys join, the ratio becomes $4:5$ . How many students are in the class now?
1. (A)
  $45$
2. (B)
  $50$
3. (C)
  $54$
4. (D)
  $60$

06Rate and speedrate-speed

1.
A car travels $180$ km in $2.5$ hours. What is its speed in km/h?
Answer: ______________
2.
Apples cost $7.50 for $5$ pounds. What is the price per pound, in dollars?
Answer: ______________
3.
Convert $20$ m/s to km/h.
Answer: ______________
4.
A cyclist rides at $60$ km/h for $1$ hour, then at $40$ km/h for $2$ hours. What is the average speed for the whole ride?
1. (A)
  $50$ km/h
2. (B)
  $46\tfrac{2}{3}$ km/h
3. (C)
  $48$ km/h
4. (D)
  $100$ km/h
5.
Jo walks $3$ km to school at $4$ km/h and takes the bus back along the same road at $12$ km/h. What is Jo's average speed for the round trip, in km/h?
Answer: ______________

07Percent and percent changepercent-change

1.
Increase $80$ by $25\%$ .
Answer: ______________
2.
$15\%$ of what number is $36$ ?
Answer: ______________
3.
A price rose from $40 to $50. What was the percent increase?
Answer: ______________
4.
A jacket costs $45 after a $25\%$ discount. What was the original price?
1. (A)
  $33.75
2. (B)
  $56.25
3. (C)
  $60
4. (D)
  $70
5.
A number is decreased by $20\%$ , and the result is then increased by $20\%$ . The final value is what percent of the original? Enter the percent as a number.
Answer: ______________

08Algebraic expressionsalgebraic-expressions-6

1.
Evaluate $3x + 2$ when $x = 4$ .
Answer: ______________
2.
Which expression is equivalent to $3(2x + 4) + x$ ?
1. (A)
  $6x + 4$
2. (B)
  $7x + 12$
3. (C)
  $6x + 12$
4. (D)
  $7x^2 + 12$
3.
Simplify $3(2x + 4) + x$ , then evaluate it at $x = \dfrac{1}{2}$ .
Answer: ______________
4.
Simplify $5y + 3 - 2y + 7$ .
1. (A)
  $7y + 10$
2. (B)
  $13y$
3. (C)
  $3y + 10$
4. (D)
  $3y^2 + 10$
5.
Factor $12x + 18$ by taking out the greatest common factor.
1. (A)
  $2(6x + 9)$
2. (B)
  $3(4x + 6)$
3. (C)
  $6(2x + 3)$
4. (D)
  $6(2x + 18)$

09Equations and inequalities (one step)one-step-equations-inequalities

1.
Solve $x + 7 = 10$ .
Answer: ______________
2.
Solve $x - 3.5 = 1.2$ .
Answer: ______________
3.
Solve $4x = 18$ .
Answer: ______________
4.
Which describes the graph of $x \ge 2$ on a number line?
1. (A)
  An open circle at $2$ with an arrow pointing left
2. (B)
  A closed circle at $2$ with an arrow pointing right
3. (C)
  An open circle at $2$ with an arrow pointing right
4. (D)
  A closed circle at $2$ with an arrow pointing left
5.
To ride the roller coaster you must be more than $48$ inches tall. Let $h$ be a rider's height in inches. Which inequality must be true?
1. (A)
  $h \ge 48$
2. (B)
  $h > 48$
3. (C)
  $h < 48$
4. (D)
  $h \le 48$

10Coordinates and graphs (four quadrants)four-quadrant-plane

1.
In which quadrant is the point $(-3, 4)$ ?
1. (A)
  Quadrant I
2. (B)
  Quadrant II
3. (C)
  Quadrant III
4. (D)
  Quadrant IV
2.
What is the distance between the points $(2, 5)$ and $(2, -1)$ ?
Answer: ______________
3.
A rectangle has vertices $(-3, 2)$ , $(4, 2)$ , $(4, -1)$ , and $(-3, -1)$ . What is its perimeter?
Answer: ______________
4.
Which point lies on the line $y = 2x - 1$ ?
1. (A)
  $(1, 2)$
2. (B)
  $(2, 3)$
3. (C)
  $(0, 1)$
4. (D)
  $(-1, -2)$
5.
A triangle has vertices $(-2, 1)$ , $(4, 1)$ , and $(4, 5)$ . What is its area?
Answer: ______________

11Area of plane figuresarea-triangles-trapezoids

1.
A triangle has base $10$ cm and height $6$ cm. What is its area in cm²?
Answer: ______________
2.
A trapezoid has parallel sides of $8$ cm and $12$ cm and a height of $5$ cm. What is its area in cm²?
Answer: ______________
3.
A parallelogram has a base of $9$ cm. Its slanted side is $5$ cm long, and the perpendicular distance between the base and the opposite side is $4$ cm. What is its area?
1. (A)
  $18$ cm²
2. (B)
  $26$ cm²
3. (C)
  $36$ cm²
4. (D)
  $45$ cm²
4.
A triangle has area $24$ cm² and base $8$ cm. What is its height in cm?
Answer: ______________
5.
A parallelogram has base $12$ cm and height $7$ cm. A triangle with base $6$ cm and height $4$ cm is cut out of it. What is the area of the remaining shaded region, in cm²?
Answer: ______________

12Volume and surface areavolume-surface-nets

1.
A box measures $3$ cm by $4$ cm by $5$ cm. What is its surface area in cm²?
Answer: ______________
2.
Find the volume of a rectangular prism with edges $2\dfrac{1}{2}$ cm, $1\dfrac{1}{3}$ cm, and $3$ cm, in cm³.
Answer: ______________
3.
A cube has a surface area of $150$ cm². What is the length of one edge, in cm?
Answer: ______________
4.
A box measures $2 \times 3 \times 6$ . When its net is drawn, which of these is not the area of one of the faces?
1. (A)
  $6$
2. (B)
  $9$
3. (C)
  $12$
4. (D)
  $18$
5.
A rectangular tank has volume $7\dfrac{1}{2}$ cubic feet. Its base is $2\dfrac{1}{2}$ ft by $2$ ft. How tall is it, in feet?
Answer: ______________

13Displaying and comparing datadata-distributions-6

1.
Which of these is a statistical question?
1. (A)
  How old am I?
2. (B)
  How tall is the principal?
3. (C)
  How many hours of sleep do sixth graders at our school get on a school night?
4. (D)
  What is $7 \times 8$ ?
2.
Find the median of $3,\ 7,\ 8,\ 12,\ 15,\ 20,\ 21$ .
Answer: ______________
3.
Find the interquartile range (IQR) of $3,\ 7,\ 8,\ 12,\ 15,\ 20,\ 21,\ 25$ .
Answer: ______________
4.
Five students' scores on a quiz were $2,\ 3,\ 3,\ 4,\ 40$ . Which is the better description of a typical score, and why?
1. (A)
  The mean, $10.4$ , because it uses every value
2. (B)
  The median, $3$ , because the $40$ pulls the mean far from where most scores are
3. (C)
  The range, $38$ , because it shows how different the scores are
4. (D)
  The mean, $10.4$ , because it is larger
5.
Find the mean absolute deviation (MAD) of $4,\ 8,\ 5,\ 7,\ 6$ .
Answer: ______________